-
Notifications
You must be signed in to change notification settings - Fork 0
/
PI.mw
412 lines (402 loc) · 668 KB
/
PI.mw
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="2021" minor="2"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false" autoexpanding_sections="true" UserProfileName="Maple Default Profile" NumericFormat-ApplyInteger="true" NumericFormat-ApplyRational="true" NumericFormat-ApplyExponent="false" editable="true">
<Hide name="Group Range"/>
<Hide name="Section Range"/>
<Hide name="Table Borders"/>
<Hide name="Annotations"/>
</View-Properties>
<MapleNet-Properties prettyprint="3" warnlevel="3" compactdisplay="false" preplot="" helpbrowser="standard" displayprecision="-1" echo="1" scientificx="true" unitattributes=""fontweight" = "bold"" imaginaryunit="I" longdelim="true" elisiontermsthreshold="10000" elisiondigitsafter="100" elisiondigitsbefore="100" plotdevice="inline" errorbreak="1" plotoptions="" plotdriver="opengl" quiet="false" elisiontermsbefore="100" elisiontermsafter="100" historytimestamp="false" screenwidth="79" indentamount="4" plotoutput="terminal" screenpixelheight="1080" rtablesize="[10, 10]" useclientjvm="true" format="worksheet" labelwidth="20" postplot="" typesetting="extended" ansi="false" ansicolor="[]" elisiondigitsthreshold="10000" showassumed="1" ansilprint="false" trailingsemicolon="true" errorcursor="false" labelling="true" screenheight="25" prompt="> " verboseproc="1" latexwidth="8.0" ShowLabels="true"/>
<Styles>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="16" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[40,120,40]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Courier New" foreground="[120,0,14]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Header and Footer" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="HyperlinkError" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Atomic Variable" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[175,0,175]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="HyperlinkWarning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Caption Reference" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Code" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Courier New" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Caption Text" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.3" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="newline" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix="."/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="HyperlinkError" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="HyperlinkWarning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
</Styles>
<Startup-Code startupcode=""/>
<Metadata-table>
<Metadata-category name="<default>"/>
<Metadata-tag id="0" category="<default>" name="Document Properties">
<Metadata-attribute name="Keywords" value="<default>"/>
<Metadata-attribute name="Item List" value="true"/>
<Metadata-attribute name="Title" value="<default>"/>
<Metadata-attribute name="Author" value="<default>"/>
<Metadata-attribute name="Subject" value="<default>"/>
</Metadata-tag>
</Metadata-table>
<Task-table>
<Task-category name="<default>"/>
</Task-table>
<Task/>
<Group labelreference="L1" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" family="P052" layout="Normal"></Text-field>
</Input>
</Group><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L14532" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Font size="10" bold="true" family="P052">
</Font><Font size="20" bold="true" family="P052">Path Integral Quantum Mechanics and Molecular Dynamics</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L14536" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Author" size="10" family="P052" layout="Author"><Font size="12" bold="true" family="P052">Kuntal Ghosh, The University of Chicago</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L14640" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Author"><Font size="11" style="Author" bold="true" family="P052">Copyright (C) Kuntal Ghosh 2022</Font></Text-field>
</Input>
</Group></Presentation-Block><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" size="10" family="P052" layout="Heading 1"><Font size="14" family="P052">Abstract</Font></Text-field></Title><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" encoding="UTF-8" family="P052">Quantum mechanics is crucial to the understanding of the way nature works. Traditionally, quantum mechanics is formulated in terms of the wave function, proposed by Schr\303\266dinger. It is this wave function which carries all the information about the system under consideration, and is deduced from Schr\303\266dinger's equation. Alternatively, quantum mechanics can also be formulated in terms of the wave vector, using the Dirac notation. In fact, there are nine different formulations of quantum mechanics. One of the most fundamental as well as strikingly beautiful formulations of quantum mechanics is Feynman's path integral. This worksheet explores a few fundamental concepts of path integrals, with special emphasis on the harmonic oscillator model.
</Font><Font size="10" family="P052">
Path integral calculations are often carried out in the framework of molecular dynamics (MD) simulations, popularly called Path Integral Molecular Dynamics (PIMD). PIMD simulations are critically important to capture nuclear quantum effects (NQEs) in atomistic simulations, simply because most MD methods treat the nuclei classically, even if the electronic motion is treated quantum mechanically. PIMD, due to its very construction, effectively does away with this issue. This worksheet also gives a brief introduction to PIMD with a simple numerical illustration using the harmonic oscillator model.</Font></Text-field>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" size="10" family="P052" layout="Heading 1"><Font size="14" family="P052">Introduction : Theoretical Background</Font></Text-field></Title><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">While traditional wave mechanics emphasises on the probability of finding a particle in a particular state, the path integral formalism (as the name suggests) talks about the path traversed by the particle. Say a particle traverses from a position x to a position x'. Instead of following a unique path between the two points, the particle follows an infinite number of paths simultaneously and the total amplitude of the particle to be observed at x' at time t is the sum of amplitudes of all such paths. Now, the amplitude for the detection of the particle at x' written in terms of the quantum mechanical propagator is</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">More generally, for an arbitrary state vector, </Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" encoding="UTF-8" family="P052">In the language of path integrals, this propagator is also referred to as the kernel. Now, to transition to a more statistical mechanical framework, a very interesting substitution can be made. Substituting t = -i\316\262h,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="2D Math" executable="false" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="2D Math" executable="false" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">where </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EnJiM5NjE7RicvJSdmYW1pbHlHUSVQMDUyRicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY4LyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGT0YvRjIvJStleGVjdXRhYmxlR0Y3Rjg=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EnJiM5NjE7RicvJSdmYW1pbHlHUSVQMDUyRicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY4LyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGT0YvRjIvJStleGVjdXRhYmxlR0Y3Rjg=</Equation><Font size="10" family="P052">is simply the canonical density matrix, or the so-called imaginary time propagator. Such transformations or rotations between the quantum propagator and the canonical density matrix over imaginary time are called Wick rotations.
</Font></Text-field>
<Group labelreference="L14638" drawlabel="true" applyint="true" applyrational="true" applyexponent="false"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="10" readonly="false" background="[255,255,255]" placeholder="false" family="P052" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="centred" bullet="none" spacebelow="0" pagebreak-before="false"><Image height="243" width="289" zoomable="false" labelreference="L14632" drawcaption="false" captionalignment="0" captionposition="1">MFNWtKUb<ob<R=MDLCdNNZij:\\Y>T:Dr=pJaJ<HQ[`Nd\\J>\\J>lQ>LP>kFLq\\\\OtHoqTPtXqjDqlvfhwgggfgVh]Oh_gfhWhbwgnww=vqxZk^h??EAdVEURcUTYeU;COMUUEM]DqnLpj`QJ@MV<L]PPkDqt@Ps`QJDMRDMS<LR\\MWHMRdmR@MJ<o`XSHqvj=ZZRLCTJcDXsFuuXTcEQIYRIWxIgGcT:Kg:[DpicZ;S:?Brwg\\cRduufgrP_i>qduwcQ_XacEacIWoehIsQGeV_sV?iusetWYtafaceFaxC]egWDiKh_USl_GEEd_KT^?iDMBqDRfYQB]oo@npixHyJJ@pblO\\dNDdTQ`yyqsKINO]q?PYCDK?xJiiYiYYglj[=MB@kB@kR`jott=<LKDLKDqOLkQDLKDLkdL?YkB@kBf\\?YkB@kB@mDPv?_b>_bFgbkQ^\\N^\\nn\\@iKF\\KF\\MGdv@kB@kBHobne>_b>_rN_\\iN>D@jR:\\CJ`:?ccZKVDJ>aDBk:?=RF:k>BMZ\\nNjBH?B\\M?^RZ\\;F@ZR<^CJKTDR>a<>kc<LFJk:@=JF;l>bBG?F\\MGpaQI?c^yh^MHCMHS_jEiv<qVmHVk@Ul]QdDLsXmclU>mWMTrj<s`Up^TlC]K=AqhIXPTk?TqWqkWqWIYuB<PFTj^MPC=ONLVxmWX@RZVrBQdKGdCgb?GaXPlL^]HvbXqkY_bhagDx\\KXu>AsT>yP^inqxXxfkGhkQqAi\\Qv\\MAuRAcEWgeQ[HpwPanLHctosWXviwytygRPmT`rhwpM`c`@mXpm`ItAw]_Y]Yay@fggiwRi]H`eIfd>ow<OkQFLEh:ETkEDOetOAyvmIHwEwkrAsEv=BQoV[mti=u:quwUYSUh`eCXQxlaEIkxtQb;AFaoSX_vIyyfysbuwbAvqwesiETWeQADEgRcyweyvAsuyqIEwyiQFYUytYxVyXyiyRaWp_UICU>mwlKcQCdUar\\EhZQXs?Wb=W:IwnMHuSIEYiAoCkcIwckaxQyaKUqpiun[Hn;tT[EVHxRueWc`TDHr;IRx]x=yMl@qr@sxXyhYViqqw=YwpULEoNdxoixnqxXxvwyxXYv:qy=\\TPmTlHV]qrVuKU]RhQPtPuB]vpDpR]ORaWp\\QXtKemtfHnghoWPwTPM:\\WpTMWTwQYphhoGPlLQTDLKDLxleqBaxnaPiiMylsCqsM`WUqpWhkUpP[ixtEJj=QV\\TOeTkatMyS]QXs@Qk]wRtrHpM_DlB]vr]t\\LXqHTv@kvmRVlKulOQXK:tnMIkMIw>qWIyuCqS=APbYwgivWYjA@PlHUhiuuxlLPlLXOHHpSiwfEuthldQ]FxkIXx;YyY^_Ia_C@kf`\\?YkByf^QxF_[:hu[wr\\gsiy_q`htfsBAsBfuWiuRi]HNuTYubN_dNq\\A]Ehr<GhkG`oixoAqWqg`pn`@wvwy=`]G@e>owPGywqgdN^enfv_gFHxKI`\\GpRnhUhkTPuT_]QIqT@o[HpKvgsGamWhm`mxfidgjAO_\\vhu`yWXrPFqE_Z<FZtYytA]Yv]aPodPkwXypIfk@ebYwgivVwxsnv`qfc>htFuoXgQVwPio=YhcadH__PVnqxpQpwmxfkYywAqWqgTYat>qaqmu?hvOjof`Qv_X_fhogHVoOQkUiw@ivnOfwpsfGd?GisngqXmCHxkor@wbQxxoHsAihvN^lwvK_qB`v:O`S`flOhLpomxfcYaYYsZAvZFoNOlWYipAphhoGXnAokjOoma^]V^]^sIys[GpRGaoOx^vetQtQHuswshNvkAaiq]v^r[YriQ`mfa=?`R>r[whjpp_hjSImSnmsQrQ>htfmq```HuSIevoq?^]HvZhwkAVwGnhLi_dn_@Iwf>^K@cZyxuI[@Vjr_aXfepf_\\V_<Gx\\Nl=FufolZ?^:irEv\\s^irA`wgqw`dN_dJwuJArkYfAA]V>]:qfqHp`gwTOkEXksFilXlKHv[_m?nc\\GxRnHufiwhQSiWIRUUYuSxmYXnyxoYXbAv;MB;sIUyXhaf[Gf[QiagYhgFR;CJKC?GhSaWNsDOCX]GINgf?yrH[C=AFKsUD;e\\Of\\crE?cf?C?YcBmCRiwpMEQeg\\ohpoccGsCmFakFBmFM_sFusjmxFIUXGY`IEPyWVAbEiv\\wiyweyQyYwymswW?YIWDakcMSc?AupgYusCw[yjsxfIuGETKED=Ub=_y=yyvyBxMx<Ykeiw]XqeXklPplLsDQshMYFEpR]k>MNH<Rddm`=Yr=ytXyKasIisK`qnEknmPUhNTDkJhs`uQwyN@]R^qNblU>MX:qWqXTOeT?<rdqvOaTN]TZYxsAXt`UvYuyuxyPvoQYQxtU`PNyPjinitY_EWwYsfaMOitOaQwIya=WhmWXmyrUwTQuRQpoUKApusuj:=P:Ar:AJulXhaq_@YCmNM]nLEW\\EpRdUauslywxuyYQVkpUumy_lMIXpR\\UthJ<mPUh^Tfq[iyV`b>ogafrE@cHHugqhfsHWgj?d@qr_gusuIvot>ITZAftofTSu_gI\\]I_cFEYEAiYREV[EF_cf_?ywqY\\CvjCeFmvPor[=E@;E@kGQWcGSEp;xAwyayEgswMUxKuFuSIsEy_wdbayZWDEgrl_XMorUMYoCLY`m\\iR^Fegp`fodendEhZAGb;ndEhvD@ikPeg`\\Pn\\hva`WpTGpYWfgGkWqga@rk`pHf^O`c[_figg`^r_QhK?dJ?pvVjlpfgQuepxsGqf_iv_m<Pj_hZ;qlEYvEYxw_g>_vHInrG\\CI`Ehr<v]mGkkhtdgyRImGVk?QpV>\\EGZlWgkQdV_e>Xoj@lNO_??aVnrdgpXwhA?vNO?oSaGBj=ugadseiT]geKFekRyKGC_vTgvLyIskT`ixLMTLMR`Sd[KDGOdCuVhWiHgFTccL_S`;hu[wrMSv[dOgdWuXI=EKCdUiSiqH\\KBfcwTWUWUTwEwnWTL?W^KXWiXmCrZ=db]H@WugqfkGhKsvGkHnWDKCiWaxhUF\\<WTepDPqTQa^O`SnfaqvBgnLwtvntq@v]N\\HVdKGd;qjGWmPOhRP^\\NkQR_[Y<gFbSGh_seiVWUYUcgeQUCmFM_evCuC=INKi\\AE=AHBufMaUr?H?=FJ;fhogXgIqquUWfKScBiuDEx\\KPLHs^ES_TlQpYYprjlowHkUmPUhUxPPBAsTttf]mItOwDPjlospL?APxeyrmPUhq_qTl=QV\\WRAp;hYuqw]DlB=xXIxM\\Ox]NXMpSaO=Xj=`sFuSMeTOerpiwUyoRyW@cL[DiKFYGB=AHBwr\\]B<CBZEwXmRK?S>_r_gUcuIfkEEWdBwrCuVl[R]GdeSS?;s`MH>MF[ivW[WMGs^Cxe]YV_TdcRvCDAAHFKFKACSYUVyv?;VOUTMsxhiiQgtGisVWIQissqeXKBxuyLAIlGU\\CdBsitUxGMb;iRpmwTirwuCVycUiwxgvQIDKCyn[Xc_hBiW\\=E@Cc>Mb:wuI=HJ[fiwgIGuSIU:Ktc_HaQiIITUUUEeY=UrlyHvuu<QB]YV]]GhkGLoSaGEUcE]=Wb=ctOitKcWqWLEgNSV]WfVGIwMe^ifS]eESTQ;whQw\\ggggeTOuTkD=WcrYBxmR@wRjyGrASaWtF]cI=Hj;p\\Pn\\MsvhVqdYMpRqXuGqjGUmrmxExskQvIxY<Ir=tJj@Uf\\oeUW=APFlN@yrs\\YbiUTLMT<YfIkAIuvhVEyVmIsNDLsHJUyXyXyWyw`QYJLNqMjfmPEasFaKApKX\\vOyTymskXnAAk>Xrr`Uh\\UhtL]YV]]kH`kJDk@EpSeoFqsFAxDYOi@x;YyiYLHdjj@UfTS[YpR\\qnHxUEL]Yv]aqvQtE]qsqrU\\NLHSVhJ?\\J=DJ`lrAISaMtn]pqXXtatclYkYxQEQvqwu@yvmQVlKADJyxMYQr<dJ?dJNmTOMvkAYhMyiIvkAYbuWiur`Upl]xjILHmmfanyxiawsVHv_ylXcgWg]yUxYgYqVIqewstWIbQ]R^Yh^EHnURLCdUQrj[ClCeFCs^Md^MHCMIOoFMgyoIgUSc?DWQ\\u<Pj_YqwtNLDKLHk>DmEun>`OPTKHQj<LKVpSVlKADuFmlR]Q@MPS`UxdW^epR=pSiwrdmHMKidWdtlB]NBmNMxTVMufAXr<Xs`UrdmHYUTARhQxTImR]O@awFaK]TN]\\OFys]AOb<nxHn;hPemtJMTLMR;ER;iLuDJE@kf`L?YkB`UQMOOPNTdkL@kAIpReoNdLODTR=UbhQW]R^tnNtO\\LN\\LfnYvM@kB@kR<CDKS<DLKTTKS>]R>aTNsO>]R>aTN^b>CkLkQDLKDLkr?]R>@]?E\\KNF;l>bBG?F\\M;\\rN]wsp]KFqow]xH]vhr\\Gs[Ac>_bPom`oe>_cBA`FN`S`chxj[N^LX\\Dx\\KVlCqfm@ywqi@NyuYhw^\\KFlV@dv@kR`c^^]`Oh\\Oj[Hn[X_Hw]C@kVi_npv?_r^_y;tjAxjsDi[U:crE?cVibNsG\\kF]yxsAEXKE\\mYxmE_WcB_uG_DiZa_fb?mZ?`BHfR>]@Hnenk>_vhPnov_\\n^]YxsA]Uv]aogxom?Av\\Fufo`QYbLF\\SGdDx\\KV\\Cafl^sGyskGx\\iZ\\GpRVb=Wb^N\\C`eIVc>_f?G_X_bF_riYxkVamVbbG`>O^XvneXwfFxR__QYrLF<ZSv]YvftQvnFmFojr_aHIwMwnBH_X_b^q_]@I]S^=Yb=ccIwc=BLCc>cuWeu>WrKcguEDKWiDOv?R@wRRGiNsGc_TDGckIX`qVaehhiR>mwdKcQlNZ=M@Dtb]lkIkk]YxtuOtkqyxqIvqYym=QtDLKhl_@YKDP;Trj<MSDM[EVxEj^MPserYhxXxw?ypj@l]HlC@kf`Q?Y[M>s`WpVxwsvcZ>\\rPwIQytWikIyvOqIIlB`uo^\\iN^sosj^[lFmFfuWgeQakQHtKId`ona_ph]TNkQFlvvfRnZC@iVXpaosJ>q@QuP@c^NrBAsix\\lQkB`uca\\iN>Wc?QVnaxnAHuSHmettudEQytUYSkEXkU[IdC?c^qb\\iR^XKglOl]xbIT\\xPRakhxqixkKHv[ewqQN\\tX?drEbSkb;=XkEd]ubI_ujqH:SxmYxFocHGHuSHmOb]WDKCsGcrE?KPTk?AqjdP?uYyuQc`TdQqAinLEO`lN@IwiywYErKIkB`v@Pv?]NIhsIysMYXhxjB]NlIpQPRImSFMtOit?HVRLqfMU>mwbMkQbl[C=GwEwDscYdatGeEyEVdMcXWXaqWrSR]KFluFJ]iB_vc_Xtcs^ar>sVHuexGg]YdCaFMyDaGwhQw\\SdCaY@YfMCDCiE?Y[d_if_kXquXOj;AvGg]i?]@VxmYhVFav_bmx_\\NhAWdv@k^IoxpuXosoghYQtfNkYyvaAykXn>VZ;fsx@kBi]EGx\\NlAPnKA_wgiw_[Hn[XQxmqj@pjbYwgi^Tfkxob]X\\KREEx\\N]YV]a?hj?k?xcjwpbAg^NsUygiytGQ]?_vHhnrG\\CYbiyqqOjkHtKycnaur_aHqyqxu\\GfxoekQ^\\vh^Vk[xhqFlvX`l^aFirEv\\Cpb]vdvny<ykx_ruywwxcr^]XoifyuvqyiYphhoGvlEIqnAj?QjWqgaWxPh_rgqX_oPgyFP^\\vhPVihx:XoOyPn<TMUTmetFIs;YjADXr\\MQ]QPIpxXjWuxVYRKETKiLIXQWmOflLEyVxlTKDlOpnrELC_mHw^rfmQgahAhr>v]Fb\\Qhs@_dN_\\@ugqecHvC@k^al`Yl?_b>_RbBD@@kBF@J>]CBKFX?cB?ccR>]R>a<>kc@?L^>=NFZk:>MZF;DLM;]rNZBHOJ\\;D@jR:\\CJ`:?ccZKVDJ>aDBk:?=RF:k>BMZ\\nNjBH?B\\M?^RZ\\;F@ZR<^CJKTDR>a<>kc<LFJk:@=JF;l>bBG?F\\M;\\rN;C@bR:];B`:S<N^`<@kc:KVdZ>=NFZk:>MZF;DLM;]rNZBHOJ\\;D@jR:\\CJ`:?ccZKVDJ>aDBk:?=RF:k>BMZ\\nNjBH?B\\M?^RZ\\;F@ZR<^CJKTDR>a<>kc<LFJk:@=JF;l>bBG?F\\M;\\rN;C@bR:];B`:S<N^`<@kc:KVdZ>=NFZk:>MZF;DLM;]rNZBHOJ\\;D@jR:\\CJ`:?ccZKVDJ>aDBk:?MumoA<N\\L^iQv?Ykfn_hNvhnhMAtRAleIvB`v?fsv@kB`v[Vrj>c^N\\vQxoxtrVi`a[ROhwN^K`y[@iKF\\CY`@HfJvkAIiaAr;n[yXiRhr?ibDOcDOhw^_K`q[Xt@O^\\Fi\\Qhn`sIySsCGCxIsYyyx>MFKMGdKokAYleQvDlvHnrELKDs=lj[=LGpRSlMXlvZIj=\\qlQtEakIxkmuu=txM?pJ@dbRV]UFgtdGCmED?Y[s?^MHsjYtQve^itQoiHar>aZxhj?NpSa_wvvt?yiwitynV`wfavqoiqyhc`of`soAd?OhHGx\\Zfo`UvkwnyrfsGYgrNi^A[YYyEyq^@pj@lYIyHyhRqpwW]XwoQWwX_B]DiK^;Vk?Qb=Wb=FxR_[ehtDhs`WnogutnpiAuHqxWVaj@enGqK@s_OasO_\\NlAof`ofrvumo[Uhs@qxgYucVxtg\\hN^YFnrG<HknMQGax?IWtYytIXr\\MfuukXjlP`sp]P@cXIdv\\Chr?ib`pn`@mWhm?idR?s`hsU`pHib^Q]Nv?Nf^?i>HtKH\\Dhuho`gOu>xn^`ZUhsPXw[Gk^i]?YkB@cX@]SF]`_f^_jLvkAhmuph\\ahtfpXib^=>^S`cln`tNs^ar>nmLv[upwsxj<Pj<`eIVc^v_cne>_blArvauVVlMVl>O^KN_ePobWgiwr[Ah^QiRO^sGckQ^\\NLoixoI`uVa=GccG_ewTihN_dN?DB[BBmFM?E@GdeIvC_vOcrE?[ZxqixmsHqsOgeWgSAqcW`kAiVx]vwYSv]YNw\\PK`q]@YKD<GgcGGPsDQCGeSG]?f:IrEwIsICUkHf=fVYwGixJaRlqc\\iR>]FI[DPKij=ugacHoclquCwxjQYw_gYAh;scAYfekc>mI<uxpKDKCs=SYqiw=qVmGDC_RbUWeuVeqtg_TOeT[uheiWT]v]_xOEF\\KdAkEr=x;mHf=u:kDEcdOcdReWT?EQCiXcrEBjGuf]TQat^QYRKF`?fnwDKCDKS<DLKTDF\\KVDB\\KVdZ>aDbB?M?G\\KRFpxsELKDLKXu`DlB=vqIyChr]]lQxlM]UV]YUyXDpTv@kBFs[@gnNkYywaG`R^qhI`PVoOVqGqjWqgAIwlGvkAibn_hnseXyXg_f^_JYhhxjxpqXOfKA]S`g@`hdfb]WvdnpfguDWeuWugWkRfrE@kB@cHfnMG_PVj;o^av^SPmTPftQv?OvkAaPVk?VqWIbkXqRPbQX[En\\LGwnndehllPplN_eV_c_gTgb]Wf]ngqXaaH^]YeR?vjIn=_qyqyuaj=GfTN]T>pSiwFxkIXhxxvvVv]WfvowCy^SQpgW_PVk_YdIhdkQ>Ds[tT[ENodpo@M:uYYuMi]qxqJMXLM\\LN\\LJUd@h_UqpKodPobfn\\]OitQ^MWlM__FysM?dJ?r]ymuOjaoqjiZp`gSQbCGcCQkIhuj^[lHufvwwxxXv_vAwA?iEYssqrqvqCqquqw=>fdOhLxwwivYGpywyxovQn\\b?eOAcsGisn`UhwMgqhPv?_BCs[sb=IbQYw__gf_c`qv`mcYsIHat^aFOcDO[IxIia;y=yItYf_YV]EhRceY[XlyHYYyXsRHsE`yryKY;GbxIBxgxUwu`IiikYkerAqeGqVCcb<]yoyUwucR]GDYXY]y\\SYqiwUmymQy@oBXsyVYDFasFAxXIx]aitQse[IyysxIEhuhuYTwoghoHLCDKCKQxS]@UflLVm_DXkEHhr^]Eyi`gpTwlyI_f^_^WypiwvwvqqiQpn`p^Vn[Afqaysmqw[Xbnamuvp\\YfI^Z<^qjYjYN`of`CWeUWagf_gxdVP\\l@ef^hfxeIwrtixFysIYxmx\\yOsFaxnFoNOwMgqh<xJhtjDER;ErouSe@UgpTVqMqTWUMUrxXiqUDXkEHk?QVFdKHDtWiuwPn]iPFTjZ=N:YMixqH=PJ\\ncHoCPqtQqepkedOgdnhpoHtkAYrNatNtNutSL\\q;Qv^Ym[@YKj]ltIHUJQWk@Ub\\XOLtkpYwlOQX[;vqYX[MWdef`>?fcQ_cHkCH[@nZ@>c`VlNodQGd`ixXghVhuhwnvPnVPytQiLFk>vwW@a;xuiyyNwogh`iN^\\Fa^?]@FwnOmEv\\h>\\IxrkGQcV_gfNodOgvt=WsEWxmYXsb=IxS_wWKV`kDE[DN;Ij?UQOFaSWR[VmorAqIi[EDShRKU^[EHSdF]NqXuclXuHOitOa@ob@wPpo<LK@LJF\\KF<LIxrkXugAYvlMDTKEtos]WCESCdXoixneXoEtOiXPhrZ=L=APxDxOuRquwyEYKDlv<lGqVCtj<]yfirQDmR@mZHXOQOpiwUyrwXYqqvt=WsEwbIl]\\LOtLMQtLQjQYw?ivlETJ=TjUUhtqoTK=APB]NM`kHpkL`S^DJbTOednhpopQqAYM@HR^\\M`xpqxkxqyxmRAmRRHmXpr[upmPosePqiuquQgiwg]LuhuqdY_<Tb\\M`MVv]]hwpUvlEihWyvPn\\PNd`i_]VmGQ`kF@kCAgDiKF\\kV_=E@Chr]e]wRHOtWit?qrGUebMWdMsoAhlqtUyitiDakSvwbq_gFgeuoXkAu]ycmWyXiINcDOcvt=WekFWoSmsIyssusBXIFNKC[EhR=WcEW_qeWYiiGYvGVR[b=EFxqxiuyPGhKITPqhn?hgUypmfi[UZicQymutJYIvGxtxEsQxY]yPrQuQyma`qv`y`prKDKAxlIeTshuhiv?mrQQVq=QjEQQpSkeN\\IKvmQYDlB]JIxrmUkyUyEuMiYLwTS>]RhUM=A`HgnBgnL_^LFh\\IxrooA`lqPlCa\\K@hRhrZ?\\YxsAwfaw^GisGawRIqMhwunhJQuTQcSxxHia_q\\HfjsVipa[iny^Gg`p_MHsjwy=v[jAyaqaAWvdhdQaiHawfa_yni[iZ@yr@AilIoa@unHimfj?hj^Nvkophwu@yiwysyijxqYwUwGyI=iwkWxGxG`qcHp^PTcLR[@L:lSQXx@XPplkEUQ=tUPTk?qQOiLAMkQDLK`QL@S^llyHNBix_TlCmLPlLR=UR=VdMXLHl[IVHxMulRwUR=dSeXmbeWgenghoWPsdPSVpSamoAXyC`NLDK`pNa@Qn=wJQTjhOhLPxlPHuWiIY@qRAAWeUW]UsPioVyy:iyfEuthXsExhyj?MNKhnGxwxEyttqkitiPpsUx`MwULM:hnbmob`o^quwXYSHmSHVZxY:XLAqkmAyMtSJeTOejOQY]YWtMtcaPk@UF<j:xQ:YOitqFIwMunhHYfxuiyniaYiyoyqWkaj\\iR>]vHELIxrS]UV]soAPFeNTdkl<Qr<sZAvZlSaXldQwdMUQipLquXIRmQuo\\Pn\\PLUTMeS?eV_lMIxrnTw]MTcaPxtqIpumyvkiOrAwhQw\\=nyxmNMQGqjGTMrmwEuU^Uuphwn\\Pp<TV]UvesIHPuTP=uvAdmFxkGHTN]U>ijEtLR=UR=q\\AMAEj=tR;EJK@S>HsCIS@yr@Iob@orAurEs`Up^XTcyUyqQWpNO`SXUyiQlFElHuni@YhHVv]y<TveITv@pN=xQxsyHk^YpZ=PBmPMHq\\IpcIwcmR@mRb\\qEpssyuCMPS`KETxmarMDKZEWtdYtQv?mj@pjl]Ql`yNDk>=s`UpQiymaR\\Dr>ar>TLMTLV<uy=jTQuTMuTYuSApkUNeQuPItrPWOlMqXm\\upUtpUiSKETKiKQQW^QlWqfAiw`Hp[HlLQlLOqHqm_N]GPvpWqcOewPmAo]w_\\ixtuWrepo`xnaHauOynnj[?h[OgD@gnNk?X_=isiy[JgeWgkOQg_pppplR__pWd[Gfk@ePxcOFivn]XhipIeX^ibIneo]u>aj>rEw_w`rcXcmV@IVyaTq?CJ]i:SCmYCvOydyssctSIeeIfB_uJuWiuGKAWnQcAqYpxmlxYyqYfymlqU[LlUDU=ANKtSjdQwdK:=Wk\\ruywwxbuyawynVvkfvaG^[nyuLIw@HwcIg`xnaDW[IBgtdef^_f>gxUktmGYEqDpoWWqRAQyHgfM]FpSuOSISqv=awFWs_QfsesTkesQraIbEUcuWfKMitOir;hyuIusXgavKyrXSff_gfQi]ec>MFFisIIVmGubEWWuRgeWGiTAqWVahKwrY?YvEyoSWdUWiMGf[EHOBVydP[uhcyjyWsOVWUsAGUfotekVX]UhOrIeDGOcQ;FTScLyXxwd=ywXksoAT>mWbCeDMdCuUsSxlmwVIi_yHUEHYSb_wWDEsEUHiCwnMesGusciYcUAMFK?i[asEic^UhSmDQsDsCusMdhqghmYtQvIExrgufOUoOcoewg]HqsHMahteHeOeT?ggGgsowqKvVEYlIgaCeUge_MWdMCywuAyUvyxysfkGXOSUpoWsowxQGKASNGiSIIFSrZGf[GbpqcpMCDKChWyTsdaUThmvwaf:IUj_Ym;sj=IFMHoewMmRj_xyix_ibbYSqerhcfbQI]miSKcQHlGGlF__i^aLF`M`vooskVksgflF]wx]woblHufFk>Oj>O^;FnJniYxksHqsnZ@BDOcEGxPgdKuuJArtoho]WTai?gcUoHLMUTMeQSE\\idPodlAx]wcj?hjssIsYjYRh[SGEx]wEvABaWh:tpgUq`=XR<MEYyv`J<TSuPuXUW[uwaDT\\IxJatvPMRMYYLS>YL^XTc]wHXoytTQxtlEUflLdXWdHxN`lZutFYkB@kBioc\\Of\\n\\Pn<PqtQYdMWeEob@OAYUXmSsxpVPsDQKdTOetlq<rEyJPUmGhpgdOv\\ybYnFlKHDX\\AykmkWdQDQuPhpNhlsEWXUtvetm]mHuN_dn_\\j<ENttQrAjoUwPiOIqlv]TlDm^\\pRLNVlKMAqdHx]uSWdlPhlKQuTQKVMuEmNVlNPTk[IXVeqqUSnLM?ypZYrhupMquKIRcEWcyrh<KxHL?YKZQOf\\n_hn?hmupX_QYb<yLXuB=:`N\\@NdLNq\\PklQHxsaYq\\aukUWeUOXtkAToPaqRPl[=M^PTclj@tJQxtmDugqXDQsDAWb]WFYkY@ymIsJAvZTkEXkq^tKhtdgrcahLOePOkQYeHgb?gZof`o^odOe?WhmQ]TvdgPn`pp`GiQquVO`hXyi>dV_eFqrGWmrQtQxqFAuRA]mWpm`]rWiyflOhdNxdNxeOn^hwpAPmTPe@yr@IiqAtu`wTihIfdOitQaqtFg`OiTHtKIdDXkWa`nn`v_wrfaXv[gf_g^tNqtj@`y@rnaxnVxEVxrOch`kQhnMih[nfaofjXugawXiqUvwonw;`he^xOGZrgqXomtOycohgQqavt=G<=wuyyrycV?Ix]yDgY:mijawm_hq]X^ayGsTxCefmHEwIJ;vIyyfHPtLP<<R;EjMpv`iPvUyY]y`yNXIjnqSoyuyawIAwhQwtHoMinpuj=Pn<_\\Ov\\MOvkAdOgeGWgUQaPyhfxf=qrG``gpg<iwpwo:AoigkKhyoIoXXg?Oe_gf_v[x^yJvfIqm_isqnuZXquXmDPsDodipeGqwuwxVGp`grUow_ggEW[iimrFbYwgivwxXyhffXQ`TYat>_dN_<Qgop_IQmVhamolKTRwGyevesHoSG\\aXtCgi=WZIfAwE`icQymJAtZTlMTLfHUmpvDXv\\IxrTxmUpf\\Of<TKEUCqmwXYkqu^qOxxt]@Y[Eo^uti=uJXw[=kv]o=tJpyUommrUv`FuwxfIfrs?y`^_Yv_WpcmV`mVjaYbyiyLHs>V`mXtfAusXjTPuTaqsfgKx[x?xwywYax_npohpo`uuwWsCv;yZSup]WaGf[YvaUDlIRdcd\\SdCaMKXwAHUflLdLOd<yqyYjyqk\\Qn<scXla@Qx]wRlPehlPiXeAofPoVmyymVgQuo`Qxar]aqlQtE]r\\EPx=ywywmDQkDrQqqxaQuqxgYrMMT<MNK@v:YuuIQvqwu`TQaTMAtRAYMYVoQYw`YmYUYQvrIp]]xqqxklPtLs=tKx<Y?IP]XN]\\KHlKL]TVw^Y`iLh`eotvOwYnpNv_\\RHgfLEGlwETyT]ceHUDF[BSSEUSrMMTleuG;s^QS?ir?aHocHkgXuqHpwwRIstixW;YEYsckGhdueHXlISpTl[EV[EjZ=PBMOO^^LFftOiT`htfiOi\\:wliVyxisyGyU_nLwiCIoMx^sFila^yIvIxyRxy_yxyi[eWeT?_f^_>IwnOtLQuDypyiriOx=ywyAjZ?`ByZiyqIAr:AZXvkAvoQYcbGhK@gfnrwy[v>rQDyevPorV=TJ=rTqdPkexmvmaisySyarCWvAIWeuWauxXgI:QtTudqmusubhqghmhheuDyIyqrqkWEyyIQcQCDK_EDufMaSF]SfcUwQx[Cs^MdXWXw[gXeuf?YsoCegtt_i@[VwqbG[hpdn[Hp;PsdPOdPodPx`QO[xk]yxuIMWDM[=VZ=jmtnIUPtLPl`XaAw>Mj;pyxmyYxQwyWfhUupjHhxeIUoPgVylpG[pXugawtxfQVb=Xj>Vj;ojApjrnifA][AcRpkHp[tNat>uvhfEVoTPmrQtQoq<Gf[G\\y`igi`@xj@@qjf`?hr\\GnZ@n:P`ixlAy]y_mapmxOk`htqphM?dehtDXs_QvEwesQ`pWqWX`axcmy`YYyXfmY^hLgeMgcyweYVr=YrfguphkavmxOk@pr@xcoHaWifsyyYgd>_vHnlDgnrviha]KykfAxWHs^?aoOx^Viqiw]pphp`AWnEychwpUprOWobGgcGfWWiUf]gi]fhgSWcWgiwoehHfsAapVmGvd[G^_gf__`qv`mitayq@ovLqcTq[AXjDPkDOcDWckOqVwdg^sqQiw`alAw]>iwhfFxkIxet_t<gdOg^_hn_`\\NBrceHmthgUEYhY]YHOgdQG@sB@CxuaY^KDC[I_cFncHoChquuxKUQihxMvuARoohpOxFyvYGf`oh@Gd[IV<kYyCU]ScOQW_usXgIfeupgcGYUp_upguFgDiKNl]vlySQyVHum`\\MHtUkyVS`S@pomxVSXmUhn_hp_tWq@pYEWgeWg]lseqnpppPp]uvHlPhMu>Xr[APoQqZPlLPl_hmyutixy>usiuwbAnwXn]qjAAUgpTTPmT@UoPWODn?iRPlLP<k>MnNeTgdU_`VqXuydtaAt\\EpJquKIRmQmoTSqTsV@m^DmHETUUT=eSgewgukDerE@kBmk^UPSLREXknuXouUouWo`WpTs>ar>TV]XVf=urHlDPkD`MGPPy`Y]YUYQnb@oBtpAaYm\\OsAr\\E`^`pNPlLQtIav]YaWpcdYweIoixoyacxny_wmvwjRF\\KFyNOjEXknghoGvmIyPxcM^iNwhqw\\MX\\MV_vNpvidSgdCGpUWg:pwpOkQF<@yP\\YvxX\\arOTmHlYNuXQup\\iv=]XYtO;drE@[V@s`WpFysIItsqyAvtWhh;hnWglAqr@AeFnZQ?hnO^sickQ^\\Nl=FrZ?lkHtKorAyri?qOii^N\\[_h^_x=wdL@kBPv?_b^vZ`v^`>auovfiduYqVWsJAtZfawfaRnjkIpAQkVi[Nv_\\rDSs`UhFsCGSXdavCYetkYb=PWiUW]nhMvxmQ\\tX=drER?gB=CB@wb@?EWcEwGg]YFK?C]Uf]_XYWIqIuH[S>aFNsG\\KFe[gaausKytQyhMwHAsj_hSgu^avNsrH_EsacAmF\\mCTafH]R^eb_eC=ovocsvmwCyFQwEUoeXoVf]WF?VZ;bAYv[Uv@icrgIX[gPifYGHQ`Uj@kfmPEhr\\Et_QrluTM]qB@kf@pOYoQUTN]TnerFYsuxjHDLHdjBlJ<\\TPmTlilipYOPgOYsqFpm@f[@cq>gNFZNv_\\JQaptePGUoQuUkAUyuYylk<hnuyLOplOHxZYrIDvoQYiUsW<Y?mwnLUmQN\\LlAlL=Xk>YvEulGUQVlKDQsDqlIEMC@sO`xOHN\\LlA\\YETK>QnK]mHuN_^aTHhKFq;fmpN\\KFs[XsUvsGasHA\\HvjkWqWadOwdeGbh@sG>g`ib>s[Srj;CAWrriYxMvkAIXscAOuTQuVuCE]FiGGX]j^_c`Vr?YkQFk>Or^WpS_uXv[oNkQFlUNdv@kB`vJOaWpf^?iR@ifn[:GcCG[oghoGaXflBoiM_qB@KdlFMtMYXX@SnLK:xteiqdQPdELsPl\\iR>]NAPTc`LwhQw\\R]DLVpSadLOdLNudHixj`blQm\\ib>_^AOpSa_K@gNHr;HZ\\GpRfdOgdNqtOIvnOamganFlvpNR^KEGOHkkIHQr<QBcaXTOy@oBTKET[XS_hByrJ]iB?kK@RZ<rcYTaHS_PT:\\PgpW\\eTMUTHxR_LlyaLi^B;HFSBywuIIgHqSLIeFkTegd`qvo[HgoTv?cv]E?Y[s>lGqfki_f>hpawSOpS`[GfkG``hPg^`n^`^QYbMFsuOkQF<sB`mV`=wwsuE=HR[rj[Cp[WVARgeWWoW@AGlUDniT\\KFLWB]YV]]ewSX@_S`Sb?QV[UypiwNyteUXtCdUGfUSHD?cf?h^MHCAsjAHaQiuGhTegNmTPMtkoY=cDOgdsoET?cc;W`iR>]V?gsGqsl;Ir[rNatNcBHQBpwonTw\\hyW]Rhmk\\iR>]V?DM@HRauVadQaQqk\\K=PRQENIpQxAQ_mUim_G_rn^\\iN>QCD]FL[efaw^wiiwEAtJohXo`uuuwXeU_]NlUKNtO\\LNe<wNuVaTJwYJ>PR[LodTor=x[xjbtobtr`Up_QYbMN`Hn?Tq\\nd:HfR^nMGgpywYysrAuR>Zoi[G^atAu]?aVn[WQ\\:_vP>?BJ?S^;ESKE`ii]yFRWeUWfv_iVgxUxV]qnGMmoELshRDxLKvmkVrj>[@NZvawawa]Qr?X[^O`SNuuNarxwxYykGqVGqXnmBHwbne>cIAUdCe\\Qr?DYcynydNNLKK]TN]rPhoU=uuxWYmoAB_crERf]V^]bQmUxEe?ir?MhSaGuwxfIVAqsW_DPkD`QYbMF`_fegc>]RxSRxuiYWHawSmqsxHs`UpNhlOHpiqquAurHWMpw]]NlIKcYOA]R^YPLhs`EwwtYXxXIdM\\MXlML:hquqxlhYAqXddXe<JKxSFunG`R>mQ]TXmXXVDQv=mMtNHXVmHujQYw`YxIuaEWXUp@UphLNYfioAkB`u`oj[?lHwnswv:e]wRHOvU=p]IxjAu]ykmhWUqPDQc_QiBP^`pnrG<mWm_WpSsjAtJsWvGxtciaysM=TJ=RMQwOayHywwqG_iDOCiXkeBGwckU>]j@EufGnJ?kyxyuxq]xpaUlCe^eWEQUXwytYxNytQYvj=IleI>EDMYtTw\\hW\\=A`ji_f>x@YwiXhnAxK^yxwaohpothiuEYbIcI>ER;ERhwbbKXA=tFYcB?sgMDFkBscXlaDyCykycSoeXorhuhmWVaqSXcYfIHdYETKXw[IKWI@Ov?]jg=lB]NrtuMYrilUwelmeuaASaXtfXUqpkAuMu]kWXqpevt=Y\\>_Dx<xn^=M@TV]UVvQwGyPseyoyU<<TN]U>yQyqrq<YbIlAHXtdmslM[@sWhRkQN\\LxcdSIuSmYpY`qBYwihyL`W`TkMIw^ypxUwqHqaushMSDMSlea\\vhVf_Ri\\KFy>PpSUr[D\\ibY[yJWBuyxm?hj?RSwhFwbYCY>wFYoYDOitOIfmHUmgAGGlurK]iB?cvMBS_S@?by;rikUwIIimisqF]Yv]AYvkEp]wRIrmyUyQIGYWPAvlEileIFEduKd\\iZU_lCafRxmUxvjYqiQxwyivyb`v>]EHsBUoHimvEsswsrwSiquvt=c\\sXnc:<lGqVC\\J<\\MylYFxyiyOxQjkIxk]WpTMeQuTAY`YKYxvSxsymMEhbQYrNFq]H_X_BWUJscAIYuyTiExqwYwytFgcGGVRkBemthgvUsuvqFIuImacPAiB_g:crE?kU`LDdjrwkyOrIyesgjkIxk_oPW_Gf[G^yhywwq]qyarAZHwlMWphN^e>bkQ^\\RF_S`@TbJvILi]qxQQ=dywAJnpoUurqxYmyPSyXyiYN]TN=VoPWqIKKhlZ@YKDLsHj>MN;ax?Ykvhxexprev_xlRTMUTr`UpKqtXqsmxUvmkatmtMLIESCpSQDkf@N?YkBVwBpb]`kGdvWxHYIviuYaygCBywEaWtCqbGWErmvEsUZYWIyIIWs_QtcOFKgD`?YKVbFVr:>^SdFcCFKxlYsiCx]wExAd>]I;WfZ?bpqcHkipixiWxfYXIIwhCt\\CI\\?YKN]Hp]sNrIoerI`Ao[Yn^Kvc:>pqwuxnqoiwiWpuwsh_]HvbHxbbNhqQdv@Ksd^UhSMFKli?y\\sWxYpu^xxvIi\\FlBnmLv[IhapA]YgixYwf?ujHj\\Pn\\fmdN\\CI^?YkB@[JVk?A]WF][ymXwi=XZAnxm^avNblFlZgsTh`v^ybYnvfyFYtn_oYwcKGdKooAP_lwtM_qB@sWgsj^[`qv`AaQiuGIn=xZsgyoxe\\YxsAhtBUsHh]vKwrXcvcwVXGfoghOUhgKFsMRkQNhQS@>^WpcmVamVrkXnAAigy\\y@vbIl]^flBIwr=uRAuBY]yLydr]yCysKEUSEeeIvD?sA?GX]R^qglEydMfNMG?axnaHyEyykyAsBpyEZmVtMEEgr<WtcaViqiw]yewwvubGYeqSvb;t<aUK_Y]?YKCduosVauVswfyI:YCyKy[SV]WV>OR[[wpUIGgcG_YoIyaIYlIgaCgewgAqwJYU^?SxKtQmfB_uoKBxuIWgeW_wyUwgmSW_ICAwbAGCaVLOsDQSpuuuwbaomFTeWQbGgggnhupuXfblilxPa?_VgVmGULEgNcIaqskIruyoRIt]]XqeX[YxsApUiwfmuvHmuuxgYv;xjX\\Veqtg`LQtLaQYBQNlIPNtO\\LXAMPFTjb]PDijEtLbyweYvJIr=`mrlXVHocHOfqXudXoixn]oiAvKxRXdvxXyiYVOUTMpWf@O\\MLDxLKDq]]UX]kU>cJNeV_fb?hJxpXQiExdXOiS@fj>[:GhkG`GfkG`uqwyw_i]YeYQnhpoHWuvYkR`k\\ib>CHIymeIvOxlYsfyYuiW`wfaGs`Uh:;YwoUXKYrIVxOyvytRiXIiItWDn?cCEGX]R>axFSrZKDC?tmmwVsivire]esSX@GgCISPsDQCHFSBaWtCYfIgqalmvaMUmphendPoDUKleRF]SYeqlurl\\K=`WpTStdm@QWopYdYMciVmHUFTrJySeIY^TmGQX[Qr?LqIqhmXx=NiIyma?gj?[yxuIOaWpnvPnVhoUwplxwxXySaq_W`eothhnf`oFWgU_bFockQ^q_lnOaGxsaYfr?gBHxkIh<IvjFo^O\\UhsHGcCG[ohho`oeWg]PplPx@H`Mn[AHmT`m^?fZ?jR__@O^K@^S@c\\I_kApcWx`OuUYuoi[jvblHUMN;AyRAQ=Xj=\\xnaxJiX`aOaysYxriYx;<TMUT=QqppPptWSQrHiUuDuxXVAlWqXU[IOlujJ]qBHWVmUFHMFlJCxr\\AQWmSDMSDmlyHN_TlCmr@OhlavCokWfa@Ix]wrB^Z<^flFgfodUneixlHhxeIibIVkXiIu=QwOYOfqXYUxopv`uVsUwQuWkYkQuYH=Pr@Sr\\]vn]aHqsHmioiuYenpppP_XodRO`S`^R^[lVamVr^av^v]vxy;vrIp]__hf_lR_`@Xr[An`pNohhocgUupGxZYRIChoUupKsvgVsoEt?cVqVDwDkcC=AHBwr]aYjquuaSHmSLUUUUsHgUuCgdOg<;VtQv?mYtQvE_iwqtUaFMGSPsDQCGccG;IVq=dCufCwr]]Yjqyu]excXLwsySyfsUwQuQAunGYmiHQqI>TjFlKH<pjtq:=PR\\NMHs:<V;<PP=xidYQTPFTJ]Tm_DmDElB]NRHmXHv^uVatWyhxPtrIhM]lLEHJZAXr<xr]QNatPQXyYjI<xVYXIItLQudhyT]RhAVDxLkdkR]O@yOyExElUuiri<xg<ybLOdLvnIwMayiyYryY:<xmxmxalmxVHAlGaVjYyv]pqhpkiuyDyI`PnlPl\\@ihQqU]yVikyN?XrKreygwQdDOcDKsvoMqtPYehpngTaryixAyiFauFa_yxxWxwjF`kFjGqf]PpdPkGWmqVgPif?^flF]<Fj:v^Hx]aAvuvwjovnI]`wf`olHGv_Vl:^\\N^\\jHiEq\\X@yVY\\v^xBEoeXo=IWoSfQIw[FluRM]iBGW^OdcksWWw[=Yr]BywsAgs`UrMMUDmHUgVlMVLGtKIH@mR@EC?oDcwgi=vuwYlyEcUWiur_QXK=UR=Sr[D`asCYTFsCGSDHsbs;yHIRTsTgOidkU<IfJsbIsE`yFi[yR?Xb[rVauV;hnot\\wxvIYxavy[YqQtIexPgvaAUgoTDUSEEy`yhygs@iSUCXYuvn]dVue[=E^MHSkrAyrssYhaEausXgfawfAGuSGUvmIYCvJ=cNMG?WfZ?b@qr@mwWyhQguuwxJQtTQRgeWgkulQXgyt\\KXQ?Tv?cc=uWkpn`o_iu=ujB]^jqlQXdMWd=o`MHnqxxvFpR_knO_Go^WHn\\Pn<hsUopZGpR?pR__Nv\\QVdYAu:Wstpd`yvaIeR?eZ_if_kCIsCYoXw^PVkkn`tnrCXvAIkAYvEykUnj;?`R^neagQidII_cF_[WupiwNplOpidYoTpw`FmFoj?ir?on`v^Sn]Tnfr?iRHkkIh`pn`FmTPMgeWgFMosZEhR=gcgg_gf_gbHgxeIwRuu;QuoWWSeiteHXwCgWYLCduWb\\iRFUrcaXlwwxWyRWeUWVlMXLOgdOWpauuwbnmF=uXQuDCaR<sR;yg=Iv]wfpMCVkCvoUicrhuHxAR:?UvkS\\YRkMhv]eMIstoho]Iuaum]Uv?YKWhausLKC??_Jpv`qfp^gVah?IxPVsLCUsHgMfsGiSsfMIySaY<kI?_TdcbIyv]mVtMeOisGadPod`aVVCeFmbb]F<auvaImYXm]sHqslEVdQB]Wf][CpyCj[Hn[Rb[D\\SeGQvj=IjTxLAtRAR=UR]doeQUQPr_XVwdkePMQXrN]RhqQDxLkn[AXjPptPoiiyeyYg<Ivjn`uhmLQtLO\\kAawvvt?k@W^RgoPOdc`\\[AhbQoaynMI]\\GtRn`Uh[EinIxhgHeLPtLQdXfifI`powTUjieq=eV_e^kDGOtJAt:YhIiIAyWyqsiABEUHkCyviCnceHUDGoRS]C@CeSGe_aysqEHiXqXUYqypQk>Yk[=M^PTcLVk@MKAWN@WnLSbEXKXkQlOlmqqosYXw[xqixkSHmSNtca`j`p@hNSG=YvkATSeT?UwtoTpuwShmupXKeUWeoMQR\\LJblU^tkSljk`qKau_yuUlj;ht`Ur\\epL@S^<KAXrReoPmj@tJcdOgdrpEYphrZQkaAJ>MNKhnJDk?AsTlJOhTO]TN]TXuxoYnKAOaxSWPVk<qBhs`UVGQmo`poxpM@S^<S_PT^Xtc]MHN[DN[jHufGayfhkIvIydpVm_><[excXDgyieiGIt]sRr?YkQFXugQwsyEvSYuxQijYwG]yhsyTOS_?eSGe[wfatvHqXKiuWisZAr:TxmYxEyso@UfTsU<KTaWpLmPuo`qmWYqsxwxYyRQqgUModPotpo]o\\LXa=Tv@SXUMXLM\\=Yb=mEtLh<PwdQw`xeijE\\J<^wxxxXoieypyWkDQodNtS`[cac@`okYweAmGVrZ?fZ?j?Hys_gpWa=XZ=^xoixLN[?@s^XtvNxbY^v>xZYZQiigAg^Nruy^Xy^LF[ifmhAk@Gap_xbviwydygr?HoE^flF]vhv_awsxhIvcwfynVeppgWGkIGsogeHhjMy^IGtsIruamsVh@HuSHe\\FlBQx_grYhjFo^=?riyf\\Of<HtKI`@wb@H]WF]__if_[YxuIO`K@exPbbQxOOb:n\\ehjtPqtOAoCpP`Uwpggncgxd_ahw[hPbQoeXpiMFlvAnrGLgr\\IXtSIuCIrqsu[R\\CDLIgNQTv]Vl[umWYqcTOitEuIsyYryeEuseqwdQvuyyryc>[y;KTc_DmUXm_b=EVLGs^scwkxrsCx[xJcCGgcQPqc`TDhrZQNMUTM]nL?]@HRaUqSv]YV>UfK]UhsD[ATRsiYyRZ;va[EHSTPmT@eY=UrDwumsfywiYGxCGC@uR@=EWCE_mWhmCYQr<ky:weNMHo_YVyFwcioEynYT:ywAywI;DB;yS=eY=VhmWPGiSII`yvaIC@Sb>UfKKr[AC[AXR?Sr[S^KD[cdtixeyDOcDkOYoQWPuHqSh`esTktp_hJuTYuR?eR_cVXQHDiiXMCEOcnEEt?cv]G?Yc^iGEgr<eXoeHqawxwbnMIGIgMwFS;wiyFK?SJETSERgeUgkWqWeJ=wdixg[Ut_wp=hy=bCGcCWSyCya;s`eCVkXACxr]e^MHs_YDYv]Or[?DMWdM_VmGeYuexMs<UTMQWpqwUYca_f>GwEsDr;YjAF=Ub=]efaw^iygWurmvEctYGSv_UXSRtceSmi=Mx_iulqutiti?S`SdFuUVoriyxy=wIygPgs`ExsqDR_eR?FOOSK_S`?K`DS_Pl^TlcLvkAMk@UF@YflSflpnYyB]NF=QVlq\\\\SPtLQDK@Tj>TJ;LR[@tOXPdlLElOQXkdPwdMOeTObPodPntpn@PmTPUdMWd=ohHo`pppplTghNVqEhh=`bKFq_OiQAlvpdMWd=gsMvcJAtRAsvayvfywgi:^`qRReuVaYWIu>sR;Wb@ob@mEr=w;mF@yFBaVl[b=IF@KyA;C@Sbnaeusr;whqYTTMUDqhgYuiOUrWwmIycyoyer_ptupXgavetUwQOIhQxAMPTooEwLUwcHO@pZ[YeR?vFImMaakavaA_f^_varywuEI`oV`mVrVauVQxXq^cadD@ivFrbAsBFs>OvDxvVPasOlIvwsVh]xkW@c^>alqw[ob@xbPxcaar]IhLFs_xe]HlbQdZ`bxg]dFvj?yDH]NXsfp`Un_aXlLPtLOkEPkbN_hnrgqhMOdLObsGisfpogpNitOItJAuBQo`p^dPodpaOyv@_b^Q`?Yk^ia=A`Bf_hN`JyuIO`S`rdgpLItkpmpqppYwxvrhwpMgeMgsyxy=xaRoif?hZ?jyIyqyiIy_YWy_FnJ?kY_qtQ_PWoOPqtQiTvalOyBypj@rsqmXNfk@]@HfJItKIrmwetQ\\I_asIq_Yffn\\en\\Eh\\=>c`Pt>Xr[YwHavVawYYxli_JnkYVa@Inqo[l^`n^hcN^<_Z=Xk^Xtcy[wprgxm@Nk?Qfvax?y\\ynxrVoOQkGqfUOeFWeJ?b[Gf[nhuh]uhuHhwLyo?ir?adNodLAtJAbwgiwf[Gh[nf`oFxyypqwhIIdWxjWvrywjmoxVhlPOuONuOHlfGmOQcB?pT?r`H`<IZ[atRaroa^WHpM``_Fhafs?w_tFyENuX_f`xpgaxdXlnqnM`xy>caHm@ioiNfjxjFXtC@^p>clGpK`sEQgoq\\wpwEpxgamX_ovHb@Ng]_[LYbxxmSfejPumXyFv\\jimmomQx^qqwO_aXvupI[FeAuDkQbWsw]iIDmgYUi`suqiVUqhLgYCewgYSXYtaawGmFoiwmsVnqrUsWByxweDEgRW=ijkfyQYwiXwit`QxaycgkGhKwlifEMgOQWlgEAuYpmvIixAyfXwulqefmx`oHpKSDCIH_IIYTIus]yiYewnIIOMs_eSFwceayUyvoYwqmuKauVauw`qIYrphw@=m>YvDhXn=OKilb]Mr=uWYnhqwhewcqwPYvI]Qh`R\\DnP@XE`VgmVNqKXmPH<vKQRv@v;XK<@R?QR;uVYaQexUvQvydlEqsbpps=t[im^TlCeymyky]tvYxfmOaHgMOgcG[qnvu`r]QuWIquqmQWn>Pb[fh_N\\TF]SFtyaqmYggv_iVwtipeQqrnh;Oq_helIyvplPplN?_N^^CgqwhqdQwdQqgYyx>yZYbg^si>sqii?WfKg]t^iBoswowhXwtomLYr=Q]HanoFakny?xrE?umahtinQ`tQPcCYhWGigFf?XrGxmBqv]wmB_^\\vtmavRqkfwrPXvrN[snkVhswGhxnyk_]AHso@ZphZkQjAProgeW>]HWwayayy[gn_hNoNO_c`ecvupqqTgo`hkGh[gfyhyHGhR_EAITpSI]GsCGs`afJaX`=UWiuWyxvyEagVSMx<IVGcCGCwDyyXEtTQytoHpkHnOhVAUg[ttGiLiVxmWHEiSaUmIhCmFMGTa]IxUuqiSVmiVAeF[Uc?gwgiWuBIcEtwg]GBheeYUxvIgMMwEefnOhvOh_iIyqymwecyhQsGd?di[HYUwWYy^otQqtnohpoxcwcg_ij=U]wFAexFIt]gcwGWpsE;CIpgGaUXIQEAIXr]v=;VAUFX=x:IUPgFa[DLMHS_d]AIdgtdecO]IxiExYfGKEI?FpEup_GEQdiYyTGeCQWlMXLUEUcVSmd_wfYoYTeIwcIYWWfkhgUgmkEQUYuUeVsrKefVmTooTMEhJ=WHmFGqNoew]xkN<y;`WUqtMyRH@OXIuSayFPYwpo_VcTHs`gptPp\\vrphlBxroxfIqmi^wH_bYO__pqNOwpxtifed_]P?ie_qv@x<Y[Dvpn@ghogPGuUHe_Wpqf`qVaaPyanwhGePh>gWgIwhITlqCaCW=;bc;cQ[InkiiYgqwxCedDgrgSeCiYLuwMcidAwbAd^cgiwgemHQWtVawfOwoQivssMqynMUCoghwswkCEmT]qC=iGquDheeeGdGqVocXoQgDYeaeF_Wtcerpsr]CS_QXSuwwWyXotmIYCMTQuTQoBpiwM_FGwcIWGBKBoaxnAGK?iuqwwwxgqdcgF]wFAexNId]KUWeUOYyMSDt_YsQhXyevuUESxmisw;UDivUywlEB:GgBwDv[DPgtBkbyGyuwiwwfeqgw]XGUXmUxGIyOcgK?c<mSBeb<ERoQYWeWgeWqaxsmiiYWsenPXXC`Uq\\nHhuuhpeuthdteiX_qVlMqkUv``y:yleIYTYtWiq_EkiE_bXhC^ojqi:r;EVLCTJXpimPpylk`O_PyuiPlawmPUSEUKyQwYbNhpEQtqweugcinmxfiIWfux]XXwdflDG_OPccinQxePQyTQq@qrxWnqxutWc]wqSVdpVmOgnVothheu`rVPe:nn]nejXnWgyjYZGwcIGoLgoBIhVf[Hn[dywy?y=Gyxxoihycytoyty>y;iag@hchtdOsGavNO_h?sqYZsoma@gnNuVA_goixoeeXoeNxwwehXwdxoixchXqoo]EGpNOtsXpaa`yv`a@rI^lFo^oxiyqiWGqlgbMX\\MNcaojqhX=tl_GowRUiHtMx^oRHgEMQv<QbhcUttWxQxQPmRtMaMlg<J]ILijXeqdHwcHWOUOOEqhxNYyoeeXoeTALtceMBunODk>]TflLiUqh`TfDwqxLiLw:MQg@Xr\\OcHxrxNQXscQvRAm`uVaeTdNgb?gBwrI_mboZJaxNapPplP`vrnpvvtMItKXnDvpn``ywec`dTvk[o`p^dixtO@c^^paXiIP[saqxYyoytO?_P^x_YvAYmIHlpXriywbFqlgeQomaIo]Xn=WRSfOgv_eCF[CfUuRABZYc:]iZurdoTdOUR=UNQslQh^Csp]WWuipeUgGdBoSFocdYSIaImutggvQsDQcxisItIh@mcWHr[HRopp@]PuTmMyoHymQEpN]Tc`TLUUuUmH`YcyknLyVYXGYwhpYrInlUPmLoOQWDxrMLQp]wRiWuPr@lqYamFTMEhrnpqppomuVIQwQuvIYoqxpQEmFmv;qsqEqAEnJUvk@UfXn=extemutO:\\kA]qZurlYJYepdeRoQYGEjTTxOMsOPkxav_ylUtjdlQkarWuoGyvmQQqmwVpnapnNPwiyT^LLKQr<aq`tN`dLleUoeXoEwbAsBpSyexePwuhV_isFmPeHysIYOYgDpr\\P]x>ijWsxq_phgehowhewYZ=NmR@]QGnJ?t?HpkfZLPsUffwWxUwuLOoyxiAomB`gSo\\aA[;>i^>xiF]p__AIhnavXiqDcxegiwgegITctxYBuixQwuyqi@kxG[WSWw\\EUPOBw]YNEfNQEcet;YRAghjsIiwxXiYqGYf?RUUUUOIpuwPId]sRnQwqsi[WRAwCiEyHqhpqHomX@iDHshbSdCAwkwrXSulYYuUXS]xesgxOFUqhoUv@iCWaisUTWGxroeycXDuVxWxWeJ>qMjyuF<JvIV]>fAQpgWeyGxwxwcfmXntnaxNPt=YrtQxkYvq_qu?vtom<@^JxwuQpfVcwgiwOyCyqwadiwqoqlhnkW?tFog@GnJ?c=Xj=Oi_Y]iPomXpmqkYXxgY`a_ty>`ZPegpp_o_FioTYnKgiaipQa`VHsbQrRAmdixtp[yfxNpmsNinHaYaZ:>xZA\\i>uKQfk@mH_mVftBYpAavtpwWvhxgpgWeANtA^hwQuogddf\\?Pb[fbUYnlgeQw^@W]uHsPYgoFsl`\\DfjNFk>owtXjfwfawnXXyDyd^FosFtqqgH^nMQcoyxEGbZvtmAkP>Zr?cBx\\fAgphgehpohxyiiIh^c^w?hdihtNwoOg\\HvjUXusyppppxOwoymvqqB_^lImXYwsouH`mUQZ:vktnlW>rrGjTVsZXk?QndhtTPeUWeiWmePZ:>in?\\i>`X?\\>NeUWeMoaYxdoPeOWinNo^welWqAhZ:>i:?kQ>]g>[<fZ;?nOhl_g\\EhbOYwogr]IhGv[aopu?g:>jA^jrGjkaiYytTQwTPoOQo^F_K@cbAv[YbUaad>Z:Yj<ajW?]ihoghcyQyMymbPegP_J`\\EpbON;wSwoC:;V`Kv?kRm_GEmhgUWYAvZqXIcB:;xJ?xRAC:;BRcbrEB:;B@EFX=B:TnJtO:<J:AO>YK:<Jj::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::^mgq]:>jIqsmQrdWgE@oTGonvemh]AOpfhgVf\\:^aV_rE>fJx\\IwqbHr[HbOXs_qveWypiwMxvtXurN_:>ir`oZ>[<hwX^Z:xs`vmIYoVo_e>xwqveGtR_c[@dBo\\qwe:^y;@^X?Z:JF=u?<J:lR[lU:<J:HTBxL:<JZ]L\\iJ:<JRdjrEJ:<J@;::::::::::::::::::::vyAny_vsP?\\wyn\\B:;B:MTKWDKWgJ;eZ::3:\"\{\}<Drawing-Root>LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlNUhGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiVdQ0YqLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image></Text-field>
</Group>
<Group labelreference="L14639" drawlabel="true" applyint="true" applyrational="true" applyexponent="false"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="10" readonly="false" background="[255,255,255]" placeholder="false" family="P052" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="centred" bullet="none" spacebelow="0" pagebreak-before="false"></Text-field>
</Group><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Font size="10" family="P052">Fig 1: Wick rotation in the complex time plane (figure from Ref 1)
</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Following a series of steps involving Trotter factorisation of an infinite number of interim points between x and x' ({</Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052">}), the density matrix can be derived as, </Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" style="2D Math" family="P052" executable="false"> </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">where </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" encoding="UTF-8" family="P052">hus, a path integral representation for the propagator can be obtained by substituting \316\262 = it/\342\204\217,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkktRiw2L1EiPUYnRi9GMkY1RjhGO0Y9Rj9GQUZDRkUvRkhRLDAuMjc3Nzc3OGVtRicvRktGUEYrLUknbXVuZGVyR0YkNiUtRiw2L1EkbGltRidGL0YyRjUvRjlRJnVuc2V0RicvRjxGWS9GPkZZL0ZARlkvRkJGWS9GRFEldHJ1ZUYnL0ZGRllGRy9GS1EsMC4xNjY2NjY3ZW1GJy1GIzYoLUkjbWlHRiQ2J1EiUEYnRi9GMi8lJ2l0YWxpY0dGaW4vRjZRJ2l0YWxpY0YnLUYsNi9RLSZyaWdodGFycm93O0YnRi9GMkY1RjhGOy9GPkZpbkY/RkFGQ0ZFRk9GUS1GLDYvUSgmaW5maW47RidGL0YyRjVGOEY7Rj1GP0ZBRkNGRUZHRkpGL0YyRjUvJSxhY2NlbnR1bmRlckdGOkYvRjIvJStleGVjdXRhYmxlR0Y6RjU=">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</Equation><Font size="10" family="P052"> </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GMDYmRjJGNUY4L0Y7USVhdXRvRidGKy8lJ2ZhbWlseUdRJVAwNTJGJy8lJXNpemVHUSMxMEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GMDYmRjJGNUY4L0Y7USVhdXRvRidGKy8lJ2ZhbWlseUdRJVAwNTJGJy8lJXNpemVHUSMxMEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Finally, the canonical partition function Q(L,T) can be obtained,
</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052"> = </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" encoding="UTF-8" family="P052">\317\201(x,x',\316\262)</Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">
Furthermore, path integrals can also be written as <Font italic="true">functional integrals</Font>, where the action (S) is the corresponding functional.</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Font size="10" family="P052">
</Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkktSSNtaUdGJDYoUSYmcmhvO0YnRi9GMi8lJ2l0YWxpY0dGOi8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RidGNS1JKG1mZW5jZWRHRiQ2Jy1GIzYrLUZNNihRInhGJ0YvRjIvRlFRJXRydWVGJ0ZSL0Y2USdpdGFsaWNGJy1GLDYwUSIsRidGL0YyRlJGNUY4L0Y8RmhuRj1GP0ZBRkNGRUZHL0ZLUSwwLjMzMzMzMzNlbUYnRlotRiw2MFEiJ0YnRi9GMkZSRjVGOEY7Rj1GP0ZBRkNGRS9GSFEsMC4xMTExMTExZW1GJ0ZKRltvLUZNNihRJyZiZXRhO0YnRi9GMkZQRlJGNUYvRjJGNUYvRjJGUkY1LUYsNjBGLkYvRjJGUkY1RjhGO0Y9Rj9GQUZDRkVGR0ZKLUYsNjBRIj1GJ0YvRjJGUkY1RjhGO0Y9Rj9GQUZDRkUvRkhRLDAuMjc3Nzc3OGVtRicvRktGX3BGaW8tSShtc3Vic3VwR0YkNictRiw2MFErJkludGVncmFsO0YnRi9GMkZSRjUvRjlRJnVuc2V0RicvRjxGaHAvRj5GaG4vRkBGaHAvRkJGaG4vRkRGaHAvRkZGaHBGR0ZKLUYjNilGWi1GVjYnLUYjNiYtSSNtbkdGJDYnUSIwRidGL0YyRlJGNUYvRjJGNUYvRjJGUkY1RltwRlpGL0YyRjUtRiM2KkZaLUZWNictRiM2Ji1GTTYoUS8mYmV0YTsmaHNsYXNoO0YnRi9GMkZnbkZSRmluRi9GMkY1Ri9GMkZSRjVGW3BGWkZhb0YvRjJGNS8lMXN1cGVyc2NyaXB0c2hpZnRHRmhxLyUvc3Vic2NyaXB0c2hpZnRHRmhxLUZNNihRI0R4RidGL0YyRmduRlJGaW4tRlY2Jy1GIzYmLUZNNihRJiZ0YXU7RidGL0YyRlBGUkY1Ri9GMkY1Ri9GMkZSRjUtRk02KFEkZXhwRidGL0YyRlBGUkY1LUZWNiktRiM2Ky1GLDYwUSomdW1pbnVzMDtGJ0YvRjJGUkY1RjhGO0Y9Rj9GQUZDRkUvRkhRLDAuMjIyMjIyMmVtRicvRktGW3QtSSZtZnJhY0dGJDYoLUZmcTYnUSIxRidGL0YyRlJGNS1GIzYmLUZNNihRKSZoc2xhc2g7RidGL0YyRlBGUkY1Ri9GMkY1LyUubGluZXRoaWNrbmVzc0dGYnQvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXHUvJSliZXZlbGxlZEdGOi1GYnA2J0ZkcEZjcUZdckZickZkci1GTTYoUSdkJnRhdTtGJ0YvRjJGUEZSRjUtRiw2MFEnJnNkb3Q7RidGL0YyRlJGNUY4RjtGPUY/RkFGQ0ZFRkdGSi1GVjYnLUYjNiktRl50NihGYHQtRiM2Ji1GZnE2J1EiMkYnRi9GMkZSRjVGL0YyRjVGaHRGanRGXXVGX3UtRk02KFEibUYnRi9GMkZnbkZSRmluLUYjNictRk02I1EhRictSSZtb3ZlckdGJDYlLUYjNistSSVtc3VwR0YkNiUtRiM2KEZpdi1GIzYnRml2LUZddzYlRlotRiw2MVEiLkYnRi9GMi8lLHBsYWNlaG9sZGVyR0ZobkZSRjVGZ3BGaXAvRj5GaHBGW3EvRkJGaHBGXXFGXnFGR0ZKL0ZGRmhuRi9GMkY1Rml2Ri9GMkY1Rl92RmJyRmlyRmlvLUYsNjBRIitGJ0YvRjJGUkY1RjhGO0Y9Rj9GQUZDRkVGanNGXHQtRk02KFEiVUYnRi9GMkZnbkZSRmluLUZWNictRiM2J0ZaLUZWNictRiM2Ji1GTTYoUScmIzk2NDtGJ0YvRjJGUEZSRjVGL0YyRjVGL0YyRlJGNUYvRjJGNUYvRjJGUkY1Ri9GMkY1Rml2RmF4Ri9GMkY1Rml2Ri9GMkY1Ri9GMkZSRjVGL0YyRjVGL0YyRlJGNS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0YrLUYsNi9GXXBGL0YyRjVGOEY7Rj1GP0ZBRkNGRUZecEZgcEYrLUZicDYnRmRwLUYjNiZGWkYvRjJGNS1GIzYnRlpGYW9GL0YyRjVGYnJGZHItRmJ3NiUtRk02KFEkRHhlRidGL0YyRmduRlJGaW4tRiM2KUZncy1GXnQ2KC1GIzYpLUZNNihRIlNGJ0YvRjJGZ25GUkZpbi1GVjYpLUYjNihGWkYvRjJGZ25GUkZpbkYvRjJGUkY1RmN5RmZ5Ri9GMkZnbkZSRmluLUYjNigtRk02KFEoJiM4NDYzO0YnRi9GMkZQRlJGNUYvRjJGZ25GUkZpbkZodEZqdEZddUZfdUYvRjJGZ25GUkZpbkZickYvRjIvJStleGVjdXRhYmxlR0Y6RjU=">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</Equation></Text-field>
<Group labelreference="L14629" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" family="P052" layout="Normal"></Text-field>
</Input>
</Group>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" size="10" family="P052" layout="Heading 1"><Font size="16" family="P052">The Harmonic Oscillator</Font></Text-field></Title>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" size="10" family="P052" layout="Heading 2"><Font size="12" family="P052">Deriving the density matrix</Font></Text-field></Title>
</Section><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">We take the example of a one-dimensional harmonic oscillator to illustrate the path integral formalism. Using the functional integral approach, we can write the full density matrix as</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Performing a change of variables about the classical path given by </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EieEYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiktRi82J1EjY2xGJ0YyRjVGOEY7RjJGNUY4LyUrZm9yZWdyb3VuZEdRLFsyMDAsMCwyMDBdRicvJSxwbGFjZWhvbGRlckdGOkY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMkY1L0Y8USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EieEYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiktRi82J1EjY2xGJ0YyRjVGOEY7RjJGNUY4LyUrZm9yZWdyb3VuZEdRLFsyMDAsMCwyMDBdRicvJSxwbGFjZWhvbGRlckdGOkY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMkY1L0Y8USdub3JtYWxGJw==</Equation><Font size="10" encoding="UTF-8" family="P052">(\317\204), we have </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieEYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Ky1GLzYjUSFGJ0YyRjVGOC8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnRjsvJSxwbGFjZWhvbGRlckdGOi8lMGZvbnRfc3R5bGVfbmFtZUdRJVRleHRGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMkY1RjtGSy9GP1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieEYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Ky1GLzYjUSFGJ0YyRjVGOC8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnRjsvJSxwbGFjZWhvbGRlckdGOi8lMGZvbnRfc3R5bGVfbmFtZUdRJVRleHRGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMkY1RjtGSy9GP1Enbm9ybWFsRic=</Equation><Font size="10" encoding="UTF-8" family="P052">(\317\204) = </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieEYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Ky1GLzYoUSNjbEYnRjJGNUY4RjtGPkYyRjVGOC8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnRjsvJSxwbGFjZWhvbGRlckdGOi8lMGZvbnRfc3R5bGVfbmFtZUdRJVRleHRGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMkY1RjtGSy9GP1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEieEYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Ky1GLzYoUSNjbEYnRjJGNUY4RjtGPkYyRjVGOC8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnRjsvJSxwbGFjZWhvbGRlckdGOi8lMGZvbnRfc3R5bGVfbmFtZUdRJVRleHRGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGMkY1RjtGSy9GP1Enbm9ybWFsRic=</Equation><Font size="10" encoding="UTF-8" family="P052">(\317\204) + </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEieUYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0YyRjgvJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RicvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEieUYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0YyRjgvJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RicvRjxRJ25vcm1hbEYn</Equation><Font size="10" encoding="UTF-8" family="P052">(\317\204). Thus, the action integral becomes</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Font size="10" family="P052">S = </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Using the boundary conditions and further solving, we simply get,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Thus, the density matrix becomes </Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052"> = I[y]exp</Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">where I[y] is,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Font size="10" family="P052">I[y] = </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Following a series of steps which includes the expansion of </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052">in terms of a Fourier series, the solution of I[y] can be derived as,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Thus, the full density matrix can be given by </Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEmJnJobztGJy8lJ2ZhbWlseUdRJVAwNTJGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYnLUYjNistRiw2KFEieEYnRi9GMi9GNlEldHJ1ZUYnRjgvRjxRJ2l0YWxpY0YnLUkjbW9HRiQ2MFEiLEYnRi9GMkY4RjsvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGRy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0ZDLUZLNjBRIidGJ0YvRjJGOEY7Rk4vRlFGN0ZSRlRGVkZYRlovRmduUSwwLjExMTExMTFlbUYnL0ZqbkZobkZKLUYsNihRJyZiZXRhO0YnRi9GMkY1RjhGO0YvRjJGO0YvRjJGOEY7Ri9GMkY7</Equation><Font size="10" family="P052"> = </Font><Equation executable="true" style="2D Math" input-equation="" display="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">LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYoLUklbXJvd0dGJDYoLUkjbWlHRiQ2I1EhRictRi82J0YxLUkmbWZyYWNHRiQ2KC1GMjYoUSltJm9tZWdhO0YnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYrLUkjbW5HRiQ2J1EiMkYnRj1GQEZGL0ZKUSdub3JtYWxGJy1JI21vR0YkNjBRIn5GJ0Y9RkBGRkZSLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZaLyUpc3RyZXRjaHlHRlovJSpzeW1tZXRyaWNHRlovJShsYXJnZW9wR0ZaLyUubW92YWJsZWxpbWl0c0dGWi8lJ2FjY2VudEdGWi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmNvLUYyNihRLSZwaTsmaHNsYXNoO0YnRj1GQEZDRkZGSUZULUYyNihRJXNpbmhGJ0Y9RkAvRkRGWkZGRlItRiw2Jy1GLzYmLUYyNihRNiZiZXRhOyZoc2xhc2g7Jm9tZWdhO0YnRj1GQEZDRkZGSUY9RkBGUkY9RkBGRkZSRj1GQEZSLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZpcC8lKWJldmVsbGVkR0ZaRj1GQEZSRjFGPUZARlJGPUZARlIvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRi82Ji1GODYoLUZPNiZGZnBGPUZARlItRi82Ji1GTzYmRlFGPUZARlJGPUZARlJGZHBGZ3BGanBGXHFGPUZARlIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font size="10" family="P052">exp</Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" size="10" family="P052" layout="Heading 2"><Font size="12" family="P052">Deriving the energy eigenvalues and eigenstates</Font></Text-field></Title><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">We know that the quantum mechanical propagator or the kernel is related to the density matrix by a Wick rotation. Moreover, a key property of kernels is that they can be expanded in terms of their energy eigenfunctions. Thus, on carrying out a Wick rotation and an expansion, we get,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052">exp</Font><Equation executable="true" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYoLUYjNigtSSNtaUdGJDYjUSFGJy1JJm1mcmFjR0YkNigtRiM2Jy1GMTYnUSlpbSYjOTY5O0YnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjxGP0ZCRkUtRiM2Ky1JI21uR0YkNidRIjJGJ0Y8Rj8vJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0ZGUSdub3JtYWxGJy1JI21vR0YkNjBRIn5GJ0Y8Rj9GTkZRLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZZLyUpc3RyZXRjaHlHRlkvJSpzeW1tZXRyaWNHRlkvJShsYXJnZW9wR0ZZLyUubW92YWJsZWxpbWl0c0dGWS8lJ2FjY2VudEdGWS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmJvLUYxNihRKCYjODQ2MztGJ0Y8Rj8vRkNGWUZORlFGUy1GMTYoUSRzaW5GJ0Y8Rj9GaG9GTkZRLUYsNiYtRiM2Ji1GMTYnUSgmIzk2OTtURidGPEY/RkJGRUY8Rj9GUUY8Rj9GUUY8Rj9GUS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGaHAvJSliZXZlbGxlZEdGWS1GLDYoLUYjNi0tRiw2Ji1GIzYsLUklbXN1cEdGJDYlLUYxNidRInhGJ0Y8Rj9GQkZFLUYjNiYtRks2JkZNRjxGP0ZRRjxGP0ZRLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GVDYvRlZGPEY/RlFGV0ZaRmZuRmhuRmpuRlxvRl5vRmBvRmNvLUZUNi9RIitGJ0Y8Rj9GUUZXRlpGZm5GaG5Gam5GXG9GXm8vRmFvUSwwLjIyMjIyMjJlbUYnL0Zkb0ZockZickZocS1GZnE2JS1GVDYvUSInRidGPEY/RlFGV0ZaRmZuRmhuRmpuRlxvRl5vL0Zhb1EsMC4xMTExMTExZW1GJ0Zjb0ZbckZfckYwRjxGP0ZRRjxGP0ZRLUYxNidRJGNvc0YnRjxGP0Zob0ZRRlxwLUZUNi9RKCZtaW51cztGJ0Y8Rj9GUUZXRlpGZm5GaG5Gam5GXG9GXm9GZ3JGaXJGXXJGYnItRjE2J1EjeHhGJ0Y8Rj9GQkZFRlxzRjxGP0ZRRjxGP0ZRLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRjxGP0ZRRjxGP0ZRRmpzRl10RjxGP0ZR</Equation><Font size="10" family="P052"> = </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Using standard trigonometric identities, the left hand side of the above equation becomes,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Expanding the exponential series and comparing with Eq, </Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">and we get the energy levels as,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Further expansion is required for getting the eigenfunctions,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Comparing term by term to our initial expansion, </Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Thus, </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052">(obtained earlier) and,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" encoding="UTF-8" family="P052">This is the ground state wavefunction for the harmonic oscillator, which can also be readily derived from the Schr\303\266dinger equation. There is an phase factor outside the expression, but since it does not impact the physical implications as such, it has been safely ignored. Similarly, the next two terms can also be derived,</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">In this way, all the energy eigenvalues and eigenstates of the quantum harmonic oscillator can be obtained using the path integral formalism.</Font></Text-field>
</Section><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRicvJSdmYW1pbHlHUSVQMDUyRicvJSVzaXplR1EjMTBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" size="10" family="P052" layout="Heading 2"><Font size="12" family="P052">Numerical implementation (model system: TiO)</Font><Font size="10" family="P052">
<Font style="Text">Maple's quantum chemistry toolbox has been used to plot the PES of the Ti-O bond. Within a specified range, at each point the electronic energy is calculated using Hartree Fock and Density Functional Theory (cc-PVDZ basis in both cases). With more powerful machines, more sophisticated electronic structure methods with larger basis sets can be used. The curves are then fitted using the NonLinearFit option of the Statistics package. The fitting function used is,</Font></Font></Text-field></Title><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Font size="10" family="P052">
</Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">
<Font encoding="UTF-8">Instead of using our system directly, we will take a roundabout approach and treat it using path integrals on the harmonic oscillator, where the force constant of the harmonic oscillator is taken as the fitted 'k' value and the mass is taken as the reduced mass of our model chemical system. The first three wave functions of the HO model, derived from the PIQM formalism have been plotted, as well as the density matrix, as a function of \316\262. The obtained PES plots also show how good an approximation the harmonic oscillator model is near the equilibrium bond length.</Font>
</Font></Text-field>
<Group hide-input="false" labelreference="L14613" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" style="Text" family="P052" italic="true">Loading the packages</Font><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GMDYmRjJGNUY4L0Y7USVhdXRvRidGKy8lJ2ZhbWlseUdRJVAwNTJGJy8lJXNpemVHUSMxMEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GMDYmRjJGNUY4L0Y7USVhdXRvRidGKy8lJ2ZhbWlseUdRJVAwNTJGJy8lJXNpemVHUSMxMEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn</Equation><Font size="10" family="P052">Digits := 15:
with(QuantumChemistry):
with(Statistics):
</Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14608" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" style="Text" family="P052" italic="true">Initialising parameters</Font><Font size="10" family="P052">
n := 200:
rmin := 1.4:
rmax := 1.7:
dr := (rmax-rmin)/(n-1):
xx := rmin:
e_v := []:
r_v := []:
</Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14609" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" style="Text" family="P052" italic="true">Computing energies using HF for different bond lengths</Font><Font size="10" family="P052">
for i from 1 while i < n do
mol := [["Ti", 0, 0, 0],["O", 0, 0, xx]]:
energy := Energy(mol, method = HartreeFock, basis = "cc-pVDZ"):
e_v := [op(e_v),energy]:
r_v := [op(r_v),xx]:
xx := xx + dr:
end do:
</Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14612" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" style="Text" family="P052" italic="true">Plotting and fitting the PES using a HO type function</Font><Font size="10" family="P052">
p_actual := plot(r_v,e_v,axes = boxed, labels = ['R', 'E'], color = red, thickness = 3):
NonlinearFit(0.5*k*(var-c)^2+d,r_v,e_v,var);
p_fitted := plot (1.11625206*(var - 1.56105199)^2 - 923.20485176,var=1.4..1.7,axes = boxed, labels = ['R', 'E'], color = blue, thickness = 3):
plots:-display({p_actual,p_fitted});</Font></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomJCIwbj9ZWV5pNiIhIzkiIiIpLCZJJHZhckdGKEYxJCIwZVRIKj4waDpGMCEiIiIiI0YxRjEkIjA/PnZeWz9CKiEjN0Y3NyMsJiomXTNGRjFEQzJBN0VFQTg2QTNGMSksJkY0RjFdM0ZGOEZBMTFBNzkwQTJBNEY3RjhGMUYxXTQwOENEOUEzODk1MEI4MzFGNw==</Equation></Text-field>
</Output>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" type="two-dimensional" width="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">6,-%'CURVESG6%7cw7$$"#9!""$!0na:YJ<B*!#77$$"0W)oPv],9!#9$!1Pui#fQ<B*!#87$$"0)oPv],.9!#9$!1LpHDcuJ#*!#87$$"0KlIhAXS"!#9$!1#ep,c_<B*!#87$$"0w`2:IgS"!#9$!00\yRf<B*!#77$$"/AW)oPvS"!#8$!10l$*QhwJ#*!#87$$"0kIhAX!49!#9$!1'\ISys<B*!#87$$"03>Qw_0T"!#9$!1#*psL$z<B*!#87$$"0_2:Ig?T"!#9$!1z%>')y&yJ#*!#87$$"0'f>Ryc89!#9$!1-))H\@zJ#*!#87$$"/W)oPv]T"!#8$!1PLN;%)zJ#*!#87$$"0%Gd9He;9!#9$!1#3p.f/=B*!#87$$"0GhAX!4=9!#9$!1i$H>n5=B*!#87$$"0s\**)zf>9!#9$!1#>:;m;=B*!#87$$"0;Qw_06U"!#9$!1)*\+gD#=B*!#87$$"/mKlIhA9!#8$!19\nn$G=B*!#87$$"0/:Ig?TU"!#9$!1#[)>&3M=B*!#87$$"0[.29GcU"!#9$!1Rq98(R=B*!#87$$"0#>Ryc8F9!#9$!/%*3__%=B*!#67$$"0O!3;KkG9!#9$!1E?f-2&=B*!#87$$"/)oPv],V"!#8$!1Y!>_1c=B*!#87$$"0Cd9He;V"!#9$!1O@`S8'=B*!#87$$"0oX"He;L9!#9$!0z!4Hl'=B*!#77$$"07MoOtYV"!#9$!1_?XJ;(=B*!#87$$"0cAX!4=O9!#9$!1%yq"[m(=B*!#87$$".6AW)oP9!#7$!0V*zz:)=B*!#77$$"0W**)zf>R9!#9$!1x"))oU')=B*!#87$$"0)ye<NqS9!#9$!0%\)**="*=B*!#77$$"0Kw_06AW"!#9$!1Eajpe*=B*!#87$$"0wkHf=PW"!#9$!1%3$Qm/!>B*!#87$$"/KlIhAX9!#8$!0.p2)\!>B*!#77$$"0kT$oOtY9!#9$!1=BL8%4>B*!#87$$"03Ig?T#[9!#9$!17'4Yw8>B*!#87$$"0_=Pu[(\9!#9$!1pa8N!=>B*!#87$$"0'pS"Gc7X"!#9$!1kAWDA#>B*!#87$$"/a4>Qw_9!#8$!1b,1Oj#>B*!#87$$"0%Qyc8Fa9!#9$!1-s^n.$>B*!#87$$"0GsW*)ydX"!#9$!1M"R.KM>B*!#87$$"0sg@V'Gd9!#9$!1"y\]>Q>B*!#87$$"0;\)pRze9!#9$!1Y0<#*>%>B*!#87$$"/w`2:Ig9!#8$!1r4A7d%>B*!#87$$"0/E_/4=Y"!#9$!1V$=dN\>B*!#87$$"0[9He;LY"!#9$!1.y<BH&>B*!#87$$"0#Hg?T#[Y"!#9$!1lC6:k&>B*!#87$$"0O"He;Lm9!#9$!1dL.K)f>B*!#87$$"/)zf>RyY"!#8$!1&Q\W<j>B*!#87$$"0CoOtY$p9!#9$!1;u'GWm>B*!#87$$"0oc8Fa3Z"!#9$!1*>#zP'p>B*!#87$$"07X!4=Os9!#9$!1[lsfF(>B*!#87$$"0cLnMpQZ"!#9$!00r"4e(>B*!#77$$".AW)oPv9!#7$!/Wi'yy>B*!#67$$"0W5@U%)oZ"!#9$!0=$e#p")>B*!#77$$"0)))zf>Ry9!#9$!1H?aFX)>B*!#87$$"0K([(\**)z9!#9$!11N*>H()>B*!#87$$"0wv^.29["!#9$!0AGk)**)>B*!#77$$"/U'Gd9H["!#8$!1aYL6E*>B*!#87$$"0k_06AW["!#9$!1"f*>n^*>B*!#87$$"03T#['Hf["!#9$!0W2Xl(*>B*!#77$$"0_Hf=Pu["!#9$!185ut++K#*!#87$$"0'zhBZ%*)["!#9$!1d3QDC+K#*!#87$$"/kIhAX!\"!#8$!1Kd!*4Z+K#*!#87$$"0%[**)zf>\"!#9$!17CzFp+K#*!#87$$"0G$oOtY$\"!#9$!10d^z!4?B*!#87$$"0srV([(\\"!#9$!1F%[b;6?B*!#87$$"0;g?T#['\"!#9$!1e;O'=8?B*!#87$$"/'[(\**)z\"!#8$!1>VUU^,K#*!#87$$"0/Pu[(\*\"!#9$!1,O?Mq,K#*!#87$$"0[D^-05]"!#9$!1TY;i)=?B*!#87$$"0#R"Gc7D]"!#9$!1e2xE1-K#*!#87$$"0O-05?S]"!#9$!17L[GB-K#*!#87$$"/3>Qw_0:!#8$!1x=wnR-K#*!#87$$"0Cze<Nq]"!#9$!19S1Xb-K#*!#87$$"0onNrU&3:!#9$!1Qb%31F?B*!#87$$"07c7D]+^"!#9$!1&Hgb^G?B*!#87$$"0cW*)yd:^"!#9$!1;-m4*H?B*!#87$$".LmKlI^"!#7$!1ibfV7.K#*!#87$$"0W@V'Gd9:!#9$!1HY"y^K?B*!#87$$"0))4?S!3;:!#9$!0xjFtL?B*!#77$$"0K)pRze<:!#9$!1Mw))))[.K#*!#87$$"0w'Qxa4>:!#9$!1/!Hm)f.K#*!#87$$"/_2:Ig?:!#8$!1p(Gk-P?B*!#87$$"0kjFb5@_"!#9$!1#4E(3!Q?B*!#87$$"03_/4=O_"!#9$!1D#eR$*Q?B*!#87$$"0_S"Gc7D:!#9$!1t1c-)R?B*!#87$$"0'*Ge;Lm_"!#9$!1hq'\hS?B*!#87$$"/u^.29G:!#8$!1a#4;PT?B*!#87$$"0%e?T#['H:!#9$!1'G<H2U?B*!#87$$"0G%*)yd:J:!#9$!1)\>$>F/K#*!#87$$"0s#e;LmK:!#9$!1yAC6L/K#*!#87$$"0;rU&3<M:!#9$!1R.6\Q/K#*!#87$$"/'f>Ryc`"!#8$!1*eYLLW?B*!#87$$"0/['Hf=P:!#9$!1E@PkZ/K#*!#87$$"0[OtY$pQ:!#9$!1$R1E9X?B*!#87$$"0#\-05?S:!#9$!1CpYoa/K#*!#87$$"0O8Fa3<a"!#9$!1@&pBuX?B*!#87$$"/=S!3;Ka"!#8$!18$GZ'f/K#*!#87$$"0C!4=OsW:!#9$!1rb&f8Y?B*!#87$$"0oyd:Jia"!#9$!1R>Yci/K#*!#87$$"07nMpQxa"!#9$!0<cmKY?B*!#77$$"0cb6BY#\:!#9$!1:`%pMY?B*!#87$$".W)oPv]:!#7$!1^[t<j/K#*!#87$$"0WKlIhAb"!#9$!0CG%Ri/K#*!#77$$"0)3AW)oPb"!#9$!1*[FC6Y?B*!#87$$"0K4>Qw_b"!#9$!1AF8Pf/K#*!#87$$"0w(f>Ryc:!#9$!1AB%RrX?B*!#87$$"/iGd9He:!#8$!1$4`KWX?B*!#87$$"0ku\**)zf:!#9$!00ga7X?B*!#77$$"03jE`18c"!#9$!10k&4wW?B*!#87$$"0_^.29Gc"!#9$!1&zL,NW?B*!#87$$"0'*R!3;Kk:!#9$!1h@Q$*Q/K#*!#87$$"/%Gd9Hec"!#8$!10'*3"RV?B*!#87$$"0%oT$oOtc"!#9$!1oEkVG/K#*!#87$$"0G06AW)o:!#9$!1xhU^A/K#*!#87$$"0s$ze<Nq:!#9$!1WK#[hT?B*!#87$$"0;#['Hf=d"!#9$!1__@M4/K#*!#87$$"/1<MoOt:!#8$!18?)*4-/K#*!#87$$"0/f=Pu[d"!#9$!1$\,DWR?B*!#87$$"0[Z&4>Qw:!#9$!1x,:K'Q?B*!#87$$"0#fBZ%*)yd"!#9$!1$o-$zx.K#*!#87$$"0OC\)pRz:!#9$!1Y@L%)o.K#*!#87$$"/GhAX!4e"!#8$!1Q*4w%f.K#*!#87$$"0C,.17Ce"!#9$!17d]p\.K#*!#87$$"0o*)zf>Re"!#9$!18vQ]R.K#*!#87$$"07yc8Fae"!#9$!1(y@1*G.K#*!#87$$"0cmLnMpe"!#9$!1nKd!zJ?B*!#87$$".b5@U%)e"!#7$!1;]g]1.K#*!#87$$"0WV([(\**e"!#9$!1\%y5ZH?B*!#87$$"0)=V'Gd9f"!#9$!1MLN_#G?B*!#87$$"0K?T#['Hf"!#9$!1,yy%*p-K#*!#87$$"0w3=OsWf"!#9$!1_$Q()pD?B*!#87$$"/s\**)zff"!#8$!1u)fXOC?B*!#87$$"0k&=Pu[(f"!#9$!1;bg#*H-K#*!#87$$"03u[(\**)f"!#9$!1joA$e@?B*!#87$$"0_iD^-0g"!#9$!1.QxO,-K#*!#87$$"0'4D]+,-;!#9$!1KZf`'=?B*!#87$$"/%Rze<Ng"!#8$!1ki.Mr,K#*!#87$$"0%yiD^-0;!#9$!1mMWyb,K#*!#87$$"0G;LmKlg"!#9$!1r'fr)R,K#*!#87$$"0s/5?S!3;!#9$!1on_gB,K#*!#87$$"0;$pQxa4;!#9$!11\)))p5?B*!#87$$"/;Qw_06;!#8$!11Ed-!4?B*!#87$$"0/qS"Gc7;!#9$!13o#>F2?B*!#87$$"0[e<NqSh"!#9$!1,GG2b+K#*!#87$$"0#pW*)yd:;!#9$!1zU(*3P+K#*!#87$$"0ONrU&3<;!#9$!1"RLt(=+K#*!#87$$"/Q#['Hf=;!#8$!1A0p7++K#*!#87$$"0C7D]+,i"!#9$!1LYP:")*>B*!#87$$"0o+-/3;i"!#9$!1'*Gr&='*>B*!#87$$"07*)yd:Ji"!#9$!1"*4.CU*>B*!#87$$"0cxb6BYi"!#9$!1(*GlIA*>B*!#87$$".mKlIhi"!#7$!1*>,f?!*>B*!#87$$"0Wa4>Qwi"!#9$!1`l4]"))>B*!#87$$"0)GkGd9H;!#9$!1J$eN1')>B*!#87$$"0KJjE`1j"!#9$!10TgYR)>B*!#87$$"0w>S!3;K;!#9$!1>*\&*z")>B*!#87$$"/#3<MoOj"!#8$!1P-rA'z>B*!#87$$"0k'Rze<N;!#9$!1VzR;u(>B*!#87$$"03&3<MoO;!#9$!1-U#4=v>B*!#87$$"0_tZ&4>Q;!#9$!11()f;H(>B*!#87$$"0'>Y#\)pR;!#9$!0fHPiq>B*!#77$$"//:Ig?T;!#8$!1pKi-$o>B*!#87$$"0%)Qyc8Fk"!#9$!1ZYe`f'>B*!#87$$"0GFb5@Uk"!#9$!1/q"pdj>B*!#87$$"0s:KkGdk"!#9$!1H@#H<h>B*!#87$$"0;/4=Osk"!#9$!1d,!>ue>B*!#87$$"/Ef=Pu[;!#8$!0b\TGc>B*!#77$$"0/"Gc7D];!#9$!1=u'**z`>B*!#87$$"0[pRze<l"!#9$!18!\'*G^>B*!#87$$"0#zlJjE`;!#9$!19#)[`([>B*!#87$$"0OY$pQxa;!#9$!1asx">Y>B*!#87$$"/[.29Gc;!#8$!1vn![gV>B*!#87$$"0CBZ%*)yd;!#9$!1Me'G*4%>B*!#87$$"0o6C['Hf;!#9$!1p>Cc$Q>B*!#87$$"07+,-/3m"!#9$!1"4@_pN>B*!#87$$"0c)yd:Ji;!#9$!13v35I$>B*!#87$$".xa4>Qm"!#7$!1cS7,.$>B*!#87$$"0WlJjE`m"!#9$!0%>hov#>B*!#77$$"0)Q&3<Mom"!#9$!1y2$G"[#>B*!#87$$"0KU&3<Mo;!#9$!1='eS.A>B*!#87$$"0wIiC\)p;!#9$!1f?dK#>>B*!#87$$"/#>Ryc8n"!#8$!1(*ek3k">B*!#87$$"0k2;KkGn"!#9$!1xNbiN">B*!#87$$"03'Hf=Pu;!#9$!1jpc%p5>B*!#87$$"0_%)pRzen"!#9$!1ch&\!y!>B*!#87$$"0'HnMpQx;!#9$!1X**)R*[!>B*!#87$$"/9OsW*)y;!#8$!1[`$>'>!>B*!#87$$"0%)\+,-/o"!#9$!1;!e!4!**=B*!#87$$"0GQxa4>o"!#9$!0#>iNg*=B*!#77$$"0sEa3<Mo"!#9$!1W%*)=/$*=B*!#87$$"0;:JiC\o"!#9$!1)[@"G+*=B*!#87$$"/O!3;Kko"!#8$!0YxX*p)=B*!#77$$"0/#\)pRzo"!#9$!1)*\^TR)=B*!#87$$"0[!=OsW*o"!#9$!1//>p3)=B*!#87$$"0#*oQxa4p"!#9$!1'Heyxx=B*!#87$$"0Od:JiCp"!#9$!1==xnY(=B*!#87$$"/eC\)pRp"!#8$!1bD=R:(=B*!#87$$"0CMpQxap"!#9$!1l/M#Ro=B*!#87$$"0oAY#\)pp"!#9$!1FS\F_'=B*!#87$$"076BY#\)p"!#9$!1v,*[/i=B*!#8-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#""$-%'CURVESG6%7dw7$$"#9!""$!1aS+()*e<B*!#87$$"2w`2:Gx:S"!#;$!0GP.jk<B*!#77$$"2yc8dm\HS"!#;$!0j%Q&\p<B*!#77$$"1KkGbI\/9!#:$!1)*eS;\xJ#*!#87$$"1OsWvm/19!#:$!0*=l>.yJ#*!#77$$"18E_6Hf29!#:$!18SrVcyJ#*!#87$$"2B['Hqk-49!#;$!1m!=@`!zJ#*!#87$$"2"f=PP3^59!#;$!1"RHaa&zJ#*!#87$$"1BY#>(f/79!#:$!1U5Yy1!=B*!#87$$"2pS"G$=wNT"!#;$!1t<nUd!=B*!#87$$"2Ou[P>]^T"!#;$!1RSH(*3"=B*!#87$$"2b7DIeOlT"!#;$!1xTn"R:=B*!#87$$"2Y#\)*Gt4=9!#;$!1Zr$**R?=B*!#87$$"2ye<N[k'>9!#;$!1Hp/u`#=B*!#87$$"2B['HFZ<@9!#;$!16Uk:,$=B*!#87$$"2#e;LthaA9!#;$!1)f`tPM=B*!#87$$"2Ge;`&p<C9!#;$!1"z'G!RR=B*!#87$$"1RycT%ebU"!#:$!0'pW!fV=B*!#77$$"2u[(\Qa;F9!#;$!1<RiA%[=B*!#87$$"2oPvI!zeG9!#;$!1Pm"=l_=B*!#87$$"2"He;s&[,V"!#;$!1n@%*Rs&=B*!#87$$"2-.1#)pM;V"!#;$!1^'z$e:'=B*!#87$$"207C[J&=L9!#;$!1"z`;,m=B*!#87$$"2#['H\E4YV"!#;$!1a#pQ0q=B*!#87$$"2rV([(=XhV"!#;$!1*Q)>jV(=B*!#87$$"14=Oz0uP9!#:$!1Mfh$yy=B*!#87$$"2=RyEPH"R9!#;$!1p-M&e#)=B*!#87$$"2w`2vIH1W"!#;$!1s0%Hk')=B*!#87$$"2Qxap))y@W"!#;$!1D14#y!*=B*!#87$$"1`18[[pV9!#:$!16lczZ*=B*!#87$$"1)e<&=;;X9!#:$!1ZT\)f)*=B*!#87$$"2Pxap@!zY9!#;$!0l!\#y->B*!#77$$"1Fa3&e`#[9!#:$!122\"\1>B*!#87$$"2Gd9H/;)\9!#;$!10m'))R5>B*!#87$$"2MnM>'=B^9!#;$!124Y#*Q">B*!#87$$"2BX!4E(zFX"!#;$!1Zbngw">B*!#87$$"2e;Lc9OUX"!#;$!1x-Vd6#>B*!#87$$"2v^.P_edX"!#;$!04E>wC>B*!#77$$"2LmKl#pCd9!#;$!1*[dfBG>B*!#87$$"1%ycj90)e9!#:$!1&[a*>=$>B*!#87$$"1JiC(*eIg9!#:$!1(=D0AN>B*!#87$$"2Z%*)yJ1%=Y"!#;$!1[u4Y'Q>B*!#87$$"2QxazliLY"!#;$!1^4P"*>%>B*!#87$$"1['H>ChZY"!#:$!1>Tt>]%>B*!#87$$"2Z(\*p<kjY"!#;$!1$\uoV[>B*!#87$$"228E7'yzn9!#;$!1_*3YW^>B*!#87$$"1;KknkKp9!#:$!1_`$4ga>B*!#87$$"21:I!R&*yq9!#;$!1vO3tv&>B*!#87$$"2W*)y<49CZ"!#;$!1H6G<3'>B*!#87$$"2BX!4N3#QZ"!#;$!10z"*yN'>B*!#87$$"2#e;L,vTv9!#;$!1B6()fm'>B*!#87$$"1#Qw#*osoZ"!#:$!1=DD=%p>B*!#87$$"2)zf>OWYy9!#;$!0h]8Qs>B*!#77$$"2Z'HfWy$)z9!#;$!1U_a#*[(>B*!#87$$"16AW'*>S"["!#:$!0O87qx>B*!#77$$"2wa4**)G"H["!#;$!1)H'Qi.)>B*!#87$$"2OtYjzAW["!#;$!1-r!4(H)>B*!#87$$"2Fb5"[r#f["!#;$!1F^@>b)>B*!#87$$"2\+,#fBP(["!#;$!1G%e(>z)>B*!#87$$"2kJj1nM*)["!#;$!1@,Oi/*>B*!#87$$"2U%)onmB/\"!#;$!1m#G\$G*>B*!#87$$"2kFb]w!*>\"!#;$!1s\[y_*>B*!#87$$"2$f=Pm$4M\"!#;$!1jJ@Vu*>B*!#87$$"2'f>R'=x\\"!#;$!1E#yLy**>B*!#87$$"2U%)oZ))yk\"!#;$!1J]Rt>+K#*!#87$$"2#\)pz#p(z\"!#;$!1"y>z5/?B*!#87$$"2u\**)R;a*\"!#;$!0oWRG1?B*!#77$$"2Fa3nz#)4]"!#;$!17yyR#3?B*!#87$$"2-17%Q(eC]"!#;$!1W)yZ>5?B*!#87$$"2c8FMN)3/:!#;$!1m#HoH7?B*!#87$$"2&3<MOQc0:!#;$!1WC#*[T,K#*!#87$$"2[(\*Rzsq]"!#;$!1-aw#*f,K#*!#87$$"29Ig]O2'3:!#;$!1>:x:y,K#*!#87$$"2sV([Mz,5:!#;$!1Zh4X%>?B*!#87$$"2`4>eb@:^"!#;$!1m5*H8@?B*!#87$$"1Pu[JP,8:!#:$!/$Q"eF-K#*!#67$$"219Gc*)4Y^"!#;$!1s]^TW-K#*!#87$$"2LoO8W=g^"!#;$!1M$z(ze-K#*!#87$$"1<Mo5Ok<:!#:$!1QJ?%[F?B*!#87$$"1=Os+-6>:!#:$!1BsX"))G?B*!#87$$"2wa4\Jh0_"!#;$!1keq;-.K#*!#87$$"24<M)G<7A:!#;$!0&=2+;.K#*!#77$$"2Qxa\X)oB:!#;$!1&\WV$H.K#*!#87$$"2%=PuVR6D:!#;$!1tFs+T.K#*!#87$$"1)e<&\xiE:!#:$!1Bop*GN?B*!#87$$"+w]5G:!"*$!1kMp+k.K#*!#87$$"2BY#\8lqH:!#;$!1<$*)*\v.K#*!#87$$"2U&3<-A4J:!#;$!1hbC)\Q?B*!#87$$"2\(\*fr$oK:!#;$!1>9YM&R?B*!#87$$"29HeE#)zT`"!#;$!1ZX*pXS?B*!#87$$"19Gcy9mN:!#:$!1^xO@8/K#*!#87$$"2$yc88V9P:!#;$!1<)ft8U?B*!#87$$"2$)oP0rc'Q:!#;$!1lS0>H/K#*!#87$$"1OsWE)f-a"!#:$!1U`)=pV?B*!#87$$"2)oPvE(H<a"!#;$!1JX2]V/K#*!#87$$"2C]+rq!=V:!#;$!1YM[_\/K#*!#87$$"2`067yJZa"!#;$!1,9ZWb/K#*!#87$$"1W)o(y%zia"!#:$!1Mcj"3Y?B*!#87$$"23=O#H'owa"!#;$!0VK#=l/K#*!#77$$"2MqS"yTJ\:!#;$!1D+nzp/K#*!#87$$"2)yd:(4"p]:!#;$!1;YK>t/K#*!#87$$"2\,.'e:I_:!#;$!1W_)GmZ?B*!#87$$"1,-/)eQQb"!#:$!1#pyn$z/K#*!#87$$"1JiCs4@b:!#:$!1LGwO"[?B*!#87$$"2`4>=Oanb"!#;$!0iK9J[?B*!#77$$"2&**)z>)zIe:!#;$!134bL%[?B*!#87$$"2kFb!=U&)f:!#;$!10ce,&[?B*!#87$$"2b9Hox(Gh:!#;$!1:%zp^[?B*!#87$$"2E_/R9sFc"!#;$!1*)3d%[[?B*!#87$$"2lGd%ysIk:!#;$!1_=J*R[?B*!#87$$"2.29)*[Pec"!#;$!1@q'>E[?B*!#87$$"2pS"G+:Tn:!#;$!1Q+:m![?B*!#87$$"2))yd&*)yzo:!#;$!1t.'y%y/K#*!#87$$"2ye<bje.d"!#;$!1RLx]v/K#*!#87$$"27D]+zD>d"!#;$!1R)[x>Z?B*!#87$$"2e9HQ.OMd"!#;$!1X^m0o/K#*!#87$$"2:Kk)zu![d"!#;$!1#R+bSY?B*!#87$$"1Y#\=EQkd"!#:$!1FV,ve/K#*!#87$$"2D]+"[(>yd"!#;$!1^7<z`/K#*!#87$$"22:I]uE%z:!#;$!01!y[Z/K#*!#77$$"2-/3'4#\3e"!#;$!1rVnUT/K#*!#87$$"2C\)py)4Ce"!#;$!1#>6dUV?B*!#87$$"2MpQZ+'*Qe"!#;$!1$o\CpU?B*!#87$$"1%yc8iYae"!#:$!1")e![(=/K#*!#87$$"2:Ji9dqoe"!#;$!1rKnw5/K#*!#87$$"2/5?S\1%)e"!#;$!1)4L];S?B*!#87$$"2AZ%*e)=+!f"!#;$!1j3Li"R?B*!#87$$"2`06#z1R"f"!#;$!1&[8KCQ?B*!#87$$"1,-/91*Gf"!#:$!13a<-s.K#*!#87$$"1Pu[$>SWf"!#:$!16J$R2O?B*!#87$$"2lJjY:cff"!#;$!1=KH=\.K#*!#87$$"27D]]#HU(f"!#;$!0P;8vL?B*!#77$$"2sV([B:0*f"!#;$!1<gJ*RK?B*!#87$$"204=;*[^+;!#;$!1wm(R8J?B*!#87$$"1OsW\t2-;!#:$!19N=I(H?B*!#87$$"2mLn%oJ\.;!#;$!1_#p5TG?B*!#87$$"2b6BE.T]g"!#;$!1HAs<p-K#*!#87$$"1He;_u\1;!#:$!1yuvja-K#*!#87$$"23=O-$)>!3;!#;$!1[\K$*Q-K#*!#87$$"2lKlIB3&4;!#;$!1-!=zIA?B*!#87$$"2sW*)GXm5h"!#;$!1N>:&f??B*!#87$$"2X*)yP?nDh"!#;$!1r-J%*)=?B*!#87$$"13;KQ>59;!#:$!1v:&H5<?B*!#87$$"1Pu[kRi:;!#:$!1UH\u_,K#*!#87$$"2:Ji%[D-<;!#;$!1,Ot[N,K#*!#87$$"2"Qw_$[D'=;!#;$!1xI6<:,K#*!#87$$"2Rzex;f+i"!#;$!1M3T^'4?B*!#87$$"2$ze<uxe@;!#;$!1Zsj6w+K#*!#87$$"19GcX30B;!#:$!1v[X5c+K#*!#87$$"2yb6$)RvYi"!#;$!1PxSKL+K#*!#87$$"2b6B;9#3E;!#;$!1ik=78+K#*!#87$$"2;Kky!)ywi"!#;$!1=!)ol*)*>B*!#87$$"2_/4e*R8H;!#;$!0VOvx'*>B*!#77$$"1V'GFuD2j"!#:$!1;[!*HV*>B*!#87$$"2#Gc7^"*4K;!#;$!1pZbs@*>B*!#87$$"2W([(HIjOj"!#;$!1ZaHk'*)>B*!#87$$"16AW'>u^j"!#:$!1j*y&*=()>B*!#87$$"2oRzG5%oO;!#;$!1)\lbm%)>B*!#87$$"1;Kka%)=Q;!#:$!1@4A+@)>B*!#87$$"2$oOtlOjR;!#;$!0'\9)ez>B*!#77$$"2*zf>xf>T;!#;$!1H^2?o(>B*!#87$$"2u],L(\oU;!#;$!1R#)=JT(>B*!#87$$"2'Rzer?DW;!#;$!1d=!yCr>B*!#87$$"2D_/Hnqck"!#;$!1#zj.fo>B*!#87$$"1BY#H\Qsk"!#:$!1AC8,c'>B*!#87$$"2u],8>S([;!#;$!1Ch^'oi>B*!#87$$"2C^-XBQ-l"!#;$!1#fK)G(f>B*!#87$$"21;Kk%H!=l"!#;$!1,i-'ec>B*!#87$$"117C.TC`;!#:$!1Y:.VO&>B*!#87$$"2PsW\/?Zl"!#;$!1*eU4e]>B*!#87$$"2*)zf*f'\jl"!#;$!1h0aVr%>B*!#87$$"2=PuG9Dyl"!#;$!1%G8,)R%>B*!#87$$"1Qw_+TLf;!#:$!1<rk%pS>B*!#87$$"2['Hfr'o3m"!#;$!1vzF,t$>B*!#87$$"2/5?5CzAm"!#;$!1m'Qd8M>B*!#87$$"2)e<NiGyj;!#;$!1)*QY72$>B*!#87$$"205?!Q]Fl;!#;$!1-![`EF>B*!#87$$"2R!3;-7(om"!#;$!1r)zH_B>B*!#87$$"2nMpyuz#o;!#;$!1,$fK<?>B*!#87$$"2.3;s"\!*p;!#;$!1^DM`i">B*!#87$$"29Gcs]r8n"!#;$!1$>0`m7>B*!#87$$"16AW@E#Gn"!#:$!1N&oy14>B*!#87$$"1MoONIQu;!#:$!1#=8q90>B*!#87$$"2sV([h(\fn"!#;$!1@ygb6!>B*!#87$$"1#Qw-Dvtn"!#:$!1rwSwu*=B*!#87$$"27D]g0*))y;!#;$!1rEf>N*=B*!#87$$"2JmKDQm.o"!#;$!1F@!)3'*)=B*!#87$$"2c7D+#y'>o"!#;$!1"pFWJ&)=B*!#87$$"2u^.(3NN$o"!#;$!1LcR_:)=B*!#87$$"2"Qw_A]%\o"!#;$!1LTnyr(=B*!#87$$"2Z&4>H6W'o"!#;$!1L<e:I(=B*!#87$$"2uZ&4&yAzo"!#;$!135XV)o=B*!#87$$"2;Mo'>cS*o"!#;$!1nD$*=Y'=B*!#87$$"2<Nqq,=4p"!#;$!1f^if-'=B*!#87$$"2&**)zH8@Dp"!#;$!1/33$eb=B*!#87$$"1KkGL5*Rp"!#:$!1ihsW7&=B*!#87$$"2e;LO,Uap"!#;$!1GZ!\"p%=B*!#87$$"2&=Pu(3$*pp"!#;$!1:'>WBU=B*!#87$$"2v],`yS&)p"!#;$!1"\)e5v$=B*!#87$$"#<!""$!1#oVy+L=B*!#8-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""$-%%VIEWG6$;$"#9!""$"#<!""%(DEFAULTG-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"R6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"E6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"-%*AXESSTYLEG6#%$BOXG-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"NiI=</Plot></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L14610" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" style="Text" family="P052" italic="true">Computing energies using DFT for different bond lengths</Font><Font size="10" family="P052">
xx := rmin:
e_v := []:
r_v := []:
for i from 1 while i < n do
mol := [["Ti", 0, 0, 0],["O", 0, 0, xx]]:
energy := Energy(mol, method = DensityFunctional, basis = "cc-pVDZ"):
e_v := [op(e_v),energy]:
r_v := [op(r_v),xx]:
xx := xx + dr:
end do:
</Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14611" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" style="Text" family="P052" italic="true">Plotting and fitting the PES using a HO type function</Font><Font size="10" family="P052">
p_actual := plot(r_v,e_v,axes = boxed, labels = ['R', 'E'], color = red, thickness = 3):
NonlinearFit(0.5*k*(var-c)^2+d,r_v,e_v,var);
p_fitted := plot (1.17555127*(var - 1.58989466)^2 - 924.54665957,var=1.4..1.7,axes = boxed, labels = ['R', 'E'], color = blue, thickness = 3):
plots:-display({p_actual,p_fitted});</Font></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUYjNiYtSSNtbkdGJDYlUSsxLjE3NTU1MTI0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnL0krbXNlbWFudGljc0dGJFExMS4xNzU1NTEyNDE4NTI0M0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjEvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbWlHRiQ2JVEkdmFyRicvJSdpdGFsaWNHUSV0cnVlRicvRjJRJ2l0YWxpY0YnLUY4Ni1RKCZtaW51cztGJ0YxRjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GXm8tRi42JVErMS41ODk4OTQ2N0YnRjEvRjVRMTEuNTg5ODk0NjY2NDQ4MDFGJ0YxRjEtRi42JFEiMkYnRjEvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjFGam4tRi42JVEtOTI0LjU0NjY1OTU3RidGMS9GNVExOTI0LjU0NjY1OTU3NDU1MkYnRjE=">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomJCIwVl89Q15iPCIhIzkiIiIpLCZJJHZhckdGKEYxJCIwLFtrbSUqKSplIkYwISIiIiIjRjFGMSQiMF9YZGZtYUMqISM3Rjc3IywmKiZdM0ZGMkNGMEVEMUE4NzQzMUYxKSwmRjRGMV0zRkY5NzAzNTYzQzdBQTIxRjdGOEYxRjFdNDA4Q0U0NUY4RjBFMTVGQ0Y3</Equation></Text-field>
</Output>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" type="two-dimensional" width="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">6,-%'CURVESG6%7cw7$$"#9!""$!1`+zCc,X#*!#87$$"0W)oPv],9!#9$!1tXsaS-X#*!#87$$"0)oPv],.9!#9$!1z]'GQK]C*!#87$$"0KlIhAXS"!#9$!19\&)41/X#*!#87$$"0w`2:IgS"!#9$!18WLO([]C*!#87$$"/AW)oPvS"!#8$!1E3%Hwc]C*!#87$$"0kIhAX!49!#9$!1e#3.pk]C*!#87$$"03>Qw_0T"!#9$!1Zz1>D2X#*!#87$$"0_2:Ig?T"!#9$!1Z![)\-3X#*!#87$$"0'f>Ryc89!#9$!1vOF$)y3X#*!#87$$"/W)oPv]T"!#8$!19q'*>a4X#*!#87$$"0%Gd9He;9!#9$!0JZ0'G5X#*!#77$$"0GhAX!4=9!#9$!1Z1j0-6X#*!#87$$"0s\**)zf>9!#9$!1f0$eX<^C*!#87$$"0;Qw_06U"!#9$!1.tv6Y7X#*!#87$$"/mKlIhA9!#8$!1&G=SnJ^C*!#87$$"0/:Ig?TU"!#9$!1ez@V'Q^C*!#87$$"0[.29GcU"!#9$!10z&*>b9X#*!#87$$"0#>Ryc8F9!#9$!1ol$[I_^C*!#87$$"0O!3;KkG9!#9$!1b)\%)**e^C*!#87$$"/)oPv],V"!#8$!1o.R,c;X#*!#87$$"0Cd9He;V"!#9$!1&*zC9@<X#*!#87$$"0oX"He;L9!#9$!1)e4w`y^C*!#87$$"07MoOtYV"!#9$!06f?([=X#*!#77$$"0cAX!4=O9!#9$!11w<=6>X#*!#87$$".6AW)oP9!#7$!1)=VlF(>X#*!#87$$"0W**)zf>R9!#9$!1&>JxM._C*!#87$$"0)ye<NqS9!#9$!1bQJK$4_C*!#87$$"0Kw_06AW"!#9$!1*og3B:_C*!#87$$"0wkHf=PW"!#9$!1/#QR/@_C*!#87$$"/KlIhAX9!#8$!1B,6snAX#*!#87$$"0kT$oOtY9!#9$!1%QPfTK_C*!#87$$"03Ig?T#[9!#9$!1([vf(zBX#*!#87$$"0_=Pu[(\9!#9$!1iNy_MCX#*!#87$$"0'pS"Gc7X"!#9$!13B"p%)[_C*!#87$$"/a4>Qw_9!#8$!1s6"*eTDX#*!#87$$"0%Qyc8Fa9!#9$!1$*oK*Qf_C*!#87$$"0GsW*)ydX"!#9$!1DLqQXEX#*!#87$$"0sg@V'Gd9!#9$!1s;e2'p_C*!#87$$"0;\)pRze9!#9$!1(G+lfu_C*!#87$$"/w`2:Ig9!#8$!1_Z*f]z_C*!#87$$"0/E_/4=Y"!#9$!1-zfOVGX#*!#87$$"0[9He;LY"!#9$!1$))R))3*GX#*!#87$$"0#Hg?T#[Y"!#9$!1(4[Kw$HX#*!#87$$"0O"He;Lm9!#9$!1urMg$)HX#*!#87$$"/)zf>RyY"!#8$!1t')o!)GIX#*!#87$$"0CoOtY$p9!#9$!1'*ftCtIX#*!#87$$"0oc8Fa3Z"!#9$!18@.$p6`C*!#87$$"07X!4=Os9!#9$!1*)44')fJX#*!#87$$"0cLnMpQZ"!#9$!1,PU/-KX#*!#87$$".AW)oPv9!#7$!1&4R&[VKX#*!#87$$"0W5@U%)oZ"!#9$!1XI%*=%G`C*!#87$$"0)))zf>Ry9!#9$!13!RhTK`C*!#87$$"0K([(\**)z9!#9$!1.yiSjLX#*!#87$$"0wv^.29["!#9$!1wx!H>S`C*!#87$$"/U'Gd9H["!#8$!1sXZtRMX#*!#87$$"0k_06AW["!#9$!1a9#GoZ`C*!#87$$"03T#['Hf["!#9$!1\!R9K^`C*!#87$$"0_Hf=Pu["!#9$!0f:)*)[NX#*!#77$$"0'zhBZ%*)["!#9$!1knV)Qe`C*!#87$$"/kIhAX!\"!#8$!0u&y<=OX#*!#77$$"0%[**)zf>\"!#9$!1@MMy^OX#*!#87$$"0G$oOtY$\"!#9$!1bxeq%o`C*!#87$$"0srV([(\\"!#9$!0G&*\pr`C*!#77$$"0;g?T#['\"!#9$!1z*Q?&[PX#*!#87$$"/'[(\**)z\"!#8$!1`**=UzPX#*!#87$$"0/Pu[(\*\"!#9$!18p"f'4QX#*!#87$$"0[D^-05]"!#9$!1zfoBRQX#*!#87$$"0#R"Gc7D]"!#9$!0-hf"oQX#*!#77$$"0O-05?S]"!#9$!1*R.Kk*QX#*!#87$$"/3>Qw_0:!#8$!1w@(eS#RX#*!#87$$"0Cze<Nq]"!#9$!1xSU/^RX#*!#87$$"0onNrU&3:!#9$!038$RxRX#*!#77$$"07c7D]+^"!#9$!1r6*4J+aC*!#87$$"0cW*)yd:^"!#9$!1%z2*>GSX#*!#87$$".LmKlI^"!#7$!1***4lE0aC*!#87$$"0W@V'Gd9:!#9$!1ACC^wSX#*!#87$$"0))4?S!3;:!#9$!1euau*4aC*!#87$$"0K)pRze<:!#9$!1p]'oB7aC*!#87$$"0w'Qxa4>:!#9$!1\FjQWTX#*!#87$$"/_2:Ig?:!#8$!1ZdG!e;aC*!#87$$"0kjFb5@_"!#9$!1tpDi'=aC*!#87$$"03_/4=O_"!#9$!1[q(\o?aC*!#87$$"0_S"Gc7D:!#9$!1VT()[EUX#*!#87$$"0'*Ge;Lm_"!#9$!1WSPaXUX#*!#87$$"/u^.29G:!#8$!1o0!>SEaC*!#87$$"0%e?T#['H:!#9$!10Y(=>GaC*!#87$$"0G%*)yd:J:!#9$!16_rC*HaC*!#87$$"0s#e;LmK:!#9$!1")*Q3gJaC*!#87$$"0;rU&3<M:!#9$!1u-m?KVX#*!#87$$"/'f>Ryc`"!#8$!1@6f%yMaC*!#87$$"0/['Hf=P:!#9$!1\6/$HOaC*!#87$$"0[OtY$pQ:!#9$!1%)yTYxVX#*!#87$$"0#\-05?S:!#9$!1xj7X"RaC*!#87$$"0O8Fa3<a"!#9$!1x&p&*[SaC*!#87$$"/=S!3;Ka"!#8$!1W![,yTaC*!#87$$"0C!4=OsW:!#9$!1i+E<IWX#*!#87$$"0oyd:Jia"!#9$!1)y,8?WaC*!#87$$"07nMpQxa"!#9$!0*pmK`WX#*!#77$$"0cb6BY#\:!#9$!1bsu6kWX#*!#87$$".W)oPv]:!#7$!0&>$*QuWX#*!#77$$"0WKlIhAb"!#9$!1=#3YT[aC*!#87$$"0)3AW)oPb"!#9$!1L6;R$\aC*!#87$$"0K4>Qw_b"!#9$!1\L(H@]aC*!#87$$"0w(f>Ryc:!#9$!1haUO5XX#*!#87$$"/iGd9He:!#8$!1vg*)4=XX#*!#87$$"0ku\**)zf:!#9$!1<9wLDXX#*!#87$$"03jE`18c"!#9$!1OdR3KXX#*!#87$$"0_^.29Gc"!#9$!1$=rT$QXX#*!#87$$"0'*R!3;Kk:!#9$!1ixX6WXX#*!#87$$"/%Gd9Hec"!#8$!1@MiS\XX#*!#87$$"0%oT$oOtc"!#9$!0;M?UbaC*!#77$$"0G06AW)o:!#9$!1HQ0ceXX#*!#87$$"0s$ze<Nq:!#9$!1^U/ViXX#*!#87$$"0;#['Hf=d"!#9$!1.^O$ecaC*!#87$$"/1<MoOt:!#8$!1%out(oXX#*!#87$$"0/f=Pu[d"!#9$!1_'Ga7daC*!#87$$"0[Z&4>Qw:!#9$!1X4)yKdaC*!#87$$"0#fBZ%*)yd"!#9$!0Z$3&[daC*!#77$$"0OC\)pRz:!#9$!16jQ(fdaC*!#87$$"/GhAX!4e"!#8$!1^u8lwXX#*!#87$$"0C,.17Ce"!#9$!1AJo)odaC*!#87$$"0o*)zf>Re"!#9$!1ytOowXX#*!#87$$"07yc8Fae"!#9$!1_D`/wXX#*!#87$$"0cmLnMpe"!#9$!0(*=v\daC*!#77$$".b5@U%)e"!#7$!1M]mZtXX#*!#87$$"0WV([(\**e"!#9$!1LsIbrXX#*!#87$$"0)=V'Gd9f"!#9$!1B,y?pXX#*!#87$$"0K?T#['Hf"!#9$!1cjTWmXX#*!#87$$"0w3=OsWf"!#9$!16naEjXX#*!#87$$"/s\**)zff"!#8$!1N**\nfXX#*!#87$$"0k&=Pu[(f"!#9$!1#)HgnbXX#*!#87$$"03u[(\**)f"!#9$!1$)3=F^XX#*!#87$$"0_iD^-0g"!#9$!1&oclkaaC*!#87$$"0'4D]+,-;!#9$!13<0ETXX#*!#87$$"/%Rze<Ng"!#8$!1J3)fc`aC*!#87$$"0%yiD^-0;!#9$!1**HnmHXX#*!#87$$"0G;LmKlg"!#9$!1aWVGBXX#*!#87$$"0s/5?S!3;!#9$!19!z:l^aC*!#87$$"0;$pQxa4;!#9$!0eAk$4XX#*!#77$$"/;Qw_06;!#8$!19JF$=]aC*!#87$$"0/qS"Gc7;!#9$!0"eV#R\aC*!#77$$"0[e<NqSh"!#9$!1'3AUc[aC*!#87$$"0#pW*)yd:;!#9$!1&3J*)pZaC*!#87$$"0ONrU&3<;!#9$!1Px'ozYaC*!#87$$"/Q#['Hf=;!#8$!1z%=$eeWX#*!#87$$"0C7D]+,i"!#9$!1Bki$)[WX#*!#87$$"0o+-/3;i"!#9$!1Y@+tQWX#*!#87$$"07*)yd:Ji"!#9$!1GY(o#GWX#*!#87$$"0cxb6BYi"!#9$!1B*>auTaC*!#87$$".mKlIhi"!#7$!1LR'*G1WX#*!#87$$"0Wa4>Qwi"!#9$!1l*3yZRaC*!#87$$"0)GkGd9H;!#9$!1(RGAHQaC*!#87$$"0KJjE`1j"!#9$!1uL^sqVX#*!#87$$"0w>S!3;K;!#9$!1#pZ*=eVX#*!#87$$"/#3<MoOj"!#8$!1FO"=`MaC*!#87$$"0k'Rze<N;!#9$!1p9R6KVX#*!#87$$"03&3<MoO;!#9$!1:)fz&=VX#*!#87$$"0_tZ&4>Q;!#9$!1)e&zr/VX#*!#87$$"0'>Y#\)pR;!#9$!1"ztJ0HaC*!#87$$"//:Ig?T;!#8$!1)*zO-wUX#*!#87$$"0%)Qyc8Fk"!#9$!1'p\'>hUX#*!#87$$"0GFb5@Uk"!#9$!1d!*G0YUX#*!#87$$"0s:KkGdk"!#9$!1xVbfIUX#*!#87$$"0;/4=Osk"!#9$!1zBr#[@aC*!#87$$"/Ef=Pu[;!#8$!1Av-v)>aC*!#87$$"0/"Gc7D];!#9$!1zdwO#=aC*!#87$$"0[pRze<l"!#9$!1"p&=olTX#*!#87$$"0#zlJjE`;!#9$!0#)[&p[TX#*!#77$$"0OY$pQxa;!#9$!1')Q6TJTX#*!#87$$"/[.29Gc;!#8$!1&)z8$Q6aC*!#87$$"0CBZ%*)yd;!#9$!1im(ef4aC*!#87$$"0o6C['Hf;!#9$!1ORezxSX#*!#87$$"07+,-/3m"!#9$!1mB^MfSX#*!#87$$"0c)yd:Ji;!#9$!1tG"41/aC*!#87$$".xa4>Qm"!#7$!1'zN!f@SX#*!#87$$"0WlJjE`m"!#9$!1<x7H-SX#*!#87$$"0)Q&3<Mom"!#9$!1eaVr#)RX#*!#87$$"0KU&3<Mo;!#9$!1dU?'G'RX#*!#87$$"0wIiC\)p;!#9$!1uuntURX#*!#87$$"/#>Ryc8n"!#8$!1oq4MARX#*!#87$$"0k2;KkGn"!#9$!1LNqn,RX#*!#87$$"03'Hf=Pu;!#9$!1rdtu!)QX#*!#87$$"0_%)pRzen"!#9$!128VbfQX#*!#87$$"0'HnMpQx;!#9$!1<h-5QQX#*!#87$$"/9OsW*)y;!#8$!1fYvQ;QX#*!#87$$"0%)\+,-/o"!#9$!14*\=Wz`C*!#87$$"0GQxa4>o"!#9$!1dMa>sPX#*!#87$$"0sEa3<Mo"!#9$!1%=l?(\PX#*!#87$$"0;:JiC\o"!#9$!1ROk*ps`C*!#87$$"/O!3;Kko"!#8$!0*e]-/PX#*!#77$$"0/#\)pRzo"!#9$!1Qu(33o`C*!#87$$"0[!=OsW*o"!#9$!1)G#)\tl`C*!#87$$"0#*oQxa4p"!#9$!1hI/lLOX#*!#87$$"0Od:JiCp"!#9$!1O2Gr4OX#*!#87$$"/eC\)pRp"!#8$!1[\"Rbe`C*!#87$$"0CMpQxap"!#9$!1QQ;8hNX#*!#87$$"0oAY#\)pp"!#9$!1PRC\ONX#*!#87$$"076BY#\)p"!#9$!1%[qB;^`C*!#8-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#""$-%'CURVESG6%7dw7$$"#9!""$!1a[7#pU]C*!#87$$"2w`2:Gx:S"!#;$!1v*Q[q\]C*!#87$$"2yc8dm\HS"!#;$!1To(*ed0X#*!#87$$"1KkGbI\/9!#:$!1$>'e9D1X#*!#87$$"1OsWvm/19!#:$!1dNTe#p]C*!#87$$"18E_6Hf29!#:$!1FK%Q"f2X#*!#87$$"2B['Hqk-49!#;$!1KB1M?3X#*!#87$$"2"f=PP3^59!#;$!1$Qy-K)3X#*!#87$$"1BY#>(f/79!#:$!1,7+nZ4X#*!#87$$"2pS"G$=wNT"!#;$!1r&3z8,^C*!#87$$"2Ou[P>]^T"!#;$!1O:tLw5X#*!#87$$"2b7DIeOlT"!#;$!1&=3qI8^C*!#87$$"2Y#\)*Gt4=9!#;$!1,=qR'>^C*!#87$$"2ye<N[k'>9!#;$!1xOxSf7X#*!#87$$"2B['HFZ<@9!#;$!1:))Qe>8X#*!#87$$"2#e;LthaA9!#;$!126]wt8X#*!#87$$"2Ge;`&p<C9!#;$!1DfghP9X#*!#87$$"1RycT%ebU"!#:$!1oxq@"\^C*!#87$$"2u[(\Qa;F9!#;$!14[K+`:X#*!#87$$"2oPvI!zeG9!#;$!1m(*y=2;X#*!#87$$"2"He;s&[,V"!#;$!1YY(*3m;X#*!#87$$"2-.1#)pM;V"!#;$!0_&fk@<X#*!#77$$"207C[J&=L9!#;$!1V%[f!z<X#*!#87$$"2#['H\E4YV"!#;$!1D1^GJ=X#*!#87$$"2rV([(=XhV"!#;$!1MtI3()=X#*!#87$$"14=Oz0uP9!#:$!1O7UXW>X#*!#87$$"2=RyEPH"R9!#;$!18g(3R*>X#*!#87$$"2w`2vIH1W"!#;$!1\r;"o/_C*!#87$$"2Qxap))y@W"!#;$!1*G0545_C*!#87$$"1`18[[pV9!#:$!1(yX)G`@X#*!#87$$"1)e<&=;;X9!#:$!1NcHX.AX#*!#87$$"2Pxap@!zY9!#;$!1Uq%f&eAX#*!#87$$"1Fa3&e`#[9!#:$!1KCKa2BX#*!#87$$"2Gd9H/;)\9!#;$!1io!)GfBX#*!#87$$"2MnM>'=B^9!#;$!1`$*3o0CX#*!#87$$"2BX!4E(zFX"!#;$!1=N7'eX_C*!#87$$"2e;Lc9OUX"!#;$!1(QmiD]_C*!#87$$"2v^.P_edX"!#;$!1m<g%3b_C*!#87$$"2LmKl#pCd9!#;$!1#p-Dvf_C*!#87$$"1%ycj90)e9!#:$!1C`b$ek_C*!#87$$"1JiC(*eIg9!#:$!1QlY#=p_C*!#87$$"2Z%*)yJ1%=Y"!#;$!1-DvIQFX#*!#87$$"2QxazliLY"!#;$!1Vh&eQy_C*!#87$$"1['H>ChZY"!#:$!1b`]BDGX#*!#87$$"2Z(\*p<kjY"!#;$!0pf"4sGX#*!#77$$"228E7'yzn9!#;$!1Nl))[8HX#*!#87$$"1;KknkKp9!#:$!1[xY4dHX#*!#87$$"21:I!R&*yq9!#;$!1RgkJ)*HX#*!#87$$"2W*)y<49CZ"!#;$!0_H)\VIX#*!#77$$"2BX!4N3#QZ"!#;$!1=f67#3`C*!#87$$"2#e;L,vTv9!#;$!0ks%RDJX#*!#77$$"1#Qw#*osoZ"!#:$!0.#=JkJX#*!#77$$"2)zf>OWYy9!#;$!1co3J1KX#*!#87$$"2Z'HfWy$)z9!#;$!0l@q?C`C*!#77$$"16AW'*>S"["!#:$!1b)zbAG`C*!#87$$"2wa4**)G"H["!#;$!10=p_?LX#*!#87$$"2OtYjzAW["!#;$!0B&oBeLX#*!#77$$"2Fb5"[r#f["!#;$!1B/]F&R`C*!#87$$"2\+,#fBP(["!#;$!1(f'fNIMX#*!#87$$"2kJj1nM*)["!#;$!1#*fqsnMX#*!#87$$"2U%)onmB/\"!#;$!1*RK5G]`C*!#87$$"2kFb]w!*>\"!#;$!1O73<RNX#*!#87$$"2$f=Pm$4M\"!#;$!1R.zerNX#*!#87$$"2'f>R'=x\\"!#;$!1HWW'og`C*!#87$$"2U%)oZ))yk\"!#;$!10a86SOX#*!#87$$"2#\)pz#p(z\"!#;$!1Wx!\Fn`C*!#87$$"2u\**)R;a*\"!#;$!0J%fF1PX#*!#77$$"2Fa3nz#)4]"!#;$!1(*phkOPX#*!#87$$"2-17%Q(eC]"!#;$!1u1LCnPX#*!#87$$"2c8FMN)3/:!#;$!06DJ/!QX#*!#77$$"2&3<MOQc0:!#;$!1EN;%*HQX#*!#87$$"2[(\*Rzsq]"!#;$!1cL@ffQX#*!#87$$"29Ig]O2'3:!#;$!10%)o>*)QX#*!#87$$"2sV([Mz,5:!#;$!1W[5#f"RX#*!#87$$"2`4>eb@:^"!#;$!0Y.$*Q%RX#*!#77$$"1Pu[JP,8:!#:$!1u%fE6(RX#*!#87$$"219Gc*)4Y^"!#;$!07by'**RX#*!#77$$"2LoO8W=g^"!#;$!1u!*oPCSX#*!#87$$"1<Mo5Ok<:!#:$!1HlSH_SX#*!#87$$"1=Os+-6>:!#:$!1nFT&p2aC*!#87$$"2wa4\Jh0_"!#;$!1<^i&35aC*!#87$$"24<M)G<7A:!#;$!1%RH1g7aC*!#87$$"2Qxa\X)oB:!#;$!1_F@o]TX#*!#87$$"2%=PuVR6D:!#;$!1Um?jsTX#*!#87$$"1)e<&\xiE:!#:$!1^i)=a>aC*!#87$$"+w]5G:!"*$!1a'3Pr@aC*!#87$$"2BY#\8lqH:!#;$!11r-5SUX#*!#87$$"2U&3<-A4J:!#;$!1yAK[fUX#*!#87$$"2\(\*fr$oK:!#;$!1'3C)="GaC*!#87$$"29HeE#)zT`"!#;$!1kj!\5IaC*!#87$$"19Gcy9mN:!#:$!1.(R*>?VX#*!#87$$"2$yc88V9P:!#;$!135#[)QVX#*!#87$$"2$)oP0rc'Q:!#;$!1V'HOtNaC*!#87$$"1OsWE)f-a"!#:$!1uDiMwVX#*!#87$$"2)oPvE(H<a"!#;$!1npaC$RaC*!#87$$"2C]+rq!=V:!#;$!1Dy*G%4WX#*!#87$$"2`067yJZa"!#;$!1%y\"=EWX#*!#87$$"1W)o(y%zia"!#:$!1")ePLUWX#*!#87$$"23=O#H'owa"!#;$!1yz<NcWX#*!#87$$"2MqS"yTJ\:!#;$!1.'4qBZaC*!#87$$"2)yd:(4"p]:!#;$!1%=D%G&[aC*!#87$$"2\,.'e:I_:!#;$!1rUK#)*\aC*!#87$$"1,-/)eQQb"!#:$!1Z%fIJ^aC*!#87$$"1JiCs4@b:!#:$!1Z'4VX_aC*!#87$$"2`4>=Oanb"!#;$!1%*H'[o`aC*!#87$$"2&**)z>)zIe:!#;$!1&p5q'[XX#*!#87$$"2kFb!=U&)f:!#;$!1'R%>()fXX#*!#87$$"2b9Hox(Gh:!#;$!1E>`vpXX#*!#87$$"2E_/R9sFc"!#;$!1b=)z%zXX#*!#87$$"2lGd%ysIk:!#;$!0:+#**)eaC*!#77$$"2.29)*[Pec"!#;$!0:FAzfaC*!#77$$"2pS"G+:Tn:!#;$!1QoP`1YX#*!#87$$"2))yd&*)yzo:!#;$!1&>IOOhaC*!#87$$"2ye<bje.d"!#;$!1w]84@YX#*!#87$$"27D]+zD>d"!#;$!1#ow+!GYX#*!#87$$"2e9HQ.OMd"!#;$!1t<H6MYX#*!#87$$"2:Kk)zu![d"!#;$!0)[()>RYX#*!#77$$"1Y#\=EQkd"!#:$!1QY2nWYX#*!#87$$"2D]+"[(>yd"!#;$!1N^q")[YX#*!#87$$"22:I]uE%z:!#;$!1>Lc2`YX#*!#87$$"2-/3'4#\3e"!#;$!1>>'QjlaC*!#87$$"2C\)py)4Ce"!#;$!1UK8PfYX#*!#87$$"2MpQZ+'*Qe"!#;$!1=7pshYX#*!#87$$"1%yc8iYae"!#:$!1>m6jjYX#*!#87$$"2:Ji9dqoe"!#;$!1EX>)[maC*!#87$$"2/5?S\1%)e"!#;$!1&zl'plYX#*!#87$$"2AZ%*e)=+!f"!#;$!1U[c&fmaC*!#87$$"2`06#z1R"f"!#;$!1)H!RplYX#*!#87$$"1,-/91*Gf"!#:$!1mb=!\maC*!#87$$"1Pu[$>SWf"!#:$!1p!4GNmaC*!#87$$"2lJjY:cff"!#;$!1sAyjhYX#*!#87$$"27D]]#HU(f"!#;$!1n*e%HfYX#*!#87$$"2sV([B:0*f"!#;$!0-A+hlaC*!#77$$"204=;*[^+;!#;$!0s.)p_YX#*!#77$$"1OsW\t2-;!#:$!1J7(4&[YX#*!#87$$"2mLn%oJ\.;!#;$!1js(=UkaC*!#87$$"2b6BE.T]g"!#;$!1Cs$))*QYX#*!#87$$"1He;_u\1;!#:$!1%4h_NjaC*!#87$$"23=O-$)>!3;!#;$!1ayvLFYX#*!#87$$"2lKlIB3&4;!#;$!1*QXM2iaC*!#87$$"2sW*)GXm5h"!#;$!1&R_jKhaC*!#87$$"2X*)yP?nDh"!#;$!1"RYGbgaC*!#87$$"13;KQ>59;!#:$!1'zfqqfaC*!#87$$"1Pu[kRi:;!#:$!1sXe8)eaC*!#87$$"2:Ji%[D-<;!#;$!1vcbWzXX#*!#87$$"2"Qw_$[D'=;!#;$!1%*=*>*oXX#*!#87$$"2Rzex;f+i"!#;$!1\!)Q**eXX#*!#87$$"2$ze<uxe@;!#;$!1'GMyyaaC*!#87$$"19GcX30B;!#:$!1w6[sOXX#*!#87$$"2yb6$)RvYi"!#;$!1P"f]P_aC*!#87$$"2b6B;9#3E;!#;$!1v%e9?^aC*!#87$$"2;Kky!)ywi"!#;$!1Q$QI")\aC*!#87$$"2_/4e*R8H;!#;$!1FwV&\[aC*!#87$$"1V'GFuD2j"!#:$!0)e<(*pWX#*!#77$$"2#Gc7^"*4K;!#;$!1(ecllXaC*!#87$$"2W([(HIjOj"!#;$!1&eLd2WaC*!#87$$"16AW'>u^j"!#:$!1@(>T\UaC*!#87$$"2oRzG5%oO;!#;$!1A2#*f3WX#*!#87$$"1;Kka%)=Q;!#:$!1>#G%y"RaC*!#87$$"2$oOtlOjR;!#;$!1G'HH^PaC*!#87$$"2*zf>xf>T;!#;$!1rgCdcVX#*!#87$$"2u],L(\oU;!#;$!1m_BNQVX#*!#87$$"2'Rzer?DW;!#;$!1$=b8'=VX#*!#87$$"2D_/Hnqck"!#;$!13xsC+VX#*!#87$$"1BY#H\Qsk"!#:$!1/#p)RzUX#*!#87$$"2u],8>S([;!#;$!08^())eUX#*!#77$$"2C^-XBQ-l"!#;$!1(G*z*yBaC*!#87$$"21;Kk%H!=l"!#;$!1i'*4T:UX#*!#87$$"117C.TC`;!#:$!0=T!>%>aC*!#77$$"2PsW\/?Zl"!#;$!1Z+:&><aC*!#87$$"2*)zf*f'\jl"!#;$!1jp@!o9aC*!#87$$"2=PuG9Dyl"!#;$!0&HH\BTX#*!#77$$"1Qw_+TLf;!#:$!0$oa7*4aC*!#77$$"2['Hfr'o3m"!#;$!0aM&ztSX#*!#77$$"2/5?5CzAm"!#;$!1:rO-]SX#*!#87$$"2)e<NiGyj;!#;$!0&G(oT-aC*!#77$$"205?!Q]Fl;!#;$!1"R4&)z*RX#*!#87$$"2R!3;-7(om"!#;$!12csRpRX#*!#87$$"2nMpyuz#o;!#;$!1V-AnVRX#*!#87$$"2.3;s"\!*p;!#;$!0([7T8RX#*!#77$$"29Gcs]r8n"!#;$!1jN+d&)QX#*!#87$$"16AW@E#Gn"!#:$!1M"*[_dQX#*!#87$$"1MoONIQu;!#:$!1,L\"o#QX#*!#87$$"2sV([h(\fn"!#;$!1E+[S&z`C*!#87$$"1#Qw-Dvtn"!#:$!1J9[KmPX#*!#87$$"27D]g0*))y;!#;$!1%p4?\t`C*!#87$$"2JmKDQm.o"!#;$!1G+Fv.PX#*!#87$$"2c7D+#y'>o"!#;$!1/9tQpOX#*!#87$$"2u^.(3NN$o"!#;$!1*H6l"ROX#*!#87$$"2"Qw_A]%\o"!#;$!1t4o*Qg`C*!#87$$"2Z&4>H6W'o"!#;$!1E:(*>qNX#*!#87$$"2uZ&4&yAzo"!#;$!1YU%4j``C*!#87$$"2;Mo'>cS*o"!#;$!17ba(=]`C*!#87$$"2<Nqq,=4p"!#;$!1<XCAmMX#*!#87$$"2&**)zH8@Dp"!#;$!1V>P%yU`C*!#87$$"1KkGL5*Rp"!#:$!1O'=B@R`C*!#87$$"2e;LO,Uap"!#;$!1N=UOcLX#*!#87$$"2&=Pu(3$*pp"!#;$!1K&3"f<LX#*!#87$$"2v],`yS&)p"!#;$!1;o&Q$yKX#*!#87$$"#<!""$!1HUV"3C`C*!#8-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""$-%%VIEWG6$;$"#9!""$"#<!""%(DEFAULTG-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"R6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"E6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"-%*AXESSTYLEG6#%$BOXG-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"Ig==</Plot></Text-field>
</Output>
</Group><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field>
</Section><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field>
<Group hide-input="false" labelreference="L14594" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">mTi := 47.876:
mO := 15.999:
m := (mTi*mO)/(mTi + mO):
khf := 2.2325:
kdft := 2.3511:
omegahf := sqrt(khf/m):
omegadft := sqrt(kdft/m):
<Font style="Text" encoding="UTF-8" italic="true">All are atomic units (and \342\204\217 = 1, hence ignored)</Font><Font italic="true">
</Font>
<Font style="Text" italic="true">Plotting the HO wave functions using the DFT-fitted k values</Font></Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14593" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">phi0dft := (m*omegadft/Pi)^(1/4)*exp(-(m*omegadft/2)*x^2):
phi1dft := sqrt(2*m*omegadft)*x*phi0dft:
phi2dft := (2*m*omegadft*x^2 - 1)*phi0dft/sqrt(2):
p0dft := plot(phi0dft(x), x = -5.0 .. 5.0, axes = boxed, labels = ['x', 'phi(x)'], color = red, thickness = 3):
p1dft := plot(phi1dft(x), x = -5.0 .. 5.0, axes = boxed, labels = ['x', 'phi(x)'], color = blue, thickness = 3):
p2dft := plot(phi2dft(x), x = -5.0 .. 5.0, axes = boxed, labels = ['x', 'phi(x)'], color = green, thickness = 3):
plots:-display({p0dft,p1dft,p2dft});</Font></Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" type="two-dimensional" width="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">6--%'CURVESG6%7\y7$$!#]!""$!0`%4!3[&zF!#U7$$!0u[(\RUZ\!#9$!0Kq:&3b-6!#T7$$!0uZ&4yn,\!#9$!0"H-QB#Hh$!#T7$$!0E_/\J-&[!#9$!/%pC]oVN"!#R7$$!0ze<:W%)z%!#9$!0MTwR-!\]!#S7$$!0BY#\H!pu%!#9$!0)e&)fy-W=!#R7$$!0#Rycw6*p%!#9$!0Mzu=Y30'!#R7$$!0OrUvQ'\Y!#9$!0^!z6[OW?!#Q7$$!0c7Dgn%)f%!#9$!0Bt$\EA-r!#Q7$$!0V'Gd0YZX!#9$!0mr8$QWBC!#P7$$!0a3<a$*\\%!#9$!/%y!eSNT%)!#O7$$!0:Hec!y[W!#9$!00>1<9J]#!#O7$$!0^-0qbnR%!#9$!/;BAK+%R)!#N7$$!//3;s^WV!#8$!0pa[,")yy#!#N7$$!0#Rycd<%H%!#9$!/)f-a#[U()!#M7$$!0sW*))3Y[U!#9$!/7g:tGRC!#L7$$!0CZ%*[,T>%!#9$!0s"p1$pO9)!#M7$$!0pQx%>0[T!#9$!0kZ\/LLB#!#L7$$!04<MQ&[%4%!#9$!0%[)fHs%=r!#L7$$!0W([(*)pq/%!#9$!0dI;rv2'>!#K7$$!0OsWfZ]*R!#9$!0p3E*)fu(e!#K7$$!.*zf+^XR!#7$!0@L"=3M\;!#J7$$!0)f>RG#Q*Q!#9$!0&GV'e%ysZ!#J7$$!0Ryc$yNYQ!#9$!0C4d5&Q]7!#I7$$!0V&3</;&z$!#9$!0D_[$o%e[$!#I7$$!/(Rzo!)>u$!#8$!0o2JM.;'**!#I7$$!0%pQxvo&p$!#9$!0O^tIMUX#!#H7$$!0u[(\(*oXO!#9$!0&o:x.C:k!#H7$$!0a2:5PSf$!#9$!0ur;v'z1<!#G7$$!0c6B10Na$!#9$!0/0q_,UQ%!#G7$$!//3;Fh%\$!#8$!0m)GyF*z2"!#F7$$!0a2:5E.W$!#9$!0&p[sHJ$)G!#F7$$!/">Q;Z:R$!#8$!0Hv'pTS&)o!#F7$$!0"4=O_YRL!#9$!0"3G;$G&><!#E7$$!0AW)o7F#H$!#9$!0O#GeaF"*Q!#E7$$!0$\)pzv1C$!#9$!0mf<!Q"HP*!#E7$$!0Z%*)y%G@>$!#9$!0fId#)=a6#!#D7$$!03;Ka#QTJ!#9$!0#\^o7l')[!#D7$$!0*yd:"p<4$!#9$!0h[-c-J4"!#C7$$!0(Qxa%G)RI!#9$!0%[W9DG.D!#C7$$!0jD^U.)*)H!#9$!0()[LScQ[&!#C7$$!0=NqgX'QH!#9$!0e_d89e?"!#B7$$!0a2:S6z)G!#9$!0%RL@:Z(f#!#B7$$!0Ryc$>HTG!#9$!0o@6"pE$>&!#B7$$!0<Mowgyy#!#9$!0z;nPlB8"!#A7$$!0JiCHr+u#!#9$!0fZ&oGEWA!#A7$$!08E_u<"*o#!#9$!0Kc<%>v!f%!#A7$$!0)\**)p[.k#!#9$!0r4;K6q)*)!#A7$$!0_.2%p>'e#!#9$!0=$\Ah9m=!#@7$$!0$\)p\0$RD!#9$!0mQunx#oM!#@7$$!0tW*)G$3'[#!#9$!0P'>80:2p!#@7$$!/17CqdPC!#8$!0ktZ1lnF"!#?7$$!0MnMz=XQ#!#9$!0OE'*e!\jC!#?7$$!0%yc8&Q(QB!#9$!0u!))RX!**G%!#?7$$!0(Hf=,g'G#!#9$!0&ee9MIcz!#?7$$!03:I+PiB#!#9$!0))yd1RXU"!#>7$$!0@U%)y1f=#!#9$!0#4<A9D9D!#>7$$!0C['H<wN@!#9$!06W#>,9nV!#>7$$!0<Lm-)e(3#!#9$!0\<ai!4Et!#>7$$!0X*)y(4^N?!#9$!0M-4n*>j7!#=7$$!0'=Pux(e)>!#9$!0sMEb^N4#!#=7$$!07C[;TO$>!#9$!0[W(*f]0^$!#=7$$!0OrUXaj)=!#9$!0xxn:k@`&!#=7$$!0oMpy$4M=!#9$!076Qz9J,*!#=7$$!0'=Pur.%y"!#9$!030\r3!=9!#<7$$!0.05S-Tt"!#9$!0a#erZQ(>#!#<7$$!0U$oO`%>o"!#9$!0**y-H#Q?M!#<7$$!0">Qwn!Rj"!#9$!0P2ybg;2&!#<7$$!0*zf>(3Ze"!#9$!00r&paW*[(!#<7$$!0[&4>#)QI:!#9$!0D3IwdM8"!#;7$$!0Qw_X07["!#9$!0h<;:[bi"!#;7$$!0<Mo'o!4V"!#9$!0ZS3jknJ#!#;7$$!0&**)z\a(z8!#9$!0znXa8AF$!#;7$$!0V&3<btK8!#9$!0">K#35WV%!#;7$$!0:Ig![h#G"!#9$!0,n@rQS/'!#;7$$!0V&3<c(GB"!#9$!0a"pUyj)4)!#;7$$!0lGd9q'z6!#9$!0AFMJl&*3"!#:7$$!0c5@i=F8"!#9$!0%R+\Mr&R"!#:7$$!0x_0JY&y5!#9$!0<Z0`Wl#=!#:7$$!/%ze(*f'H5!#8$!0TBtbPDH#!#:7$$!/3:I]*G")*!#9$!0w])*p3'GG!#:7$$!/kFbqv#H*!#9$!0E5;<"R([$!#:7$$!/a2:]^q()!#9$!0#4"**eI"GU!#:7$$!/sU&3_`H)!#9$!0<g&oSqf\!#:7$$!./3;]2z(!#8$!0:qK")o"yd!#:7$$!(3$)H(!"($!0dy5]fLf'!#:7$$!/E^-b\kn!#9$!0())fht*)eu!#:7$$!/>Qw#*f-j!#9$!09t@wlt:)!#:7$$!/<MoY4sd!#9$!0&oS%omc&))!#:7$$!/iBZCRt_!#9$!0@B>2:YO*!#:7$$!1^C['z\k-&!#;$!19W"yY\'\&*!#;7$$!/(Gd92&zZ!#9$!0.KG:IMo*!#:7$$!-*zfPfl%!#7$!1FLSnOjH(*!#;7$$!/8D]!oB`%!#9$!1Fq*))>a7w*!#;7$$!0&>QwKeqW!#:$!0&QXE2Vr(*!#:7$$!/E^-&)z3W!#9$!1EME&[nxx*!#;7$$!0DV'GP,ZV!#:$!1WY!3E/-y*!#;7$$!/Rxa*G_G%!#9$!0k#*e9$oy(*!#:7$$!2E"oN'R7AA%!#<$!1-qY@r*Hx*!#;7$$!1D(Rz$e>fT!#;$!1`V!4')zIw*!#;7$$!1PE_z#zh4%!#;$!1XW'Q$z()[(*!#;7$$!0b06siJ.%!#:$!1#G+)*zS.t*!#;7$$!1v8F/'Hr!R!#;$!1QD&yvt+o*!#;7$$!/sV(['4"y$!#9$!0A1"3d$>h*!#:7$$!/E^-0"R^$!#9$!12O4P982%*!#;7$$!.)e<XsYK!#8$!0/?y"3$)="*!#:7$$!/Qu[xvcF!#9$!07c7h*er$)!#:7$$!/f;Lw4tA!#9$!0,kTSvLO(!#:7$$!/$['HH2c<!#9$!0f'yY6-7g!#:7$$!/'=Put,C"!#9$!0A..:uOU%!#:7$$!2*\"Hem['35!#<$!18Xodm!zk$!#;7$$!.(RzeBrx!#9$!0t#p&=(eTG!#:7$$!/&f=Pa'G]!#:$!2QM2A0nf&=!#<7$$!.AV'G2'G#!#9$!0"\")HeX#[)!#;7$$"0.+N!3;#z)!#>$"2&\$>b*R&oE$!#?7$$".Hf=dOI#!#9$"0)4&><>va)!#;7$$"-05?'=n(!#8$"02P#fQR1G!#:7$$"/OtY$H&z7!#9$"0P:)*ya?b%!#:7$$"/Pu[2*pt"!#9$"0#e(\&[Adf!#:7$$"/&)pRRX^A!#9$"0(pe()*\AJ(!#:7$$"/JjEtKpF!#9$"0x%)4=mUR)!#:7$$"/)e<NRZG$!#9$"02\??')\;*!#:7$$"/>QwAfiP!#9$"0h$e6*3/g*!#:7$$"2'*HjE`*G')Q!#<$"1&)>UD&[+n*!#;7$$"/Z%*)y')*4S!#9$"1i%=fQBCs*!#;7$$"2.5E_/%oLT!#<$"1Z#ylT\yv*!#;7$$"/v],8QdU!#9$"0@GBm)ow(*!#:7$$"1))f?T_M@V!#;$"12:\Qh0!y*!#;7$$"2`Z/4=4`Q%!#<$"0[F1fc"z(*!#:7$$"1jHg?JF\W!#;$"1z^vBK0u(*!#;7$$"2/X,.1PK^%!#<$"1_Q&R$>"[w*!#;7$$"2cU)pR\;TY!#<$"1)e<p&>>M(*!#;7$$"/a4>G4pZ!#9$"/$*Q(Qtyo*!#97$$"1^gAX!GT-&!#;$"1AQ3vO:^&*!#;7$$"/nNrK;z_!#9$"0vh6a=(f$*!#:7$$"/c8FM$Q!e!#9$"0>:0MGz"))!#:7$$"/'Hf=jfE'!#9$"0il$)y)p4#)!#:7$$"/f>R=@'y'!#9$"0Np;\5YU(!#:7$$".<Mo'f3t!#8$"0eE6'GOwl!#:7$$"/>Qw7,7y!#9$"04Aq!Q8Vd!#:7$$"/Qxa*f"p#)!#9$"0"f.Z6K,]!#:7$$"/([(\Rv7))!#9$"0xu(fHalT!#:7$$"/T$oO\KF*!#9$"0UtK;%p8N!#:7$$"/-05]"*3)*!#9$"02-C!)HL$G!#:7$$"0nMp)pIG5!#9$"0G$GPE^1B!#:7$$"0u\**GH.3"!#9$"0-81Zi4"=!#:7$$"06BY#o')H6!#9$"0N(z()RD;9!#:7$$"08E_/a:="!#9$"0Ltv3$\y5!#:7$$"0rV([!>!H7!#9$"0F2HD#Rz#)!#;7$$"0oOtY;-G"!#9$".ef$*))>8'!#97$$"0T#['>'RL8!#9$"0x!>["4fT%!#;7$$"0<NqI*oz8!#9$"0Pb4,AOF$!#;7$$"0OtY8(oH9!#9$"0L]:,KjL#!#;7$$"0d9HyR8["!#9$"0(42/*yRi"!#;7$$"0b5@#=(=`"!#9$"0)[F">a47"!#;7$$"/<MoTw!e"!#8$"0f]H"*4Es(!#<7$$"0d9Hy]]j"!#9$"0$)4:pr]-&!#<7$$"0,.1sHQo"!#9$"0AW))*)QqO$!#<7$$"/7C[;"ft"!#8$"0[m<w<L;#!#<7$$"0)yd:c5$y"!#9$"0r:M+F)H9!#<7$$"0=Pu3,Z$=!#9$"0Y\8@CH'*)!#=7$$"0jFbS[K)=!#9$"0#45bZV(p&!#=7$$"0.17M%*R$>!#9$"0'R;n;[)\$!#=7$$"0AW)oxg$)>!#9$"0&\pztyT@!#=7$$"0C['H%[b.#!#9$"0MH<o6FE"!#=7$$"0['HfMd&3#!#9$"0^L$*R<U[(!#>7$$"0$pQx7tO@!#9$"0ekz@O8K%!#>7$$"0d9H[lu=#!#9$"0`YjC>4Z#!#>7$$"0rV([\3MA!#9$"0Z_#Ga)*f9!#>7$$"0$ze<h^(G#!#9$"0m'*eiU9(y!#?7$$"0zf>f0`L#!#9$"0Q@XlG+Z%!#?7$$"0(f>R"fiQ#!#9$"0(HSQ3a6C!#?7$$"08Fa=G]V#!#9$"0#oV^[==8!#?7$$"0f=P%*z"*[#!#9$"0$*oOi'eQm!#@7$$"0=PuQrg`#!#9$"0L]hDY"=O!#@7$$"0Qxaf$H*e#!#9$"0x\![.b!z"!#@7$$"/:Ig)*zPE!#8$"0/')**Q1[I*!#A7$$"0xa44e3p#!#9$"0AnS1T4[%!#A7$$"0Fa3PQmt#!#9$"0'G4]><cB!#A7$$"09Heww()y#!#9$"/%o2Lzu6"!#@7$$"0.29))R"RG!#9$"0.)HRa^g`!#B7$$"0*)zf4q%*)G!#9$"/\cesZPD!#A7$$"0'Qxa^hRH!#9$"0(GyL$)4)="!#B7$$"0%*)yd))y()H!#9$"//1ts>ec!#B7$$"0mKl!f')RI!#9$"0f;$\0!=]#!#C7$$"0D]+6*\*3$!#9$"0Y?jydP8"!#C7$$"0)zf>dtTJ!#9$"0a?5E$\e[!#D7$$"0v],VA!*=$!#9$"0)**z#zVvA#!#D7$$"0V([(4$GTK!#9$"0@IPM1sF*!#E7$$"0D]+rR8H$!#9$"0R3j[MS&R!#E7$$"03<M[u7M$!#9$"-N=q7m;!#B7$$"0pQxaJMR$!#9$"0&Q<ZfIfm!#F7$$"/-/3,ZTM!#8$"/NvV?hCG!#E7$$"06C[;o1\$!#9$"0>.W.(\e6!#F7$$"0jE`m))\a$!#9$"/*4*3AFlU!#F7$$"0sX"H9<%f$!#9$"0,m$G1\-<!#G7$$"0$ze<+ZWO!#9$"0fCpF"Hml!#H7$$"0:KkQAcp$!#9$"0T$HRDLdC!#H7$$"0oOtOTEu$!#9$"/;I=dTL)*!#H7$$"0&>Ry?w#z$!#9$"0'zHLs3cO!#I7$$"0oOtE,D%Q!#9$"03%y_EW^8!#I7$$"0Y$pQnq&*Q!#9$"0l>eONEf%!#J7$$"0b6BEeE%R!#9$"0Dwo[z&\<!#J7$$"0MpQdIo*R!#9$"0-]dH#zhc!#K7$$"0rU&3prXS!#9$"0$fY8i$z,#!#K7$$"0.29Q(3%4%!#9$"0"[$*oPjzr!#L7$$"0Z%*)y65YT!#9$"0.8)*)=EIB!#L7$$"0d9HQD$)>%!#9$"0;zo)[n>u!#M7$$"0RzenTeC%!#9$"0(>H%H8he#!#M7$$"/<Mo=I'H%!#8$"096tB+GL)!#N7$$"/@U%3YbM%!#8$"0\$p,(GJs#!#N7$$"0&3<Mt#*)R%!#9$"0D@lH*)G)z!#O7$$"0"Rycp6XW!#9$"0O;3*H/FF!#O7$$"0$ze<u;)\%!#9$"/)o@')R3$y!#O7$$"0\)pRw.[X!#9$"0nb*=/@!R#!#P7$$"0C\)phU(f%!#9$"0nLN+mMG(!#Q7$$"0sW*))R&ok%!#9$"0.$\(*f])=#!#Q7$$"0RycBnsp%!#9$"0>Mr97UL'!#R7$$"0JjEV/2v%!#9$"07%30%=on"!#R7$$"0tZ&46q*z%!#9$"0)*GK^F6*[!#S7$$"0_067n![[!#9$"0LYyA[8V"!#S7$$"0Gd9fp(**[!#9$"0#oIuGP&z$!#T7$$"0C]+^f8&\!#9$"02G*z82]**!#U7$$"#]!""$"0`%4!3[&zF!#U-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""$-%'CURVESG6%7]x7$$!#]!""$"0o/Su"*eq"!#V7$$!0u[(\RUZ\!#9$"0x21S$fQo!#V7$$!0uZ&4yn,\!#9$"0R`]<O=E#!#U7$$!0E_/\J-&[!#9$"0Ms+hK)o&)!#U7$$!0ze<:W%)z%!#9$"0t^)zP))GK!#T7$$!0BY#\H!pu%!#9$"/H5os2#>"!#R7$$!0#Rycw6*p%!#9$"00%4JVO^R!#S7$$!0OrUvQ'\Y!#9$"0vG.[J#\8!#R7$$!0c7Dgn%)f%!#9$"0WRIJb%RZ!#R7$$!0V'Gd0YZX!#9$"0#f0'>_`j"!#Q7$$!0a3<a$*\\%!#9$"0PKCCdFw&!#Q7$$!0:Hec!y[W!#9$"0xS(*)4eE<!#P7$$!0^-0qbnR%!#9$"0_jN?o%ee!#P7$$!//3;s^WV!#8$"0,e!4a:p>!#O7$$!0#Rycd<%H%!#9$"0F!o%3UuC'!#O7$$!0sW*))3Y[U!#9$"0A(p#G*)=w"!#N7$$!0CZ%*[,T>%!#9$"0*4W:QQef!#N7$$!0pQx%>0[T!#9$"08*)Q0x@l"!#M7$$!04<MQ&[%4%!#9$"0wK(oS+N`!#M7$$!0W([(*)pq/%!#9$"0)Riz"Qn["!#L7$$!0OsWfZ]*R!#9$"0_l9^bX^%!#L7$$!.*zf+^XR!#7$"0&Q^\py#G"!#K7$$!0)f>RG#Q*Q!#9$"09N.*GMhP!#K7$$!0Ryc$yNYQ!#9$"0$Q#3Bac(**!#K7$$!0V&3</;&z$!#9$"0KXa0[&=G!#J7$$!/(Rzo!)>u$!#8$"0(3$4^9"p")!#J7$$!0%pQxvo&p$!#9$"0G'3z/$y.#!#I7$$!0u[(\(*oXO!#9$"0M^^AN)*R&!#I7$$!0a2:5PSf$!#9$"0nxz$=Hd9!#H7$$!0c6B10Na$!#9$"0')*=]ko'z$!#H7$$!//3;Fh%\$!#8$"0BL%Qs%fY*!#H7$$!0a2:5E.W$!#9$"0B*e4M"=d#!#G7$$!/">Q;Z:R$!#8$"0#pe#>o)Hi!#G7$$!0"4=O_YRL!#9$"01#\>A3!e"!#F7$$!0AW)o7F#H$!#9$"0yx@Lnpi$!#F7$$!0$\)pzv1C$!#9$"0xb*epOv))!#F7$$!0Z%*)y%G@>$!#9$"/Vdj%*eL?!#D7$$!03;Ka#QTJ!#9$"0.-%='4Nx%!#E7$$!0*yd:"p<4$!#9$"0N-*\&G\3"!#D7$$!0(Qxa%G)RI!#9$"0dj*fk,FD!#D7$$!0jD^U.)*)H!#9$"0rY:su%Gc!#D7$$!0=NqgX'QH!#9$"0l*[.'e"f7!#C7$$!0a2:S6z)G!#9$"0Cr-fK+w#!#C7$$!0Ryc$>HTG!#9$"0ijtFF)3c!#C7$$!0<Mowgyy#!#9$"0%)*>K`TY7!#B7$$!0JiCHr+u#!#9$"0.)o9dQ8D!#B7$$!08E_u<"*o#!#9$"0u]7)HnQ_!#B7$$!0)\**)p[.k#!#9$"06r&yF[W5!#A7$$!0_.2%p>'e#!#9$"0wnX'QF9A!#A7$$!0$\)p\0$RD!#9$"012xIv7>%!#A7$$!0tW*)G$3'[#!#9$"0%Gu:%4d_)!#A7$$!/17CqdPC!#8$"0k>l-6tg"!#@7$$!0MnMz=XQ#!#9$"0K)>r'y-<$!#@7$$!0%yc8&Q(QB!#9$"0m(=6mwGc!#@7$$!0(Hf=,g'G#!#9$"02j%)3Zx1"!#?7$$!03:I+PiB#!#9$"07jEo1[&>!#?7$$!0@U%)y1f=#!#9$"0#p(3q!fHN!#?7$$!0C['H<wN@!#9$"0y$**e.oui!#?7$$!0<Lm-)e(3#!#9$"0:yc\)*o2"!#>7$$!0X*)y(4^N?!#9$"0"*4D!fM/>!#>7$$!0'=Pux(e)>!#9$"0'*R.%3.NK!#>7$$!07C[;TO$>!#9$"0i_b(G<rb!#>7$$!0OrUXaj)=!#9$"0o<#)f8&***)!#>7$$!0oMpy$4M=!#9$"/vowv*z]"!#<7$$!0'=Pur.%y"!#9$"0-O<')e!RC!#=7$$!0.05S-Tt"!#9$"0F=m4p%))Q!#=7$$!0U$oO`%>o"!#9$"0%y(*peOSi!#=7$$!0">Qwn!Rj"!#9$"0w3+39^_*!#=7$$!0*zf>(3Ze"!#9$"0OF_Vl-X"!#<7$$!0[&4>#)QI:!#9$"0L(3clusA!#<7$$!0Qw_X07["!#9$"0-$pXxonL!#<7$$!0<Mo'o!4V"!#9$"0c?%yXTo\!#<7$$!0&**)z\a(z8!#9$"0Cz#z=exs!#<7$$!0V&3<btK8!#9$"0&fP]:.@5!#;7$$!0:Ig![h#G"!#9$"0-')p@LgW"!#;7$$!0V&3<c(GB"!#9$"0aXSWld,#!#;7$$!0lGd9q'z6!#9$"0*Ru%yhU$G!#;7$$!0c5@i=F8"!#9$"0v'G#3H6y$!#;7$$!0x_0JY&y5!#9$"0HYT%G$o>&!#;7$$!/%ze(*f'H5!#8$"0[fs*oMKo!#;7$$!/3:I]*G")*!#9$"0h$Q*\7b%))!#;7$$!/kFbqv#H*!#9$"0nw9_/;:"!#:7$$!/a2:]^q()!#9$"0"Rww([$z9!#:7$$!/sU&3_`H)!#9$"0D$z]LrM=!#:7$$!./3;]2z(!#8$"0))>P[EfF#!#:7$$!(3$)H(!"($"0%)[x`YAx#!#:7$$!/E^-b\kn!#9$"0^NKIeOQ$!#:7$$!/>Qw#*f-j!#9$"0Z%4=*4<(R!#:7$$!/<MoY4sd!#9$"/FT#H&)zq%!#97$$!/iBZCRt_!#9$"0/zfJ!Q\a!#:7$$!/(Gd92&zZ!#9$"0hKdEzr@'!#:7$$!/Rxa*G_G%!#9$"0lU:<3D+(!#:7$$!/sV(['4"y$!#9$"0C1$y@#3!y!#:7$$!.)e<XsYK!#8$"0V'z4[o=')!#:7$$!/Qu[xvcF!#9$"0`O^RF(=$*!#:7$$!/f;Lw4tA!#9$"0$e;D?XS**!#:7$$!/$['HH2c<!#9$"0xtRdq00"!#97$$!/'=Put,C"!#9$"0tK-$4e%4"!#97$$!.(RzeBrx!#9$"0;0>Tl?7"!#97$$!/&f=Pa'G]!#:$"1ZhGK=dK6!#:7$$!.AV'G2'G#!#9$"//FH+iQ6!#87$$!1D1/3mN7<!#<$"1LGi$o8$R6!#:7$$!0Df<NS'Q6!#;$"2b\"\P&3)R6!#;7$$!0vyZ&4C\c!#<$"2&4Q`JV5S6!#;7$$"0.+N!3;#z)!#>$"2-W%p54?S6!#;7$$"0v[3<%3De!#<$"29vSVA)4S6!#;7$$"0DmLnCi:"!#;$"1VqIEjzR6!#:7$$"2[iZ'H4%*H<!#=$"2j^Z[P&HR6!#;7$$".Hf=dOI#!#9$"0-)\KcfQ6!#97$$"2&*\*)zffx)\!#=$"2C*)3^+&pK6!#;7$$"-05?'=n(!#8$"0rxrmAD7"!#97$$"/OtY$H&z7!#9$"0fLp,.<4"!#97$$"/Pu[2*pt"!#9$"0J[.LJC0"!#97$$"/&)pRRX^A!#9$"//Kw&Hj'**!#97$$"/JjEtKpF!#9$"0y!Q&fe:I*!#:7$$"/)e<NRZG$!#9$"0(4_W$e?c)!#:7$$"/>QwAfiP!#9$"0:L^G&yHy!#:7$$"/v],8QdU!#9$"/<%z=uo/(!#97$$"/a4>G4pZ!#9$"0G-Tx9OB'!#:7$$"/nNrK;z_!#9$"0lHw=x0W&!#:7$$"/c8FM$Q!e!#9$"0")3A&fGiY!#:7$$"/'Hf=jfE'!#9$"0by')3h0-%!#:7$$"/f>R=@'y'!#9$"/D%pAEtN$!#97$$".<Mo'f3t!#8$"01t;b27w#!#:7$$"/>Qw7,7y!#9$"0&z^x,(fD#!#:7$$"/Qxa*f"p#)!#9$"0b4oiof&=!#:7$$"/([(\Rv7))!#9$"0-T/+l/X"!#:7$$"/T$oO\KF*!#9$"0'QqG6ti6!#:7$$"/-05]"*3)*!#9$"0Us![7(Q'))!#;7$$"0nMp)pIG5!#9$"0ip?iSI)o!#;7$$"0u\**GH.3"!#9$"0)*3W]&*R9&!#;7$$"06BY#o')H6!#9$"0'pm\&fk%Q!#;7$$"08E_/a:="!#9$"0Gskv')4!G!#;7$$"0rV([!>!H7!#9$"/7EM?An?!#:7$$"0oOtY;-G"!#9$"0BL4mB)p9!#;7$$"0T#['>'RL8!#9$"0Yrz(yE;5!#;7$$"0<NqI*oz8!#9$"/&fESe5G(!#;7$$"0OtY8(oH9!#9$"0N3TO_Y,&!#<7$$"0d9HyR8["!#9$"0CR2hJTO$!#<7$$"0b5@#=(=`"!#9$"0WKpB)\XA!#<7$$"/<MoTw!e"!#8$".'His9*\"!#:7$$"0d9Hy]]j"!#9$"0)eF#*>,J%*!#=7$$"0,.1sHQo"!#9$"/b7L!oh8'!#<7$$"/7C[;"ft"!#8$"0,:?c%>CQ!#=7$$"0)yd:c5$y"!#9$"0-J'*)=ngC!#=7$$"0=Pu3,Z$=!#9$"0U/mt."*\"!#=7$$"0jFbS[K)=!#9$"08*\fel$G*!#>7$$"0.17M%*R$>!#9$"/zGTe+^b!#=7$$"0AW)oxg$)>!#9$"/.9xRN8L!#=7$$"0C['H%[b.#!#9$"01;m?vN!>!#>7$$"0['HfMd&3#!#9$"0-6J-075"!#>7$$"0$pQx7tO@!#9$"0&fY+B01i!#?7$$"0d9H[lu=#!#9$"0J.`%yGmM!#?7$$"0rV([\3MA!#9$"0veYTx`+#!#?7$$"0$ze<h^(G#!#9$"/)o'\c$f0"!#>7$$"0zf>f0`L#!#9$"0fec]GP(e!#@7$$"0(f>R"fiQ#!#9$"0>9;)3;,J!#@7$$"08Fa=G]V#!#9$"0%*>\8">h;!#@7$$"0f=P%*z"*[#!#9$"019_s=S=)!#A7$$"0=PuQrg`#!#9$"0Av$o8'zP%!#A7$$"0Qxaf$H*e#!#9$"0ZgX*[.A@!#A7$$"/:Ig)*zPE!#8$"0LnJIiC3"!#A7$$"0xa44e3p#!#9$"0Jp")oc+6&!#B7$$"0Fa3PQmt#!#9$"0Z0'fX-UE!#B7$$"09Heww()y#!#9$"0O$*R(fiH7!#B7$$"0.29))R"RG!#9$"0<z#es%Qz&!#C7$$"0*)zf4q%*)G!#9$"0"eYV"H[p#!#C7$$"0'Qxa^hRH!#9$"0v['p)\-C"!#C7$$"0%*)yd))y()H!#9$"0(R$Q**G8"e!#D7$$"0mKl!f')RI!#9$"0z7#H$*[DD!#D7$$"0D]+6*\*3$!#9$"0l'*=c1h7"!#D7$$"0)zf>dtTJ!#9$"0*>))R+ZXZ!#E7$$"0v],VA!*=$!#9$"0'\fNGYV@!#E7$$"0V([(4$GTK!#9$"/)Q%RS4$y)!#E7$$"0D]+rR8H$!#9$"0j;7n1lo$!#F7$$"03<M[u7M$!#9$"0(>v5D=I:!#F7$$"0pQxaJMR$!#9$"0$\)y9]>-'!#G7$$"/-/3,ZTM!#8$"/k-Tnh=D!#F7$$"06C[;o1\$!#9$"0V;XwN%=5!#G7$$"0jE`m))\a$!#9$"0$fD$p[@p$!#H7$$"0sX"H9<%f$!#9$"0uq-(3c`9!#H7$$"0$ze<+ZWO!#9$"0/Iv`F)Gb!#I7$$"0:KkQAcp$!#9$"0cIX.R//#!#I7$$"0oOtOTEu$!#9$"0s\NUpD1)!#J7$$"0&>Ry?w#z$!#9$"08wL_o!eH!#J7$$"0oOtE,D%Q!#9$"07yE$>Fz5!#J7$$"0Y$pQnq&*Q!#9$"0*>Yn.i<O!#K7$$"0b6BEeE%R!#9$"/$)elDth8!#J7$$"0MpQdIo*R!#9$"/i56$epM%!#K7$$"0rU&3prXS!#9$"0fqQC"fI:!#L7$$"0.29Q(3%4%!#9$"0%3c&=l8Q&!#M7$$"0Z%*)y65YT!#9$"0UWuD%pC<!#M7$$"0d9HQD$)>%!#9$"0%zu4b?Ba!#N7$$"0RzenTeC%!#9$"0%*e7_$4p=!#N7$$"/<Mo=I'H%!#8$"0#eb:Lt^f!#O7$$"/@U%3YbM%!#8$"0M35rjH#>!#O7$$"0&3<Mt#*)R%!#9$"0.(*p!pyob!#P7$$"0"Rycp6XW!#9$"0iD:T"f#)=!#P7$$"0$ze<u;)\%!#9$"0R@QM)>U`!#Q7$$"0\)pRw.[X!#9$"0\?HY@Fh"!#Q7$$"0C\)phU(f%!#9$"0c**Rj.:'[!#R7$$"0sW*))R&ok%!#9$"0e'fjnAX9!#R7$$"0RycBnsp%!#9$"0M')zNR!QT!#S7$$"0JjEV/2v%!#9$".zQ#o6$3"!#Q7$$"0tZ&46q*z%!#9$"00v;=-r7$!#T7$$"0_067n![[!#9$"0eE$H;"*f!*!#U7$$"0Gd9fp(**[!#9$"0'Hm!)H)pP#!#U7$$"0C]+^f8&\!#9$"0nqK(fkmh!#V7$$"#]!""$"0o/Su"*eq"!#V-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#""$-%'CURVESG6%7iy7$$!#]!""$"02a(oUQ!>$!#T7$$!0u[(\RUZ\!#9$"/K_wq5_7!#R7$$!0uZ&4yn,\!#9$"0oiJ#pwkS!#S7$$!0E_/\J-&[!#9$"0zH&R7j2:!#R7$$!0ze<:W%)z%!#9$"0`h0Ih)fb!#R7$$!0BY#\H!pu%!#9$"03Rnd:'3?!#Q7$$!0#Rycw6*p%!#9$"0')))[G.S_'!#Q7$$!0OrUvQ'\Y!#9$"0,F.k=3=#!#P7$$!0c7Dgn%)f%!#9$"0oO*yj:#\(!#P7$$!0V'Gd0YZX!#9$"0AFk/')y_#!#O7$$!0a3<a$*\\%!#9$"0c]8@AEq)!#O7$$!0:Hec!y[W!#9$"0Bt"es!Qb#!#N7$$!0^-0qbnR%!#9$"/,mQk)GY)!#M7$$!//3;s^WV!#8$"0v/s5Nqx#!#M7$$!0#Rycd<%H%!#9$"0*z_:]a1')!#M7$$!0sW*))3Y[U!#9$"0oI&e/`vB!#L7$$!0CZ%*[,T>%!#9$"0t"HBvEGy!#L7$$!0pQx%>0[T!#9$"0*H?:-,B@!#K7$$!04<MQ&[%4%!#9$"0([(fIz%ym!#K7$$!0W([(*)pq/%!#9$"//())3N!==!#I7$$!0OsWfZ]*R!#9$"0D)ophsy`!#J7$$!.*zf+^XR!#7$"/XdXfW!\"!#H7$$!0)f>RG#Q*Q!#9$"0TY=i)ybU!#I7$$!0Ryc$yNYQ!#9$"0W$4a%z65"!#H7$$!0V&3</;&z$!#9$"0\MNQ*\GI!#H7$$!/(Rzo!)>u$!#8$"/%o\(zuJ&)!#G7$$!0%pQxvo&p$!#9$"0$of%R.c2#!#G7$$!0u[(\(*oXO!#9$"0WrRh#4^`!#G7$$!0a2:5PSf$!#9$"0W%p/e@.9!#F7$$!0c6B10Na$!#9$"0^k#yT(Hb$!#F7$$!//3;Fh%\$!#8$"/*f;BBPh)!#E7$$!0a2:5E.W$!#9$"0.X7emvE#!#E7$$!/">Q;Z:R$!#8$"0K,0JtpL&!#E7$$!0"4=O_YRL!#9$"0)p@CD-78!#D7$$!0AW)o7F#H$!#9$"0p"yQVTEH!#D7$$!0$\)pzv1C$!#9$"0G*fXSVOp!#D7$$!0Z%*)y%G@>$!#9$"0Ts0vP;a"!#C7$$!03;Ka#QTJ!#9$"0&RL-*HN]$!#C7$$!0*yd:"p<4$!#9$"0V*zU2#4r(!#C7$$!0(Qxa%G)RI!#9$"0j6Y_%fN<!#B7$$!0jD^U.)*)H!#9$"0b!))='R#QP!#B7$$!0=NqgX'QH!#9$"0u1kXNh2)!#B7$$!0a2:S6z)G!#9$"0dh?b&**3<!#A7$$!0Ryc$>HTG!#9$"0\'oQ%f/O$!#A7$$!0<Mowgyy#!#9$"019T1Ni=(!#A7$$!0JiCHr+u#!#9$"0fj5'*Q#*R"!#@7$$!08E_u<"*o#!#9$"0oi4aBw!G!#@7$$!0)\**)p[.k#!#9$"03qx+lRR&!#@7$$!0_.2%p>'e#!#9$"0la'*eXk4"!#?7$$!0$\)p\0$RD!#9$"0K.'ozv**>!#?7$$!0tW*)G$3'[#!#9$"0_h$*)*)e'*Q!#?7$$!/17CqdPC!#8$"0hu7N(zdq!#?7$$!0MnMz=XQ#!#9$"0<v,tz6L"!#>7$$!0%yc8&Q(QB!#9$"08HU"y3sA!#>7$$!0(Hf=,g'G#!#9$"0W:4osm6%!#>7$$!03:I+PiB#!#9$"/Rn)[YB?(!#=7$$!0@U%)y1f=#!#9$"0%[E6HYT7!#=7$$!0C['H<wN@!#9$"0Vqc$[)[5#!#=7$$!0<Lm-)e(3#!#9$"0%p`&=0![M!#=7$$!0X*)y(4^N?!#9$"0.c@tr-z&!#=7$$!0'=Pux(e)>!#9$"0PFlyL9N*!#=7$$!07C[;TO$>!#9$"0i&*)oMzC:!#<7$$!0OrUXaj)=!#9$"0zj88P5M#!#<7$$!0oMpy$4M=!#9$"0;O#p=d-P!#<7$$!0'=Pur.%y"!#9$"01C">x)ol&!#<7$$!0.05S-Tt"!#9$"/#oh/Ib])!#;7$$!0U$oO`%>o"!#9$"04p6#)4:G"!#;7$$!0">Qwn!Rj"!#9$"/2'p`F@%=!#:7$$!0*zf>(3Ze"!#9$"0f;!e;KKE!#;7$$!0[&4>#)QI:!#9$"0"H!fW*QOQ!#;7$$!0Qw_X07["!#9$"0Jvw:y+J&!#;7$$!0<Mo'o!4V"!#9$"0/;"zJe(G(!#;7$$!0&**)z\a(z8!#9$"0ipP7Q*)))*!#;7$$!0V&3<btK8!#9$"0=4sQ:'*G"!#:7$$!0:Ig![h#G"!#9$"0*=L=!ySo"!#:7$$!0V&3<c(GB"!#9$"0\!>#Q6#e@!#:7$$!0lGd9q'z6!#9$"0M)4E"f8w#!#:7$$!0c5@i=F8"!#9$"0cIvS2cP$!#:7$$!0x_0JY&y5!#9$"0j$y&\:?<%!#:7$$!/%ze(*f'H5!#8$"0*=OKFCc\!#:7$$!/3:I]*G")*!#9$"0iMzQ<0x&!#:7$$!/kFbqv#H*!#9$"0Jt6nDLl'!#:7$$!/a2:]^q()!#9$"0>/ueD*)\(!#:7$$!/sU&3_`H)!#9$"0AIYr(4$=)!#:7$$!./3;]2z(!#8$"0*>AS\uj()!#:7$$!.-/3HXa(!#8$"1n/BX0Yu*)!#;7$$!(3$)H(!"($"/;53!p!G"*!#97$$!0:Gc([&[;(!#:$"1i2pbK3&=*!#;7$$!/jD^<SJq!#9$"1*o[E#zMA#*!#;7$$!1v.2*=vY'p!#;$"1_,'H+tKB*!#;7$$!1\W)oi[z*o!#;$"1UWtIi!*Q#*!#;7$$!1C&)pk?AJo!#;$"1%R8'>r8R#*!#;7$$!/E^-b\kn!#9$".%*pIfQB*!#87$$!0DZ%*QZN`'!#:$"1u8\97nr"*!#;7$$!/>Qw#*f-j!#9$"0)>]=([&Q!*!#:7$$!/<MoY4sd!#9$"0OX1"z^\%)!#:7$$!/iBZCRt_!#9$"0"*3_!Q1Ev!#:7$$!/(Gd92&zZ!#9$"0l*o$>D&oi!#:7$$!/8D]!oB`%!#9$"0#\Y%>y8_&!#:7$$!/Rxa*G_G%!#9$"0Vih!\O/Z!#:7$$!0b06siJ.%!#:$"1w%yH:/!3Q!#;7$$!/sV(['4"y$!#9$"0ik$H%H'eG!#:7$$!/E^-0"R^$!#9$"2."GLIQ13=!#<7$$!.)e<XsYK!#8$"0#3r^6Oys!#;7$$!/f;L6u,I!#9$!2..<=$3lPF!#=7$$!/Qu[xvcF!#9$!0#*p5E&Qr7!#:7$$!0&[&4pF\^#!#:$!2(3yH:#\zB#!#<7$$!/f;Lw4tA!#9$!0"z!>*46sJ!#:7$$!/rS"G&e9?!#9$!2OTDY&\#*=T!#<7$$!/$['HH2c<!#9$!0PtIN()e*\!#:7$$!0X$oOL7)\"!#:$!1J')p+Yg&y&!#;7$$!/'=Put,C"!#9$!0v!G(3#pvk!#:7$$!.(RzeBrx!#9$!/N+m<NDu!#97$$!/&f=Pa'G]!#:$!13&3T;KMz(!#;7$$!.AV'G2'G#!#9$!0@07rvl+)!#:7$$!1D1/3mN7<!#<$!1FAP\)y5.)!#;7$$!0Df<NS'Q6!#;$!1J.>>nc[!)!#;7$$!0vyZ&4C\c!#<$!1fifBG-f!)!#;7$$"0.+N!3;#z)!#>$!1fe"oHPC1)!#;7$$"0v[3<%3De!#<$!1(H8o"p!)e!)!#;7$$"0DmLnCi:"!#;$!1esN4^8[!)!#;7$$"2[iZ'H4%*H<!#=$!1UwpV>VI!)!#;7$$".Hf=dOI#!#9$!0of)>Tr0!)!#:7$$"2&*\*)zffx)\!#=$!1jPg"yjxz(!#;7$$"-05?'=n(!#8$!0blRX88W(!#:7$$"/OtY$H&z7!#9$!0$fYxLPxj!#:7$$"2*\'Qx/g#3:!#<$!12F]mBOcd!#;7$$"/Pu[2*pt"!#9$!0(f_?FTd]!#:7$$"/6AWBA%*>!#9$!20Vd*R+v!>%!#<7$$"/&)pRRX^A!#9$!0ZOowcOD$!#:7$$"/e;L1R5D!#9$!2d84-4=eD#!#<7$$"/JjEtKpF!#9$!0<3n#p_?7!#:7$$"2.&f>RL.FI!#<$!2%\SK?/(Hq"!#=7$$"/)e<NRZG$!#9$"0ZZ.31p#))!#;7$$"2.NqS"emBN!#<$"1/_sjc/Z=!#;7$$"/>QwAfiP!#9$"/hj+6<(y#!#97$$"/Z%*)y')*4S!#9$"2M5A5o_Fs$!#<7$$"/v],8QdU!#9$"023?x(G3Y!#:7$$"2/X,.1PK^%!#<$"1f*RWyF0Y&!#;7$$"/a4>G4pZ!#9$"0V$[4%[&Qi!#:7$$"/nNrK;z_!#9$"0i^6"[yQv!#:7$$"/c8FM$Q!e!#9$"0`JWCGh\)!#:7$$"/'Hf=jfE'!#9$"0L&R^Eq5!*!#:7$$"0viD^(3El!#:$"1z(*[7")\o"*!#;7$$"/f>R=@'y'!#9$"0R?p*z=O#*!#:7$$"1PNsW*4:&o!#;$"1YrjN\kR#*!#;7$$"1v6D]!3o"p!#;$"0*>7Fq&yB*!#:7$$"18)yd:1@)p!#;$"0hsv5D4B*!#:7$$"0X18E/u/(!#:$"16`uHP&*=#*!#;7$$"1D<Os/+yr!#;$"1_(oV.G.=*!#;7$$".<Mo'f3t!#8$"0;')f3#)G7*!#:7$$"0X**)zRIgv!#:$"1'p_#)f*fi*)!#;7$$"/>Qw7,7y!#9$"0R?YS(4V()!#:7$$"/Qxa*f"p#)!#9$"0WZ;aLu@)!#:7$$"/([(\Rv7))!#9$"0RHz^/MV(!#:7$$"/T$oO\KF*!#9$"/oCIm)fo'!#97$$"/-05]"*3)*!#9$"0k*>+gHxd!#:7$$"0nMp)pIG5!#9$"0p;/)\iy\!#:7$$"0u\**GH.3"!#9$"0HtP7mW9%!#:7$$"06BY#o')H6!#9$"0/-(*G%H:M!#:7$$"08E_/a:="!#9$"0oZ)HhHQF!#:7$$"0rV([!>!H7!#9$"09Ut(ec)>#!#:7$$"0oOtY;-G"!#9$"0HU*>3+0<!#:7$$"0T#['>'RL8!#9$"07`e%G%\G"!#:7$$"0<NqI*oz8!#9$"0'p(fbyE*)*!#;7$$"0OtY8(oH9!#9$"0&yPj_EUt!#;7$$"0d9HyR8["!#9$"0M:nBwaI&!#;7$$"0b5@#=(=`"!#9$"0=$em\0)z$!#;7$$"/<MoTw!e"!#8$"0w*f1*))pq#!#;7$$"0d9Hy]]j"!#9$"0#3&G!pdE=!#;7$$"0,.1sHQo"!#9$"/@#eOMIE"!#:7$$"/7C[;"ft"!#8$"0"y4,i'HQ)!#<7$$"0)yd:c5$y"!#9$"0tL<`u3q&!#<7$$"0=Pu3,Z$=!#9$"0='zMIC$o$!#<7$$"0jFbS[K)=!#9$"0oBGa)y1C!#<7$$"0.17M%*R$>!#9$"0'G7gK%)>:!#<7$$"0AW)oxg$)>!#9$"0)QaA;Ub&*!#=7$$"0C['H%[b.#!#9$"0zx"Hj9)y&!#=7$$"0['HfMd&3#!#9$"0wq;qx)=N!#=7$$"0$pQx7tO@!#9$"0e$H?Nz$3#!#=7$$"0d9H[lu=#!#9$"0TB1sr4A"!#=7$$"0rV([\3MA!#9$"0kUwv$=ut!#>7$$"0$ze<h^(G#!#9$"0ul;?cW2%!#>7$$"0zf>f0`L#!#9$"0JAZ1"*QO#!#>7$$"0(f>R"fiQ#!#9$"0U/;4"4/8!#>7$$"08Fa=G]V#!#9$"0&=xge*)ys!#?7$$"0f=P%*z"*[#!#9$"0&>%H*3*)\P!#?7$$"0=PuQrg`#!#9$"0#QM)>MM3#!#?7$$"0Qxaf$H*e#!#9$"0J%>r_K`5!#?7$$"/:Ig)*zPE!#8$"0'f(yOl"zb!#@7$$"0xa44e3p#!#9$"0nq=\&GUF!#@7$$"0Fa3PQmt#!#9$"0ck))3CrY"!#@7$$"09Heww()y#!#9$"0pY$pA:%4(!#A7$$"0.29))R"RG!#9$"0&=uML*fY$!#A7$$"0*)zf4q%*)G!#9$"0%)zZCW/n"!#A7$$"0'Qxa^hRH!#9$"0*p(\Hk,'z!#B7$$"0%*)yd))y()H!#9$"0kj<8IW&Q!#B7$$"0mKl!f')RI!#9$"06&*z%))eM<!#B7$$"0D]+6*\*3$!#9$"0ce0N?<*z!#C7$$"0)zf>dtTJ!#9$"0lZ`#4u$[$!#C7$$"0v],VA!*=$!#9$"0CDu:T<i"!#C7$$"0V([(4$GTK!#9$"018o`:p'o!#D7$$"0D]+rR8H$!#9$"0B+1"evsH!#D7$$"03<M[u7M$!#9$"0kZS6x>F"!#D7$$"0pQxaJMR$!#9$"00&z_mjk^!#E7$$"/-/3,ZTM!#8$"0*Q%[1_@A#!#E7$$"06C[;o1\$!#9$"07;lz#QY#*!#F7$$"0jE`m))\a$!#9$"0$GIrC1eM!#F7$$"0sX"H9<%f$!#9$"03)Gv'G(*R"!#F7$$"0$ze<+ZWO!#9$"0sj_')G_Z&!#G7$$"0:KkQAcp$!#9$"0yNNZ'=y?!#G7$$"0oOtOTEu$!#9$"0B5*yqYB%)!#H7$$"0&>Ry?w#z$!#9$"0G*f$GqV<$!#H7$$"0oOtE,D%Q!#9$"0s*4(Rp*)="!#H7$$"0Y$pQnq&*Q!#9$".A(H&fr4%!#G7$$"0b6BEeE%R!#9$"0E#*e5r)z:!#I7$$"0MpQdIo*R!#9$"0x$o%)*)p$=&!#J7$$"0rU&3prXS!#9$"0bs:n,/(=!#J7$$"0.29Q(3%4%!#9$"0$y$QB)>Nn!#K7$$"0Z%*)y65YT!#9$"03:'>x49A!#K7$$"0d9HQD$)>%!#9$"0k."QMdRr!#L7$$"0RzenTeC%!#9$"0'[E%z\p^#!#L7$$"/<Mo=I'H%!#8$"0TCJ7Ot?)!#M7$$"/@U%3YbM%!#8$"041$GN=8F!#M7$$"0&3<Mt#*)R%!#9$"0nGS'HT_!)!#N7$$"0"Rycp6XW!#9$"0sck%z&*zF!#N7$$"0$ze<u;)\%!#9$"0,#p$zl*y!)!#O7$$"0\)pRw.[X!#9$"0HFgnRN\#!#O7$$"0C\)phU(f%!#9$"0z0/!\f"o(!#P7$$"0sW*))R&ok%!#9$"0&=T`-<LB!#P7$$"0RycBnsp%!#9$"0bcW>:o#o!#Q7$$"0JjEV/2v%!#9$"0)\C8p&z#=!#Q7$$"0tZ&46q*z%!#9$"07(3n]V(Q&!#R7$$"0_067n![[!#9$"0x/fS0Ef"!#R7$$"0Gd9fp(**[!#9$"0NG8&*f$oU!#S7$$"0C]+^f8&\!#9$"0PVaL")38"!#S7$$"#]!""$"02a(oUQ!>$!#T-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%*THICKNESSG6#""$-%%VIEWG6$;$!#]!""$"#]!""%(DEFAULTG-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"67-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q'&#966;6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-I#moG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6>Q0&ApplyFunction;6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"/%&fenceGQ&false6"/%*separatorGQ&false6"/%)stretchyGQ&false6"/%*symmetricGQ&false6"/%(largeopGQ&false6"/%.movablelimitsGQ&false6"/%'accentGQ&false6"/%'lspaceGQ&0.0em6"/%'rspaceGQ&0.0em6"-I(mfencedG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-%*AXESSTYLEG6#%$BOXG-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"Ig==</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L14595" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052" italic="true">
<Font encoding="UTF-8"> Plotting the density matrix as a function of \316\262 with specified end points (keeping things real, as plotting the kernel directly would involve complex numbers):</Font></Font></Text-field>
</Input>
</Group>
<Group labelreference="L14592" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">x1 := 0.0:
x2 := 15.0:
denmatdft := sqrt((m*omegadft)/(2*Pi*sinh(beta*omegadft)))*exp(-(m*omegadft)/(2*sinh(beta*omegadft))*((x1^2 + x2^2)*cosh(beta*omegadft) - 2*x1*x2)):</Font></Text-field>
</Input>
</Group>
<Group labelreference="L14591" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">with(plots):
logplot(denmatdft(beta), beta = 0.0..15.0, axes = boxed, labels = ['beta', 'rho'], color = red, thickness = 3);</Font></Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" type="two-dimensional" width="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">6--%'CURVESG6#7]x7$$"22kFbN-XY#!#>$""!!""7$$"1"Gb5r/!H\!#=$""!!""7$$"1AHemq]$R(!#=$""!!""7$$"1j06A%4!e)*!#=$""!!""7$$"2We;LT,(y9!#=$""!!""7$$"2D6AW)=gr>!#=$""!!""7$$"2)oJjEGSdH!#=$""!!""7$$"1DU%)oP?VR!#<$""!!""7$$"2wLmKl0["f!#=$""!!""7$$"0X)oPvS')y!#;$""!!""7$$"2DQw_!otJ6!#<$""!!""7$$"0#RycG$[Z"!#:$""!!""7$$"03;KkFlC#!#:$""!!""7$$"04=OsPL-$!#:$""!!""7$$"0a18wbkz$!#:$""!!""7$$"0@T#[^B8X!#:$""!!""7$$"0lHfo=aD&!#:$""!!""7$$"0c6B'f)H-'!#:$""!!""7$$"0_.2k"4)y'!#:$""!!""7$$"0'=Puo4vv!#:$""!!""7$$"0#Gc7:Ho#)!#:$""!!""7$$"0KiC\k'[!*!#:$""!!""7$$"0)Rze<CK)*!#:$""!!""7$$"07C[OO(e5!#9$""!!""7$$"0#Hem'3t7"!#9$""!!""7$$"0:HewZ)37!#9$""!!""7$$"0'>Ry?#zF"!#9$""!!""7$$"0Pu[#>Fe8!#9$""!!""7$$"0&)oP:&RH9!#9$""!!""7$$"0Y"H3'Gu]"!#9$""!!""7$$"0^,."\t"e"!#9$""!!""7$$"0.17ul#f;!#9$""!!""7$$"0T#[YKYI<!#9$""!!""7$$"0'=Pu$fs!=!#9$""!!""7$$"0X!4o*Gq)=!#9$""!!""7$$"/'>Rjok&>!#8$""!!""7$$"0*oPv`YJ?!#9$""!!""7$$"0pQxMW*3@!#9$""!!""7$$"0mKlSUZ=#!#9$""!!""7$$"/%ze#43eA!#8$""!!""7$$"0pQx%3^RB!#9$""!!""7$$"0OrUDzET#!#9$""!!""7$$"0kGd9-3\#!#9$""!!""7$$"0nLn4$fhD!#9$""!!""7$$"0hAXI')*QE!#9$""!!""7$$"0He;G2=r#!#9$""!!""7$$"0)e<&=Ezy#!#9$"0n]*H*=:w#!$A$7$$"0<LmKYB'G!#9$"0oO%)H(QBd!$>$7$$"/#RyJd-%H!#8$"1C4`()HtJ#*!$<$7$$"0c6B'[H:I!#9$"/@]!GGdh'!$7$7$$"0CZ%*eJ?4$!#9$"0`X)yNmML!$5$7$$"/(Qx*G8oJ!#8$"0$='pU:*35!$2$7$$"0T#['4i!QK!#9$"0j6>fmbK"!$0$7$$"0v[(\)3#=L!#9$"0QSj9[iP#!$.$7$$"0`181$*)*Q$!#9$"21&[uY")[g<!$.$7$$"0"3;#QBjY$!#9$"0p$fX#*>d7!$*H7$$"0a2:&pZRN!#9$"01Ps)pU2c!$)H7$$"0tW*)e/2i$!#9$"0,k`;"*f!G!$'H7$$"0iAXvT5p$!#9$".*fHpsTl!$$H7$$"0#Hem](3x$!#9$"0jW?'fy>=!$$H7$$"/">QYMO%Q!#8$"0V7iPfe/$!$#H7$$".*z4=ABR!#7$"0(y3(=XON&!$"H7$$"0C['HA*=*R!#9$"0o>I!3Do`!$!H7$$"0c5@#)*4qS!#9$"0,'="**)>=i!$*G7$$"0Rxa\Wc9%!#9$"0\x&)yXlh&!$)G7$$"0pOt")R6A%!#9$"0#fk=BfdV!$(G7$$"0kFbSdjH%!#9$"0v*\Bdn>H!$'G7$$"0D]+'zhoV!#9$"0ae#zvH2;!$&G7$$"0$e;LNtYW!#9$"0Uc">)Gz'*)!$&G7$$"0@U%QL=@X!#9$"0%eCf!yb7%!$%G7$$"0#Qw_#Q&*f%!#9$"0s!e%4J>%=!$$G7$$"0(Hf=$o/n%!#9$"0**=t%*3#=l!$$G7$$"0*zf>$f)[Z!#9$"0%))Q)[>+S#!$#G7$$"0@U%QU%R#[!#9$"0C]RAn#yw!$#G7$$"0Z#\)RY))*[!#9$"0Q&)p"eXmA!$"G7$$"0)[(\*>3x\!#9$"0([)\%f#*)\'!$"G7$$"09Fa$)R"\]!#9$"/u`!)y!og"!$z#7$$"0-.1#p$H7&!#9$"0&f(py'zAQ!$!G7$$"0zc8n<W?&!#9$"00(yzg;<$*!$!G7$$"0V&3<=>y_!#9$"0XFV"G6u>!$z#7$$"0v[(*pRON&!#9$"0:lF=cF/%!$z#7$$"03:IDo.V&!#9$"086u'\Ewz!$z#7$$"0'=PCn*3]&!#9$"0yL*\^mH9!$y#7$$"0ya4zxgd&!#9$"0a#yF'Gub#!$y#7$$"0'=Pulo]c!#9$"/o%fC1?Q%!$x#7$$"0/29y%\Id!#9$"0$QG(Hq<\(!$y#7$$"0<Mo1A4!e!#9$"/*=#>R([;"!$w#7$$"0'3<M0=#)e!#9$"0$\*\o+D(=!$x#7$$"0"4=O+^bf!#9$"0R'\i4a*y#!$x#7$$"0Rxaul!Gg!#9$"0Tyzy5B.%!$x#7$$"0b3<W'31h!#9$"0.U*QfnLe!$x#7$$"/(QxuAW='!#8$"0&)Ro6/RB)!$x#7$$"0$f=(=(pbi!#9$"02no4&)G5"!$w#7$$"/%zeZ(QJj!#8$"08$>^'QLZ"!$w#7$$")QD0k!"($"0m8!RJ=<>!$w#7$$"07BYnD`['!#9$"/Hr$R%y*\#!$v#7$$"0sU&3,hal!#9$"0c$e()fr&4$!$w#7$$"0v[(*z&=Mm!#9$"0yC-Q17*Q!$w#7$$"0e9H8"**3n!#9$"0'=8S!Q3v%!$w#7$$"0rS"GR2$y'!#9$"/^1S7F5d!$v#7$$"0#Rycc@do!#9$"0K;Cpvrx'!$w#7$$"0V%)o_NG$p!#9$"0"yAeF(>(z!$w#7$$"0"=OA8*H,(!#9$"/<L&\j'\$*!$v#7$$"0X)oPj['3(!#9$"/Ejk_cq5!$u#7$$"08D]NN!fr!#9$"0xn!p9B77!$v#7$$"0x_01*eOs!#9$"03S*428r8!$v#7$$"0AU%QR(RJ(!#9$"0#33(eng`"!$v#7$$"004=YJMQ(!#9$"0<izcv$)o"!$v#7$$"0=Nq!*3dY(!#9$"0ZhOo7D(=!$v#7$$"0&*)yd[bMv!#9$"0B')y&yYG?!$v#7$$"0w],$z2:w!#9$"0DU/(He6A!$v#7$$"015?SH>p(!#9$"08z54scQ#!$v#7$$"0c6Bh[0w(!#9$"0$QH(4n%RD!$v#7$$"0ya44=x$y!#9$"08RwYY%4F!$v#7$$"0)\**)4*R:z!#9$"0ULG/ki(G!$v#7$$"0#Qw-4r#*z!#9$"0hxly#*p.$!$v#7$$"0Hd9%))Qk!)!#9$"/D"QH20=$!$u#7$$"09E_>2'Q")!#9$"0B\6()fGK$!$v#7$$"0LkG#RO:#)!#9$"0T.:(fziM!$v#7$$"0_.2\u=H)!#9$"0t#o13T%f$!$v#7$$"0OqS,v0P)!#9$"03-hU$=@P!$v#7$$"0X*)yZ%*)R%)!#9$"0wbQ$HPDQ!$v#7$$"/%zexJz^)!#8$"0='f$)y6MR!$v#7$$"0d7D]*G'f)!#9$"09KRp4T.%!$v#7$$"0Hd9p,=n)!#9$"0m.K&=u@T!$v#7$$"04;K*RPS()!#9$"0=fbM_R>%!$v#7$$"0KiC48>#))!#9$"0kMp%Q#3F%!$v#7$$"08D]S()4*))!#9$"0;d]Tb%GV!$v#7$$"0a2:DP8(*)!#9$"0xT)\()3(Q%!$v#7$$"0--/[gC/*!#9$"0PyL&GoJW!$v#7$$"0jC\$R\?"*!#9$"071E#=,tW!$v#7$$"0oMpB+[>*!#9$"0<5o<!G0X!$v#7$$"/#Ry1JBF*!#8$"0k"y,2#>`%!$v#7$$"0e:JdGNM*!#9$"0Y&Gh?P]X!$v#7$$"0.05qC.U*!#9$"0OIm)G;kX!$v#7$$"0iBZH%4+&*!#9$".Bb=b@d%!$t#7$$"0x_0'R`p&*!#9$"0Z/zAuTd%!$v#7$$"015?qIXk*!#9$"09;6t::d%!$v#7$$"0(=Pu'4?s*!#9$"0Ck'f_$Qc%!$v#7$$"0%e;Lx!yz*!#9$"0/N"o'3=b%!$v#7$$"0d7DDY6()*!#9$"028K;Ki`%!$v#7$$"0(=Puhd_**!#9$"0N7/*eu9X!$v#7$$"0X!4eWd-5!#8$"0knZHv>\%!$v#7$$"0=Osu'Q55!#8$"09d(fqMkW!$v#7$$"0oOB%eY<5!#8$"083h:,mV%!$v#7$$"0e:J;0_-"!#8$"/&y5')yNS%!$u#7$$"0:H3E([K5!#8$"0tos!G<qV!$v#7$$"0"4=^"*4S5!#8$"0">K"*\1LV!$v#7$$"0jE`;Tv/"!#8$"0D$RiX$[H%!$v#7$$"0CZWEK`0"!#8$"0&*4=agHD%!$v#7$$"0Z%*)=g$G1"!#8$"0vgzzO5@%!$v#7$$"0/3;p402"!#8$"0^zRELn;%!$v#7$$"0>PC#)>"y5!#8$"0vYR9T:7%!$v#7$$"0c6Bu7^3"!#8$"0B&=q10zS!$v#7$$"0>QwTFJ4"!#8$"0%o$=+r$HS!$v#7$$"0(RzQeH+6!#8$"0&R(zgwT)R!$v#7$$"/%z3()Qz5"!#7$"0W`@]D`$R!$v#7$$"029yAa_6"!#8$"/2Q_g.))Q!$u#7$$"0zd:*pPB6!#8$"0>y$4x.NQ!$v#7$$"0e:"32TI6!#8$"0ux4G@))y$!$v#7$$"0h@$RSRQ6!#8$"0*4!*Q&*4OP!$v#7$$"0BX!z*pc9"!#8$"0T^I)R)yo$!$v#7$$"0AVOrGO:"!#8$"0ijvAZ]j$!$v#7$$"09Gcv&\g6!#8$"0H?pfQ%*e$!$v#7$$"0Pu[^;$o6!#8$"0/6<*)Qv`$!$v#7$$"016A)4(e<"!#8$"0l,)R!4v[$!$v#7$$"0*pR90U$="!#8$"0)[fLrmPM!$v#7$$"03;KFU4>"!#8$"06m0V6#)Q$!$v#7$$"0Mo'G$o")>"!#8$"0lr'H9$4M$!$v#7$$"/*zf))zf?"!#7$"/rpEn6!H$!$u#7$$"0a2l'[U87!#8$"0ka)>)3?C$!$v#7$$"/(RzNg7A"!#7$"0V'[A>v">$!$v#7$$"0hAXO`$G7!#8$"0h$pl^hYJ!$v#7$$"07BYY#>O7!#8$"0\8c+`r4$!$v#7$$"0a2l&4qV7!#8$"0tW;(e@]I!$v#7$$"0c7D<">^7!#8$"0$HB38%Q+$!$v#7$$"/3;KZ,f7!#7$"04w$p+!f&H!$v#7$$"0.1i^?iE"!#8$"06@Dt3A"H!$v#7$$"0iBZA+OF"!#8$"0K")44Pz'G!$v#7$$".*z*H[<G"!#6$"0R$QPli>G!$v#7$$"0'=P9d7*G"!#8$"0Jdh/7kx#!$v#7$$"0>QE]qmH"!#8$"0x/uQVFt#!$v#7$$"0#['zNVVI"!#8$"0#)>UN')))o#!$v#7$$"/050iR68!#7$"0a=T+q!\E!$v#7$$"0ze<J9*=8!#8$"0=*QG_:2E!$v#7$$"/05!>vjK"!#7$"0_c:[,hc#!$v#7$$"0-/3,cVL"!#8$"0)G]')oyAD!$v#7$$"0tY$R()RT8!#8$"0;/-:!3&[#!$v#7$$"//3'eC&\8!#7$"0Av%em<UC!$v#7$$"0T"GOv&oN"!#8$"09<@<8SS#!$v#7$$"016s58TO"!#8$"0>p*>%onO#!$v#7$$"0<Mo<:>P"!#8$"0E"GP%*GFB!$v#7$$"0>Pu!)[(z8!#8$"0w5^zV#)G#!$v#7$$"0">Q^i(oQ"!#8$"0<JT!=B`A!$v#7$$"0E^-GXWR"!#8$"0)[q&\$e;A!$v#7$$"0KjE">$=S"!#8$"0N<#[TM"=#!$v#7$$"0jD,5R)49!#8$"0`VeoEP9#!$v#7$$"0f<NannT"!#8$"0*Q,)>i;6#!$v#7$$"0>QE6DZU"!#8$"0$[@MaQv?!$v#7$$"0xafk0AV"!#8$"0K^7=:=/#!$v#7$$"0Rxa#RhR9!#8$"0K'ek@24?!$v#7$$"0rT$)4GqW"!#8$"0n+2B*zw>!$v#7$$"0w^`3!fa9!#8$"0sBVz)QW>!$v#7$$"/&**[m0EY"!#7$"./A$ee5>!$t#7$$"0;Kk;b*p9!#8$"0y0Q*[3!)=!$v#7$$"0$e;o+@x9!#8$"0@%*=uL/&=!$v#7$$"0f=(Qa'\["!#8$"/Z(HYL#>=!$u#7$$"0a2l#Rq#\"!#8$"0O.z#fg)y"!$v#7$$"$]"!""$"09wyM&=g<!$v#-%%VIEWG6$;$""!!""$"$]"!""%(DEFAULTG-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6(-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#"""-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&_MODEG6#"""-%&_MODEG6#"""-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q'&#946;6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q'&#961;6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#""$-%*AXESSTYLEG6#%$BOXG-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"NiI=</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L14590" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" family="P052" layout="Normal"></Text-field><Text-field style="Text" family="P052" layout="Normal"><Font family="P052">
</Font></Text-field>
</Input>
</Group>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" size="10" family="P052" layout="Heading 1"><Font size="14" family="P052">Path Integral Molecular Dynamics</Font></Text-field></Title><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">To understand PIMD, the prefactor of Eq (1) can be written as a set of Gaussian integrals over the momenta </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052"> and the partition function can be expressed as </Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY7LUkjbWlHRiQ2J1EiUUYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNigtRiw2J1EiTEYnRi9GMkY1RjgtSSNtb0dGJDYvUSIsRidGL0YyL0Y5USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0ZLLyUqc3ltbWV0cmljR0ZLLyUobGFyZ2VvcEdGSy8lLm1vdmFibGVsaW1pdHNHRksvJSdhY2NlbnRHRksvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYnUSJURidGL0YyRjVGOEYvRjJGR0YvRjJGRy1GRDYwUSJ+RidGL0YyLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0ZHRkkvRk1GS0ZORlBGUkZURlZGWC9GZm5GWi1GRDYwUSI9RidGL0YyRl5vRkdGSUZhb0ZORlBGUkZURlYvRllRLDAuMjc3Nzc3OGVtRicvRmZuRmdvRltvLUkobXN1YnN1cEdGJDYnLUZENjBRKyZJbnRlZ3JhbDtGJ0YvRjJGXm9GR0ZJRmFvL0ZPRjdGUC9GU0Y3RlRGVkZYRmJvLUYjNiYtRiw2I1EhRidGL0YyRkdGYXAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRmhwLUZENjBRMCZEaWZmZXJlbnRpYWxEO0YnRi9GMkZeb0ZHL0ZKUSZ1bnNldEYnL0ZNRl9xL0ZPRl9xL0ZRRl9xL0ZTRl9xL0ZVRl9xL0ZXRl9xRlhGYm8tSSVtc3ViR0YkNiUtRiw2KFEicEYnRi9GMkY1Rl5vRjgtRiM2Ji1JI21uR0YkNidRIjFGJ0YvRjJGXm9GR0YvRjJGR0ZpcC1GRDYwUSMuLkYnRi9GMkZeb0ZHRklGYW9GTkZQRlJGVEZWL0ZZUSwwLjIyMjIyMjJlbUYnRmJvLUZENjBRIi5GJ0YvRjJGXm9GR0ZJRmFvRk5GUEZSRlRGVkZYRmJvRltxLUZncTYlRmlxLUYjNiYtRiw2KFEiUEYnRi9GMkY1Rl5vRjhGL0YyRkdGaXAtRmpvNidGXHAtRiM2Jy1GLDYnUSJERidGL0YyL0Y2RktGRy1GPDYmLUYjNiZGQEYvRjJGR0YvRjJGR0YvRjJGR0ZhcEZmcEZpcC1GRDYvRl1xRi9GMkZHRl5xRmBxRmFxRmJxRmNxRmRxRmVxRlhGYm8tRmdxNiUtRiw2J1EieEYnRi9GMkY1RjgtRiM2Ji1GX3I2JkZhckYvRjJGR0YvRjJGR0ZpcC1GRDYvRmRyRi9GMkZHRklGYW9GTkZQRlJGVEZWRmVyRmJvLUZENi9GaXJGL0YyRkdGSUZhb0ZORlBGUkZURlZGWEZib0ZbcS1GZ3E2JS1GLDYoRmN0Ri9GMkY1Rl5vRjhGXHNGaXAtRkQ2L0Zdb0YvRjJGR0ZJRmFvRk5GUEZSRlRGVkZYRmJvLUYsNidRJGV4cEYnRi9GMkZoc0ZHLUY8NigtRiM2KS1GRDYvUSomdW1pbnVzMDtGJ0YvRjJGR0ZJRmFvRk5GUEZSRlRGVkZlci9GZm5GZnItRiw2J1EnJiM5NDY7RidGL0YyRmhzRkctSSttdW5kZXJvdmVyR0YkNictRkQ2L1EmJlN1bTtGJ0YvRjJGR0ZecUZgcUZfcEZicUZgcC9GVUY3RmVxRlgvRmZuUSwwLjE2NjY2NjdlbUYnLUYjNigtRiw2J1Eia0YnRi9GMkY1RjgtRkQ2L0Zlb0YvRjJGR0ZJRmFvRk5GUEZSRlRGVkZmb0Zob0ZmdEYvRjJGRy1GIzYmLUYsNidGYHNGL0YyRjVGOEYvRjJGR0ZWLyUsYWNjZW50dW5kZXJHRkstRjw2Ji1GIzYxLUkmbWZyYWNHRiQ2KC1Gam82KC1GLDYnRltyRi9GMkY1RjgtRiM2Jy1GLDYnUSJpRidGL0YyRjVGOEYvRjJGNUY4LUYjNictRl9yNiZRIjJGJ0YvRjJGR0YvRjJGNUY4RmZwRmlwL0krbXNlbWFudGljc0dGJFEsW25vbmUsbm9uZV1GJy1GIzYqRmh4RmB1LUYsNidRIm1GJ0YvRjJGNUY4LUZENi9RIidGJ0YvRjJGR0ZJRmFvRk5GUEZSRlRGVi9GWVEsMC4xMTExMTExZW1GJ0Zib0YvRjJGNUY4LyUubGluZXRoaWNrbmVzc0dGYXIvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXHovJSliZXZlbGxlZEdGS0ZgdS1GRDYvUSIrRidGL0YyRkdGSUZhb0ZORlBGUkZURlZGZXJGXHYtRlt4NigtRiM2Jy1Gam82KC1GLDYnUShtJiM5Njk7RidGL0YyRjVGOC1GIzYnRmJ3Ri9GMkY1RjgtRiM2KC1GX3I2J0ZqeEYvRjIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjdGR0YvRjJGNUZjW2xGOEZmcEZpcEZbeUYvRjJGNUY4LUYjNiZGaHhGL0YyRkdGaHlGanlGXXpGX3otSSVtc3VwR0YkNiUtRjw2Ji1GIzYoLUZncTYlRmF0LUYjNihGW3dGYXpGZnRGL0YyRkdGaXAtRkQ2L1EoJm1pbnVzO0YnRi9GMkZHRklGYW9GTkZQRlJGVEZWRmVyRlx2LUZncTYlRmF0LUYjNiZGW3dGL0YyRkdGaXBGL0YyRkdGL0YyRkdGZVtsRmZwRmB1RmF6RmB1LUZbeDYoLUYjNidGZnRGL0YyRjVGOEZgd0ZoeUZqeUZdekZfei1GLDYnUSJVRidGL0YyRjVGOC1GPDYmLUYjNiZGZVxsRi9GMkZHRi9GMkZHRmNwRi9GMkZHRi9GMkZHRi9GMkZHRi9GMkZHLyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0YvRjJGRw==">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052"> </Font><Font style="Equation Label">(2)</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" style="Equation Label" bold="false" family="P052">where </Font><Equation executable="false" style="Equation Label" input-equation="" display="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">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</Equation><Font size="10" family="P052">and </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" family="P052">Eq (2) remarkably resembles a classical cyclic polymer chain of P points moving in a classical potential U(x)/P. P can now be interpreted as the number of beads or replicas of the classical particle needed to obtain quantum effects - it is simply a measure of the <Font italic="true">quantumness</Font> of the system. In other words, a purely quantum mechanical expression has been mapped onto a classical expression, hence the term <Font italic="true">quantum-classical isomorphism. </Font>From this, a Hamiltonian can be constructed and the corresponding equations of motion can be derived and simulated. However, such a framework has quite a few drawbacks, including the immense computational effort required for converging the simulations. Efficient thermostatting and the use of Generalised Langevin Equations (GLE) are some advanced ways of tackling this convergence issue.
</Font></Text-field>
<Group labelreference="L14620" drawlabel="true" applyint="true" applyrational="true" applyexponent="false"><Text-field opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="10" readonly="false" background="[255,255,255]" placeholder="false" family="P052" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="centred" bullet="none" spacebelow="0" pagebreak-before="false"><Image height="270" width="484" zoomable="false" labelreference="L14618" drawcaption="false" captionalignment="0" captionposition="1">MFNWtKUb<ob<R=MDLCdNVZ@j:TU>T:;RkaV^K>CrV?TLcD<KB<KBYKBSK>mBWEDPcuNYeScuW=eVEmmtpqpplplsHPsPpltps\\pqLqqIjYu=@MtPNfVblgf[_hcwgh?^NGgggFGdVMES=UX;SFkCBGTS?eVeUR_UX;cF[cF_CB[CHocFmcH_SG;CNUd;SUSQ[ZRLCTJcDXsFuuXP[FSiXYIywYYHiUlEgwuwdowhouqqRqCBJSEk_CrWR\\oXH_Hl]SF_fJwFf?cCsb=ySxExEoefyBAWrKkEA]cWkxRIVIAWfssB]f^Gfr[BcKdZ\\UjxPtuRidtoxwOEUshuwam]yjUHmOhu:DODMNBLnuaYTDkFQsDQsFQshAqqqyhIQayyQlrRTj_EUPhVSm<wBT_ybwu:gVSmd_EUPfinagj>pfVsl`?b;Arl_GEDElPR<El<hjGlJPhVSWSNr@VZE]l\\jHr:QpfVSS;SEF[?hFQ:rlbj:_?[?BEBU:Q`E:VSNRZl\\:vx]pi=:`ohmJ=HP@Tj@MNKLRpmwA<km@Mg]tWuxsPr=ilhlknMxuik[hyA=NJPrXXKo`oyhkjlrRxktiSRml_EUPNgAN:=FJAWj;TGQGfcFE[gaWgBEFroUyOR_CuFyEeGFHUDpqDaGuQMe`wSH;TLcFHeCWWrq]YVCvZ[bbai@?RVixogVSUif=Hj__l`oI`mpNqoW_yVsY@wNHqrq`mIxWnvMH]PNlSodmh^VFvjv]HQdIWoRfmAVj^FcRFh@I]oorcVwXNc`xjmfiaI]myxj_pyaZuQy`HwoYytVnANZ;oyYh[BnlOis@VZE=wcFUyj[FY?I^GCOUdGaW=gr^mcYkHYMvW?xomTOQF[cS\\MV^?drQtAMEA[h;Ao<`NCEk]`JWDO^MvL=SE]StTYsMV^IUXTMwaLAqJIMPTmM]`vOHlLmX<LjWdQj`oWmPR<eEEEQyB]hICRnCybERbOBhsBQ;y`ewi?Yo[yPSU\\UBQYXc;i?[UcQF__rRSbLQIIcBT[cl;dKwB>_SZMTJEh\\ccLMb@=RPATF=cckeVCYHwurKxu[InCyC_IV;CsuttWBU;DfSs@SBErloI\\Kub]C@Cc^qSrUciqtxGrqQrQCi_wg[iDV]beCDL;DgWCZ[CRSdAKbH=HJ=VlSbCaCtcBM?ENMfkCDbAUMoHL=C^SVFMxUubyudi[erQDAsbICvtkuhax\\SEF:VSmyTIfZCtkSxKiExyeGwyOWGdiEp]ug]dQOvroCLIdg?TJQINEWYEWhQEk;HgAVJObCeCtcHbaR]MDjCh[SCNCUZ?FJ_d]qYXWetaCyGX`yhsMwjYHqego;h[Art=tSQX_od_EUPgVwaUowsCmBdGsgAxwky\\UyyivoavOKEXeCIYxjaIY[EMIwp_tx;VqkBj;F^GrRCdAkB;KR:GD<[VxYH<MbJOBMQyTMYLssQ[VSoVwGh<yXhaiBGT@CW^sSVCyNmId=V=Eb_EuZ=VSmd_EmYxkhij@InD<qSaq@YkutYCytUtU;ywkAOtiJ>XOjLT]\\nByKlyQjIkRiy@UYDHTuMqK@J]<w>\\J]TxUqRT\\je<Mbyw]PpsHsqxWxUjn\\sbixtAQkxwNlUQap\\Tst=TSqWYll_EE<wTikBQuQYpGYuveYmYOvenlyNreRQttomXI<v_@RBxKBdJgHL=xMmQJY<xJDpupQ;mv]LKSDMwdQw\\TLiWxYtOyyByylQvyarHUpLxlEePuHv?QpX\\Rp<MRWShxmUNJ\\RS=sYaWwiPYqoxeMa@OkaQitQ\\Dl`qwn<VxMrgqx?uvQqjhHo@mvAayJ@sa@McDnc\\lD\\VlDvOYUYYvAttXeVaHqmuT=hPEQYJDuZ=VScfSw=yVFuffCwUihQAiP_U^GwQIGNOCBsE>wFJkg:=QAhumdygXjyUtxLxQqnmumJQnomlY`yxemyEVtPJ=qwJLjRiq`tUq@NVER]TomyoxHxiDYiExTDUPHN>@rRTMJ\\oATlGlJPNpfVstAdSVlI?^Lo^]G`RxvuXaYAfXasZqlW^f;OjANr]v[@noBYcNphOH_o>lARayD_gHSGsBAsTeuIgSaYYugDE_SeqHuWrCsXGeDl;Sc;Dh[URWYEwEXuyxSsUUc:uXQkVEQYj?uZ=VSjIdTueU;MoMmOQqu[iwZiPp]mg]y\\xKhmqb<UtHy;Mqj]RxElsiPL\\jMQon\\Rx=tXYwnQpi@pIHOyuOh@xJQs:PPs=Kbaj=Lq<TReQunxRN\\SaiQCEOCeX<YOQxU\\QuviTl`OWiYYqXNArt=rRAVZEE_Gepnw=JhHt>POZiuZiOdLXMTvc\\MIMNV=lH@jH=NbeJ;tNY=kVmxD]KQljS\\xADLH@REerxPtxlmiyyFtspiQAukYYjPMqOYtZht;DqwLYZ@qu]vZXP<@VtTtM`kk\\LEhRh\\svhsuxpYInLuoZdjnHn:QYZDuZ;fl:?fnpfuFu^ix`Y_bwe[y\\v_k]Oa]PZWy\\[NxH_rTIdvNwwOlYixxI_Y_xy`jeYqRF[wocyVd\\w_M^w;Y\\hWo;IeuHuSou;F]Oq[DFybObaH\\Tp^yqee_^;VZxXeZWqkXreywwHrUy`YQZfah\\Vw;afuA]Rol_GePhx[Ht@W^J^o?YovPpsi]PVpsN[hxj]QqWgsBAggx^rXqE@jJNZ;@^OF`[fcnN[QAqVA[YYfgNe=gnDhm`g\\[_bxN`JQ[?fmH?sDav;H^Ui]G?qe>^npnQF]GnkN^ohw_kVqlVZ:X^WxkZYtl`oIplGnZPhfSSSuEt_r>]WeiCLsF\\?vr=sPuU;oS=QBSQWLmt?MECiGmUdo_WG?R?;wfsW:mTIUwNiTWceT[XPwBISbSie<]dS[Xa]vZWIj;euwRPKUqYW_=XWsdoiwomWicsJsFkcBy?B^Ir;qX?mhX[Dp;ERmd_EUPgx[GWIGB^kF[OWd;SImvWec?GwNeEtWw:YiWMfN;dBmTNQCEMYsghr?IymHgWUAKySGwvASayrTYcGWUYytSGuWCHBqXa_DKqES=WGOFB]FGAgCqSwubrcStCr:QhX[Fpec;gVSTcwasSptYF^lQi]htnwjs@f@vtoA\\L^kbqifwdeNppwZ]qdoA^[hZLWc^plWxgE>gG``BphONtHYlnO_MppQi]^_v[A^ggj?`peqhuQnqwijNc<O_Oi_UawFQiZFuZ?fSkfTwa]vhpk\\eMCpkSAkQEqW\\qAXOVqoAqpiMmHum;pS=QphxWoMmPhXyuqeHnSUyxpXsLTKQyxUQB<tDLJtduGLKthqpAnOlKVEvLaK\\loVQq@yXYAyHLebgog?ajp]bn`R>ePLEQiLNZVG_c>axVq=OZVim[^sA^eTgsCQx]wyWqkAimuYuIfwd?fPIea?l:pclAfZXeQNeQiwKWZWPwv^]nx\\\\vfZP`GOm_vx`W]EQiZ>uo:PpxIJtxkhiRaqMTeS>QxOEJqvg=F`bGuSwZ:pZ[HrB`qyGbqIusWtw_tYIoZ^bQAw:yZoN`Ey_tF`bAdYi\\D^clXigOdpWZ<wdcVtpYwVieUFs`^ZeIr[Wj;hfSkfxqaTXIyTdqmcxPH<pB\\yBTni<nmdkKqsWeKAak@DNTiWJQqQlMnpnBdpH\\yuXJ:txndOmdu]@KSHRApJWtvEtkuDnZhYCUxeayxlXEYmpXsRpV^imNhOeIJ^UZEQPniDfuAVsuhn=`[S>\\;fclN_^pnCon;?wX_^w?yhykjnvg^ctHjH`muP]FhpInxcg_Jo\\<awxPdu_r:gp@WZNiuA>xsgl\\VtdagvXyRf]S^dMgv[>noprZha_@gq>^biuuQu_YcmVjJ?vEwk\\xehQsbnpNGooAvjHr:QP^oY@rvxyPWiHwkj>]T@ghVZQI[FiZphxffxBOfTxbkgt;oxHve_@_q>h\\Q^hg_]F]kOawaZTieHhkkFyZQbAWwxVbe^bfqj<pcsNdWi`?>c_ywCwb@ftJ?o`psYvmjqqKVZMvp@W\\LhuXqZb>sLfjefZuor@?aw_x^NdB`yqips@rt?jRAFm<gxM[hIeuqWi?[h`awZCbW;vo]ByqD=ecRarNQekSGeIDOig?Myu]I@My@Gweiwauw:AFY_ESIvUchW[EIyRtOFYox=;SasEk;HqqSgywTuHJqU=;tciIJIwb]eAiDO;ELiS?MUcec@;GtSf>KGHyGnwtR[hAUCtOI]Sg>EvBsdkGfCkcHuE==CcUH;gx:Ih;ArlJqAwhdLNxMXTW]HP@UN?XRXLKl\\PQErv@kZpb?gnSPpjv]kwv`WlDqf<Y^aWyk_lA`\\AFxnOccnm=g^TVta?`XqgSG^gHbrNneawvWiwGbeiinxnLf^`XgDGdeOaLOmQx]GW_SFeOGn]fuCfZdFtR`\\>ofjg`>In`fkFNpWyqZfnmgoMgc;IhcNy?_iIyysiiNqloY[>qZ=VSbI;tXwwygc`UbBaGMKwDkEuAtcuG?sH;YXiCvjuB;WRBoVwUG_mxP=rGYS[chdmrcgy\\sIBuf;EtIEefYXjuWS[xJGRuYiGysTYt=_Ru=T\\ux_ItCGFeWGlOgHYGGchTwdCQb:IGC=rJgwbKhgcRPAtWGG<MIEyRCkxpIYfyEb;TNObOghRGu?Ac@]fTeIGKUwmClCRTCWH[wWYr;Ig=AYhwbPQEccWOuXeIr\\Ub;gVSTst=NWYqp=Vq]XZtl\\=U>loJHXUpjshrPMpHPKaHS=IJ@YyWlRtmTkeM=PPhdKOaVweQ\\EV`\\VhqT=@NJ]WPMV<aP\\DV;toNTpi=u_@qh=T]MK[QjBhJ<ILBQj:mLByL[tXXYl;`K\\ixF`VgTsa@K?IYWPT]@rcIlrUrHlSC=LipV>UuDLlPUXmpTIQJK@MpilwmMSPOMyUnEUdLYrHJvxL>`tl`KTEJ<=O;PSFtJatkjmxRIQvtsAEO?\\ve=NfTw;EV=H:NiZ@muogUXihyl:Prjpj`yu[Fq:ofp@[l`lgQe@Qs\\ib<AujovZA]wivKO[nAl[FoAXefwgbNgUo[[gu]peIFeWIcb`fkff=FpJ?aBNiPi`uVdTfo;a`oFeZHxa^eDViVai>>no_]h^^^VmDpvuG[cqhPx_:?\\nOcOPo`p^UIdrf^;_pXHnMVrJGt_xuqGldvwf_oLfsjGs?O_;pcFV^_wlmViD_ggo^nNoSFg\\?\\S>_g@_PN[VNuy?k=YyIvpXwu@NZeIr]Wj;hfSol_gajOqQV\\qw]:VwPyhQAtvi[Lx=wRZOsfwTT[svwDl?X=IRtQb]Sf@CiAMVR;FmcYNQem_b;?v[YhY=vcwbHSxwwTxQdDqtGMGKAFwmr]kHDOb];eX;GJEuCEcTOCmgfBsdL]u;ud<adEusCsEy]tgagkmCaMTLiG?oS:=SWQgJ]FlIT=cWBSgT?ILaSnIyvmxfADYwIu;sCIcX]Y[Qbp[fTElTPYLPptHLkUyP=jCeKwMRL]P<@Q?tTBLrb\\vfInmaQkmwCmkHuM?AMmuSMXPE?fjHR__lp]RVqOnjFF[DhjvQfNFlHHhna^?Ga?XwfV^FYmB^aL^[OA^[GgkNvpilJHyUH^?pe;gwnw_Da^bopBFuZnkOfs@Pf\\_f<xnXnyoocY@i>x`XYyYA[]hbpph\\>`L@_Na[]AvHib>figq[?qZgIg<YuCNno>_Zikr@otp^XWcKg[WipBFaywwdVsu?]fy]b>xVY^=`itAyJvZ@wbR@]RNnq@nJ^wZ?l^_f>qbMyoWNiui]tqjWOs?FsWhtRFqNfv;>nZ>hlFsaqmxa_aqcv^jeAqbWnKP^YweZ_kkXtC`oAnjGnZPhFgVWyXpufACehgh=KfmusTkbq?tVMFkSsNaX<qXm[Fc]cJYvhIVnwG`=irGBr_r>awnKDPwD=mWYUu[EWp[V^MfFUFJ]RtSr[GSbMT\\AUMoFTCGWmR@orS?EY_reIWjOEyYUpwHhAFW;CTKcxQhEuwFGfTeT>qSewx:Wf;ARruF;=iJmWoySMeCGOCnUgiMBsQF_UVJMsjAtxoEx?Xh]dIaeTHlktM[IqbDlKuPCDoDHsn@RSdR`]KSHPbEKwdYHTyI`lrTyJuOeixNPwVULgArXHnCmKGxM\\dKllv`qvbyMbyVj=VJqJ<J=:owUkva[ui;H`SRKerjQH<wTjKvHChdMhK[bfkG?[TpcB=eiw;sweyF_DEAbZCRMEg_[Tp[DS]tAEteStbgtcgHMKedSB=CbP]FCUg\\=dk;W]GxvQHAqfYoVoQsE_WQuW]AiScs@ore;CtQD;WUK]VLuwpQSm=FSutWGRGOvxsCOCEn=dykRnoYG?GKaERSGlIiMUrvEw[IT`kbD[RtcfXktb]FOMeKmRJkF>Eh@EGG_X>kgeCdgoBdmci;It]gFQxPMrTUF[OuN[eTYXT_fTGXoQxO]IYYVv]WVGtKIT`sFaCwiywAiXmYr_SEN[guieGkBPgVSTw]uwhiJ?qnOUJNUL\\]k@=vZ<OZHKC`xu<Y\\yojeRGdV^dpRyVsEQ[qsOujghkBHwwAXj]p:\\xZHjRUR_PL<mtAIuMxvbTy=ouIpyVPi]VnTffRv[<@cKprsYg@IgWpbJGnaxnQF^vNn@w[Oh_;HlKFgfA\\@OkLX^ci[>fc_?[w?`Spse`\\C?k\\`\\WV]>x_JGbxNfZ_he@fKHjr>dvfy^AZIamV^fjxelVufXtFV`pp`MnppNfdVmcfxWfcR>_^@j\\Gs[xnIInaxs_`T]f];dL=XZMsaaxPuEmUcwaIt=wCkXpSgfmgfEb:ssmAXVsbamesmbmsVHAHv[IvITvifTmtIieGk:fi]hag?_=Gp;?sIFkng[AwcK?vNnon^ntibDog:TB_XDqRg[vHic`stYiWJug_[CoYirke>AfC=sBSt>_FP[cIsE_Ixawy:WhaoE=MYTsSxAdGgg:xw[HTIASLDSThJVeqkQP_tWNxutQtyeSk@T`]nqaOqxVYIVwPp>xwoItfHOvPj^=qbQnU@pK@WpPmKdQ_uqOavFULgtv[ANeXOF]WtdUKhp<HpLXsMxNtIOGLKhxWPIuRUSRemI@myhLk@QMLpv`LkXTIAOuqM=UjxDoL=y_=MYYwmxVd@r:AnAEp^QNoPvrqm[mMSyyvtmtdyI@SMAmblkBXn>pR]ps`qv`toypytdQwdqFlKHLuXpJPYJ;qJ=TCgVw]gvAicQRZGsj[u>ku@UxhCHm[W_GBGoRC_fs;R;MYVkumoCBKH[GCL_dGgsRGuUcHheUi?FFwRRcx[_E=]FLMFncsrcrZQHv[HCaxxWVrogAygw?xA_UWmTNYGyKrkMF\\?sJkHm[fjAUWqU^iwEuu]axkyvskX^aG]SBA?FWcV_EF;yx\\KvbSfNYv\\Ai;sB@qxlIymsSkquPQIi_ioQHS?ckiYAcEcMf`MhucsB=bL=foGvnIhxKyDmCeUgKsh`UefwsAasXaCSQUI=wY[xrcYhwcXoEQWtAuBsCYj]eUwhq;UUagMmwmEERcxZ_BoOi`CcokinEIxcI?Iv=uBCSfJ?HFCc\\?cteiHEfJ=VauVAcgOKUe]EAIyscywQUPyRAqB=SsllloIpJium=vhIqhqNyDoHMseASXeRDXWbTT[HlOAUUAKRuUGAS\\<MYLOlMXd]J;uMSHKb]RCTQOdRjXT\\]XZ=mOip_mPpLRpTOKTl]hJTpRKdnT`NK=wjHRgpqGAxJAMuyxXdVe<QAas@iOPxLiUvDqMThxFdlDLvr\\VuuV;htgXOVDQnMlcHk]]wU@QIinEyLRXUR=rOhJ`lxOHXvdSYuWCXXAmsmQraqsJhJCtWYaYMpVTAroiMFUNyiPG@PB<RcTjPmJIUr`qRFCqsgqCUWWcSmeI?HRkcYcw_IgakRs[XZ=dkIdXmR@;VYatncx@Mc]arrcrN?sKaWnSTDgITgfS_c_gtqAxXSdBsfVwS<QH@_GEAwcIw[;C<[bJ;WgGH`uHJGuooBPiyDqB=S;XKIaXwyUmutbHjK<MZTn<PvuASXqrRPQKPjGQm[EvppVxmN<IXody?uLYmLKlnY`S>aP<ajr\\XSyPkmkaxsyDsOXWQDrsukohpBXjAUP<`TKtr@`NCAUUEqCYmvUlwXlADXwtm;qm]V_uGeUAqDGqbYde`f>Hj<Ag;Olp>mUOiUxrHiylfywW^v^hlIiPodPGuVWydfxtgmDqb>wcs?k]xbIGhtar=amuVy^VmUWgfYiww]igsxHrfqxFFhRP^\\?lB>l<^dxYoi_o_^eupeaV[GVkqO^pxtM^q<@v^Itxomt_h>xrHykjxfv?[^waThf@pxN@wqfZnH\\b>^<WvFF[>GnQfo<ovihu\\bGMyEYYCUdNofh=NG`lL`OM]TddPdhttTV]UNp`XchXYYXxAyIxyrykyLwqDVSml_EUPUuAdSOLPR\\L@pJjpj[ejNaWL@mGLnfUlbdoZ`ro\\UsQPhdXNlMO`N\\qvvUjetWOAqoepCMlRlxgYOmMWt=LCuOK@KR]uVqVeUpBIvkyLrQtayyJHwwxnjLNZlPEVmBGk\\>gNg\\UXgkVhmVgf^si@h`arm^xNXyjnbjPppvrgHmE`j;obgPnbhw^`rKHbcfc`P\\XVayi^DgrXobAonRn]TYbL`^bgn:w\\sfhvYlvoXyhr]vvyf;;Im]vfsFH[e^?Ub;hO[WKOYSCUL?fLSbCAsuEEbUdqUGH=fSETNqhL=HjaraobsicYmuAyFYCE`=VBYFNADdODo_WUOSLaVukWlgDA_T\\ab@MdK_VTsrK?IX;WWGHJMIFavrIH>?xbgtd]HTcSL_F`eXoUBggE@kB@?EYsECYg]CC[Ur;gXYQh]kBPg^I^amY\\`iwqWyjQq[qqyixGiuyYbCP[DxpK^iE`lSohBGo>H_ufd?OtfVhr_gFhawXuBw`]f`TPgVPpvv]kwv@Wj?HmB`_gFtb_f>_`bV\\[Ht^Gm[VcoRjEB;IgMwCKMERIv`Qu`SXmsu_=fi]d@eH=AGCKrjGhossEwYmyVvEyQyymmBuyfbCYM_WgGCNGCBOe<?GJ]FKORUcKiHS``TeYjM\\Mu\\YHxydykxYYpMoU\\oi]OmlPlxlkHtCqsf@O]]KAuKVTvIpNxYSx@y>yOmixUtYCythlYOXkitqAeWxHj]hJhXNSeuP]KrqO]lmIXkZMWyElyQvIlKmDPRySZTVPaTWPYVTTg]u[HTq=KTDMC]ojLSZdM;xwE]UI]X@]JtqjMlWihYGhyMuvSlMtlRJ\\PSUUUuNCMLThsNpR]TNCw[cywWQpxGpRAfZGePTPyG>wCTuIZ?BA_c_]DYQRjiGV<WL@pOUKRMUC@uTuSKPL`xrd@NpQnciNPeTdesDTMEIOCUp:PSLLrZdnPUSbXnk<MnUw_dkp<M]PQi@Uh\\w[@NHLPypwJhjkdktmRJAsjLUZ\\V<YYmuuZpuviP@pJA=Qldy>tmt]vq=YmQyyproM[Pg[[W`?FgBXb?@`lXxUF]:OcAHn;IhtQiA@hVv\\=Hw>h_[^Z@A]vvu_Av^I^xIuBy]lIqApqBYwY`iGx`hnqHilUxlSXuRHrfOc`YoGodNgmMXtw^alAyrVnwga>HcFaeoDqGtZeYskVsmG^EWx;fXUt^EGBEC?Qh=AtbwsjAgAAtjwRswt;AECQuDYevGvvIEIseviW@sBaCETkE\\eV_ecWgeFouXUbL=UPYB;qB=S;IbMqE[;wf;GOsI?AW:GsuSBRSVJORxaXySxMmiUoS=KHNUwJgIYeSVwIyWb`QG<aU>iVAcc=eGGEUTMcrgXwGs`QW<uw:WBaQsZkBlAVJgHb]BCCT=MxUwUtyDnKWjsitYFpmXh;hK@XEPlFEMFpXbmJGluXhyHtJ`pQCIv=tVcIOGHTpunSIUqAKdINC]VbxTm`qIEjn\\P\\hNPyp`=MYduIqmkYJv\\XlYPVqUreKq]Y;PXYemWhWCukqdsMxmrysbiwW<RBDKB\\jbuOTilBEw^iYCLq<ERU`LLPjQ=rqqRS\\wS\\VfxVVxRI\\YLhxWhPdDR?`oLHX[EwWMOGiP`lJe`SYFbE`lGQeBipeh`hfeWIfwG`_Hdm?uyFa?AuX@ZFOkKP\\[qnnaxu^xpQqRffbhw^?[c>k\\frOY]y>fv?v[nsYpaFqywyZr`icokWh]?AxjHbcFttyxlY`rYwp`oY?fp>]Rol_s=SrR_isyTqIbbGrnMgHayrGg]qfo=dh[bBYR;my=?WnuvxyeliEneuP[wpSFM=ROcsgMDPAco=RLGIJocZYI=AYXiBvEi<?RL?E=qXwcVxmF^qtO?bDqRDAyXQBSOdbUTAUDLKgTCVBCU\\CIymxSMyDYTVuiwwdUUGLgdOYInawkAR;MeBKrjKvHay?kUyUy?mb@srS?EUofy_IGwWH?hnsypKRu[HdMej;t^Gg[UYeubSIyeaSIeI>qekYRFuwwcrmucxIBGSxpchjmdnKXScwu=eImesiCDefXosaMuXCDByWayiyiiYWeJKfMQc;AE=wFvmxniSkCtuwBw=HYsvBQdFwSfeI<qSrGR];i:=DvebUUGu[gimFVeiVuvlYUoMbtoVvMhYwVYseZ]W^CBL[CXKSb]UIAvrIEGaF_OE_]BSOFEQsfgsgOTgwW[QIHciwSr^EuRcs`aC[=WA]CfwBAgC@k<iYIahHArUoxYSVJqRMaToMgSqCOaWAobdGF?uTgOypeCJUBDEWDMh>uiq;s:wH>Aby;cNKHySfYqeaStlIr[CrvwyPUgBui`Gc`EDQWEbEx]KBmUeGAi<qS=MdNyFS[wSOViArLcr<]b@YFLIBUed>gfs?c_WI[chdmbeYC<_RJSeO]hKabdkFC]FTUEnoHFocFWxCOvaGwW;HVAUxyEcyx\\[E^cc@oFE]Ccmt^iwEuu^aySwfSSES_VbwYysBqay]kGvWytKS_]FKGFH?FCgHUUUomdPwDcmBG[cKaCnycjIwamYQgvowRcobq?GriR@mBHOHNyX:oxKmYuYHSiyfmYv=dduI`gE:acHye=IHLCFV]IYYvfavs[dH=is?DkigeICeYGoKgUQeUutT_WiwVF_ctaIpAWisSvMt]]Wr_cKKEj=HF;VBAtfUDdAddOTfeHM[i<[BoAE^=SL_b^EWSOUgMbbKw_CS^CU`ubD[gASbGkBykRaEFTGwTKXxICEWtTUevosoysh=cSQhfSstYydqgwsuHcBDAG\\cDJuTokGAsWmqS]iChoHiKXakiCErg[vIgt:oseGvJgvaeta[v^sFumE\\ayZYfvCIpaCwqyZcIXuCX_xiQu`ywP_hfqua=wPQI\\ERxcVBUFTuwaSv`CGyqCQWSR[D;mfRQg@aGgkbfeWFAhyMua]hvCbf[SL?EYofCGuVacbwwr_VkEcfCCcwTMKw[mR=uD:Id>MSJgFTSVnCSLKfNmRyuuBSd]urs_ij;rfQvHkg]CuSIsJEGrqYKghgWwVIUvUdwWYICHt[hYwbH]YPwivYwyYeOgbsqtVcYIcfFCR=MvCqIVCwaiDt]c:=S;qiCYDfYv>qwagutaExqiO[YTyeaWFWguywImWI?[ScURR;rtQBf[GN=uXusb_W`]cHOyvmwMYVvquyCe`?vcMHgGt\\cF]SF]?S@mRTQyyGX_ciwqCAyspIfOGRDgTpsX`EDdaCeWg=[fcaFSmvJgVSiIyqgrIh]WSPgxkmV=GBqub:oCkuxqQuu[dYsyVSiayI>[hdQSYYxrUEP[GEQhxmwTYu\\EbZuFg?XsGypsGhayOSXdqDeqVO?RnCHxoRN[FKCBRSbKAVN;fFKIo;EQkd\\IUPSWm_inGy\\sy`qtRsBwYfvMYdYxvcHsaEuUyqyhXurZ;diYYA;FCYr;Mc@EFk=BQSrTKdEaDrGBnADJShkWtZqsg?cSWW[SuUOe[OXSciasgT[fjEcN[ghsWmMxJyvrmy[yfRmUS=viwimyImGiO;Hlkv]CD>Ed[SSZouVavWWSYIVZwWIsBpye^_UVcV^_xrshayy];CG]DBMr:UfN;IxMS_GHIUHRaV\\]xjSv]WysiyyMxYQxYkipyIjeywWSNYgu[DvqIXWYdYCvEvmsi=qiwwbKKR\\cE;?RZ]shuY?CF^ybLMtmuHvEWVur]=iyABMWrIEx=wTyyCLAhFatxODYWyFAGyGyeSyciGqQDE?edGCb]VCCVLGD_SU^Cg[SspufHGE[;HTKYtaFUYU;ogwaI:<L:`N\\@NdtY:YYEhN`^]ZGgCO\\?wjRoeXGfcGo;>j]Auw?qowimHrZXcqIry@wtYtxQyiW_awhiIbywxSikHEOQhfSkmEtXuS:<nFmrUhxYLxleyU]UDmu`ek_LTiDREejJpVqMUJHsaAqUdtDtJSHRB=PHmYg`n`dlCTWkQLUikGlVYYq?yKQtU[IqcxslYSAqYGttkERR<WWhOIyUwDrjujFXQ>lVPPmTmj^MMQuM\\`vi=TlqO\\YS?Hr[Hm_]ofpRVIYi<vpitJPYoTvRIk>`NOaVn<kFembTkBT]DPr]OglA\\Aw[WxbtGZGPsEagia^riZCWpXxlRa_Nfih`urGm]vZXffIar[^iixlKqyA@imQvQIcN_bP@[dglN@aL_j[@fpohHhk]W]Vnm@Pb[`ssXtIQvrI^mWsQ>uSIoJ_x@AaqOv?nxiYaDxvpgkN@]TWkFxheV_wao=HbaOuP>^_oalQ`xNh:xnYVyAaevwxLvpiae_InAWsvnyfA`wgiH>mFhngpZmil@VwUH\\Ohs>Pg_V^Ff`xx_cvlWNcwp[_qeAPb;ovE@lMP]Eitq@muHxaa_fnaI_\\H@tfo`Shm?@^BH_QXkyVtYIslpiKaajHrZhaYapwidqaiAqx;fq>?lS`kJgZ>P_ZNt[oiP^noH\\fWttvevodlOibVq_OcHsweCtOB=ut<ehpiUp]B;QPPysXpPseusas^`o?UsvptrelYljYYvTmXKPkVArkiNHXw\\QSqqotLyR<R=Hl@Tn:AK=LJn@sEQWD]MF@P^=O\\dLlttvhs`UXWhvtQLEUQE`Qu=vMaMTDQDuS[xJ]]P<]V:Ym:yKCAm[HnQIuBlPcmT@<tCAPMUr@hq=EN<tkFdSwLSSuUGHUThkRMme=LnTPdepxMrFELLTLbakrDsBQTJmo;yxE`Mt<XLtojYuVuUgHTWQqF`x\\Ln`@NHdPXXUZEXhqNqlwvHs;IwM]SFxMZMYdILvmKjPptejj<kBUV;MLcMj:=pspU_HtB<jvajPuYYAKY@QwIYH`MttRNtPkeViTV=xRkeUY<uWpRuXqeTysawMQx?`sJMOpIXnAva<yoyLxiJieUyYLHxQnpkMynSEo?aSoIQVQmiXxhivdTSmIKkUTMMx[xpAYV[UQ\\dTTpq;ul[IXYHj[uLIylbenBLwE`OVaypTOetmZTSAAjKlv`aMPmT\\lkVDOneS]LpuyWeqymAr@TjpTtTxxcTq@=KNHsJmR]=LndT=hrbmm_AW;htrEKQMYr<QuXxPekZdsL\\M]Qpi`PGqulaPuQY`XxWxJ@tTtXqE<oByLuhXHaSSml_EUyTXgIl<`Ra\\oaTsvUoliPxQqxyvfHQEAs\\@n^ylJlkbaMnyp`yY\\Lu[@nmuUeeUkUqT@Wueu;XVJpm>yOtAqr`RGAlqUOi=X_Ex\\TWOiLxexnylsdPkmjLxW:XUBlq;\\U\\lPOMo;PVoEQ`eWkULGiXt]y[lxGtk\\=OLPLMUW`\\TqhPHpM_usbaLmIrWLMoaktMlKaPT@ReMnbtYMHWTLl_EP_PTiTyqqmZUpkAPqpPh@n_=kCaYThX?pTL@QHDqm@xPTxEyvSPum]jwTVA=QvxwcmWWamaeWcUM;xkPqj`UP?ILw<YhEhYhfKy]_`dRfwtxwaXe>_y[QuWWrKo_oIxcyfyWkKYZU^dnytsXpn`[;OsHAk\\QSOs?ytU?gb?r[YR=[Eu[fR_m=ikUiXpxX\\Mk_uj;pQQPVI`NCaKS>k]AjdWvPFotXbwp`Bpt=`sFAgXIiaNvBIlxykjyhp`oIvu=v\\FNqaXZSpsBGj`F`kfhOWfmfeaWaUanLhgKatsgpDhwfWlG`fGhwnW\\Av\\C`saQddOeUvvNFoWnrTXiRfhAA]lqbcYhtIwmOySFxAA]gnkkNeTvnbalTWkb`suQg[VupQwPhfSwyjfwMn`TfklNKCU[YYusu^yyVqyQ?eloriKyrkg>srZ]ElYDWiwGuWueURmiN;FYqFESdA_BCmIW?S`yhkMxEGXnkrk;ixWcfSS<_H\\yuvWyiGtDAvCsbMYYE?CkyfrovdKSBMECEdOgcTshh_bfks^_cFWybGwLkcjEt@UdZGgQYVNMT\\aucwvr[xSyfrExUyY@MEyWRoKScWgFoVLGD@KCQixSquV]VuuVS_HE=rB]XTYspQE^_fBEFbgTmKrZSfNmGlgUugslqroKtfYkwPJIhY\\iJhtUs@s<auTDXVDvtlOSmTZAt;XpF]kiYjPEKQEuSyVoXtK<K[ay<]mktsAeKn<nbllVmR@pxk`PM=V`mq@eX]lv_qr@TOEdKPylZIxAyNsYjymXBXnuQJFHxsmys`LOhvWLmO@tNiS@Qrt=sLQW<ptDpy;QQ]UTiQTipm@eV=\\usXLmioieNvQsi`nrqqQIOwPWqiuPiy`IjBlJqqoG<wXpR^HT^LQ[HndaO>YpVuKiDXaDq?aYlTrDMqBeTgAnBAKoUWdDLltmxLuTxYDpJOPWBaJ_LsrMsAIsVmNVISpQyMaMddM[AUyIOHuKYXVn`P@uW[xKCUY>AvhqWIpX=TVSmloyK]HtB]NEIx<tuRQyEly^PxyXNDqJy@v]\\UKxoO<W?PjqioKlWMtMvEs=QJBpTZ=LL=N^HREUJH\\LEeR>MLkilEuy;@OXwaqyslOf\\o\\jIkC?uhxbfns?_sVgkRxqWarkWs^Hex@]SA]G__FftT?r^ar]^]YYxvvfHhi@X`avm^inqwyuNnniePypU>nwOj`ojaqlRhutHrGHmQAal?x[o[fYa;Iw]vm_iuewuZghgWZ_Xm>GZ>fkF@aNatFOcRasJP`YW[j?yZI]xwyqwyUnkYVa?iveyoZ^hCXhaom^IsAyeZOiiIh:_p<GbxIjvQfiymlyxPWo^^_IqbFquFFuTGcS?mc?\\?qjMvru?i^ae@qyCpZRPZbwZYi`Bvc`I^L`[A>_Fwxjnpa@sRal:Am:xwy@]Z^j[wynw]=VZw`uth\\jQseVavfxNA[wfasyfmY[wIpRotYYr=F\\FNutxvvyf`V^oF[mHxgnw>yprh\\Ywf[Vq=Qhp@b:WlBoZ>qiF>g^NjlH_K_`WiffQeg_vOo]L>d:PlJHjHW`pftTfpbwjuFrGouc`q;atDqiHvxWvvrArcnkGvm^OpqO[ah`qht@PZEQpfxiR`itAdXN[PNjsnydWvyYvUhxyP^mQ\\vvsEyslypHay]^Zqgs>HwVXada[Y^wXytxFdh_rWggiWxkpvPYhCWtTfcJAi?vkZH]kp\\vXsTWfUX\\Mf^FnjBaffwdMnviatrwwDQ]UYwTHo=hZ\\`tJNl;NjJfcL@_^n_xxvM__PF]UV]]aukxe\\GnkhspQyG^nF?gPQ`NoZSolkWh`Q^uq^x?r[HwMaxqqkl?fIYlFisGQpr`iMFfD`ZG`knfj^Ncbxt\\_d`HxV?l<Iv:qy]_[F^yMoaoAyQFtDO`n>a@AbyA_xxdtAegYlTYhxYnJndPPbPnfT`^Gq]JPjYaylaZIwapNrCYnw?ahd>MRfaF^KI]cTD_TcMT]?TT[dKaFTAvQ_UHsebCxsyGYUVuUVMWxIcE^atcOHUUUjywyiYOWtagDwgiHyuxqrfSw]=wxoC@sENYc:EfBgXBqVtGrdMi>ixbQDiirQGiSoU]URiOtZocn]FhWv\\ASACG^kC<CbA_HlsusAehOEQQCbeb=_GM=WcGtLUD@iSdEuHCWVOHYou[qftucSQuFScOIYTCSW?W^aG]gvkMsxuCxWvqmua;uceRPgVSuYQsXOKYj;xPexA]iPAYOgDPCGQKcsAC;_fomvygDDKil;rhiTX;CTeR?Oi<EBWWITYCNwIjoRWUwsiUYMThsFnadL;v:KSNICMAdTeG?]V=aer[YVgRqebTeVMgp;dPOmrKPj`]o;Aqfpoi<tiasj]yJ]R[@TZMXnaKmXM=aWp\\LXxnb]tNDVZ@Lr\\JKQMUhtU\\Nc=kiilrdXfIUhlUxUlqutiPl`DKhXvMaW@\\kFtSJMOFlwhLMP<Tb\\lR@Mu<rrAunUw>dl>my=LyH\\YnlXYywxIsA@mTdYRXo`mkjLojmykHNxtxcITHlMdIrc<KPQlBpRVn]^_tUF]Gqf@_m^YkNiaYOvtAvrN\\[>bt@hlaudvfYViOX\\Ax^rNhba\\DGivgxep_Qp__^xpQc@nZv^p@FgEp[TwxKXytBgewl[f<CR^WRPSfSmUimYYwddyuZOFpCgEQGDIs:yHnIsxosScfWyFbesUeHseu]]xhqi\\WiMIbj;FGmUuGU\\Cx^wbp]CtCHb_F_qTjeeUidU_sQuVssIlAGI]SwcsKGv]aSH[SomDEIulofPgVSuYAmFYqCeSfRwWVIvOQwqGUnsXjQShKtQ?EIAFVCdiUuUIB[WxmgUIILKHpcuxl<wDtJqeoGTwDTKqeTcXrZQqLHjXum[puX<Lw=O\\LrNEL>Lm[qq]\\QsijYIVgeYSxth\\Y?PWoPs`eQ[xnAinKaS;AyfxWFYN\\xpsDYnIUHdSYPna@Q@pkA@ofXKF@KBULCUnPHnoXR`PMfuTaEUUAm[uw^ISpySW@vnIxa=mWhmamXpqJcMlJ=xuAQt=wM\\Mx<XTttoQqTtkS\\kcelWALsEPHxkteu:yuOmMlQxwqvXiQAIY\\IvYeVaUqCikSylrMxsQP]YyD\\PFMspqTDqXoDVmUN[UV_lVaUQ]LKnLOGYYS<qx@nqxu[xW:YnNYvZIY<ttEEQsmy_lJDtRcxPpIpsHt=ayvXrQuqTuV^]RjAx=qKHXNutyhlQPEYDQpx]kuQPR\\YJuq;`Sa`s?UPFarq<qS`U_QUlEkSTX=`sCEPHPrkeUVtrCyLAtuOauFavEPtTYQ;pwpxxgyTduwJ]n:=QghJGqjvXM^<NJaV@El`HOC@WlUpkemZDWlhuVQvKHsAIYdMySlJDUjNhqv`qWHWQyRlXUSTsl`oY@snmpNQm`mtZYwexU[imbiP<PTWpmLuKTYtBuS^YuaqsCuMMiYpunmMraquJ=liUxUEJ[hP?`lHiwPAs;pwvHlHilNpJcAjnMTnTu>aPCTtF`P;HjxHKxdxryLctluExwujtXxY@UYUU]]Xv`R]plKpN<`PEDUTUq<iveyOm=VYIXvuq>ukqdSVuM^UXaeMAmlbpWa`r[\\PUHLmXpm]uRHYUHskYVrmW;xnXTy_Ls?_qtYriX`mViOXjAnclauapiOX`ap]yXwmXsU@lowumIhvF`Oi`Q^sBnsWpiPPds@sux`_VlAyu\\GaC@ogxffh_Aa_Iibffs>_oivrB_Zwf^QPniFcmfsPqc<wyjXsRanIAxrxcsxt?OcQHjKXunrU_sHqe\\QsOybBWVrYtycgmMv>WrnahAar>weAWGuWipowMsx_=HBiuWkCLcejqRgYyvugkiShWgE]RX=bY=xkiIIsrcKV>orBStcsUakwwMgPiRRguhwBWWwPauMEvnovtKevOY?GXFKiOMuHIX_cvLEcLWU`OUi?hxghDib?whREggCHV]E[avrIWteyx[hP=b;=CusYKQhfSwaGFJ[VTUhOsWjQT]Ye^gfRsiV=rrmFIcBH;CAwxGEFlkBlce;OB[]F<uva@qXXjK@n\\ekPMWqeSSUoULpKYqwqKTIvZuX:DrZ]p[dsFDRPTLk`RBHNDMxspyXPtbdl[]k[ijIiyhtwFaWk`qsylBLV\\@tJ\\Pm\\MQyVeUXSxXhdYUxvX@yAaxoiKl=YtIShxutulEtLhLvuMlZpm\\hp^HtBEupQJpppd@W]=tTEPt\\Q;ynYhyGlmxMv?Lv^Lri\\Lkiq\\muvekuyXtPokLMQilfYmTpRsuSlUXwyR>Ej\\eWclV[qX:aug@lohnRHr[ukYqyoIOXhYd]jKHVYhwDMsqyYrhSd`P_pYCxPZ<kGpVoEQ]\\KndxtYMfhWW`VeUxf<ncxtE\\ycymPAMSDLvqyiykTAVZeuQmwu@VjXQT=NTUrEqjqQje\\qWuYGxM@xOktVhEVvUjiiLlQpoMLF`tWHq[hmWpjbQoYeSu<KnXoBdpD=uoeTb@Wq\\sNLPYISnxX:MRBpte=mvQNFlqiYNEMlFAOhuTiMxatwvyUvmyRyOmatnYPFhxGXTlQSbUlqLRmXTE`OEQ`rgwggvPOp;YoUyu[Gms_]Y?vsq_<iZVFjjWeUXwHq`xv[:N\\CAlu>kjNj@Ou^>k=nbDX^v@drQ\\@A]Xa[XAvL_iSvdsho<V\\sIbyoqh`ooNeZ`cegqSwtbXj<`^Kat]aktHxcOgGOl<O\\a^ZohcPot`GaLYxJfn\\wa?wfyFcm_jOAiKFbKpbgV^Eh^DwZnNlu^uV_iCXpAwq:avrIfHh]rOjEv\\XavdipE>yXw[<FbV@_DXl=`ciia;`lHwnuAp]AaNVk_Ok?QheYlTialgqYQj;Wqi>lKFycQqrfgjHqw@rfiwDfsWP^EYhkV_mI^OhoNvsQ`aqasBvmv?i>hquojjgaQPd[Fv?xs_Y^pQtCAdHPnhO`Pxk>aurPfrPyPq`kO`AOm?^vAhcHvdipjvwwugcXfin`sSYpw>_Oxoo>suN`UotAytww\\F>jHAf;_n]NocgjqW]iOxqftypfHau\\pvfAdpYijgeIF^mQmOqb^yt\\XaR^pno`rfwR?lIa_dqi:wdcVqPYcqwlrXluxt@_v[Arog]^x_KNa]gokPr\\qr<f^a`cColsvqiI\\paxIOvsn]\\whlPtwwp[vpfVstIebw```o_WaVW[iNlsI_hxd:?a<Ne_Hc?`SQfsICY_YuOgFOV<mckaivaGTAWx]rqIiWou@MCCwGwqTQOYSwEryhD[S^yDtctbqwxQIy?f;UG=Uhh?uTqSSKEHACMcRVCEL_F]UWuEbEsTyWs;IwM;YXEcLwICoc@AUTQiHEi^QTUqsuaD^Ch`OUgOX]qtU]Ey;xVcywWNuMxcMoudPTd`UVme@_OH`t^qQXdAq]_Au[yjj_nmwtxPbnojBohI?mWyuuQlvwjU_xA@wg^][GiPAdWQ[SweD?ohwfFn[r_ipIyknmyof<hyuWcrneCf_E@_iW\\i?c[@`bVlqhao_kZ?obQhbAiiFcNanlpd_ow`Qajx[[Nm>Hn^ivQXZtYyQAy]xaT@vjIvlnma>tTAuj?fw_oWyl;AnWynZGaT?vuWuYavG@wA^uFqo\\N[Joxu?lLObepwnYydgdyapTIbZqu_a[qqtwpjWq_ThoJ@lAF\\Mx_TOxW^h;Wx@QrI@oNwpCWt>xbaxmZwyBa`BNaWPlgVsl`oWguafcnptfafUauHogZqlV^nUQmx^^?Ww<qwBngQysuQta?bF^pTNj_ij]Nrf^vWAyW^lLag>WwBg_uPcMWjCacxGdWwtDah@W\\>pjnV`fgtlnvQQf@yrwOnRWtfO_NoZOQy@v\\hfiAxR]yLSYasCk[uy=bxsyRSeesgL=G>_HeEEGOe\\KCFCSRCX[Qvu[IyaRWoulAHumrI;xFYdyObkKb?ivSKhfcVr=WVWHaoE]]VruSaYxbuwFacs=T<CRhgY\\sgN=E\\]fiaD`Ke\\eWcqHoQW@AsbEdakEU[vQuURYrbqeLkrK]TNUdrkcCSt`CTPSdb_IR[h@WdjKBvQbEavnWsKWHU[GHaU\\qroYBbew:kGmWhKsYkyDUAyxmriiyXaDAoCO?GO_EUkCfwcoWy`;EnWgtahu]DfwRe_Uc]iEyCdyGksVhUDuCF?uh>Wwr;EcmuYah`WUqQU`owQAYYiChIGauXIyxTusOqCAKRnWR<uTqcSA=vtmGUgcoMvjKVbQyBCUTGvskG=ei][dwQxWeCSqE>gcugVSmtYQsJIu`yRt[V]cU]EIUwroeev]h:Mdi;IhquHyhpse<avMaHeqf@yxsebNeffMgG[E]QtFQBXAcYAr^oBK?S^KHYGF^Mi<;bl;efWW^?FUiCG;G=mfFSEoadSitBWF]eB\\UVbwTm[T`CSM_bSixe_UvOyDcywYRFgCW;ViAus]RtCsVQvW[X`Ad`;d>QE_WD`Uh?MbZ;rRSbNoCMSvuAyGyUsyv^MG?;sEMWusEvWGy=tpyD\\ghj_uo]UtYYAIIw]vm_uxoiCEfRevvYFwaYkYS]acGEyfuf[cxjcfPau`OTG=ghAE<qf`SslIWcmga;GN[FxETpOevGW`kxIYXfayqEYaihIMTSQG\\ghEGPPlL<myOyqTMnVmXrQxQxNrLYn`kiYsvMkktKXyu;hxkyXyaJ=\\SaXv_]o<moOyOlQUoiTXiKYarN\\Pwirx]pMxxR<wFUMtYqy@shitwhneqww]msXy`uNe]XPqNnPjF@Lrlo=XwULwGQQilUxQMOPwpTN_IPHewuTSIASIlrnpYqTQl=VSmloqQO`VEhlrEKgQOVtrGyRC\\rwTkGxwSavEUNcPwTTUtQJ@UjMHQBENj<je`uPEoLUjLLqmYv@aqy<KbqwKYjF_[>pjb>df_o?aoFnbJ?l>fh?_\\^i^iX`Mav<YiYWVmxCmbAsFRYxyYhqqV;QdVuvWwuiaeVQgdquUuXYYYYyDZGtRYEGKB^CR:_dbkWDCW^EW^GckOrPaca[EH?X>arriri[YR?xEWVXqrImcjAIvkTbmRl=Gn?dPAs=ETNCCD_FB;b>UBG[X]GtbixhYYgGiWWXvAdEeVWqWBUR[WE^UBsywBqgtGYmotUGYHyxysyyyxwUTAAIrsyfsuuqwe_CG[cZAuhkYJCF>gr=urHMTYKEGUbyaVpChfSEUqX:oed;T@yew;E=Sv]WhvqwimYWgt?Abg?viGIwPV\\ukEYQGqNuTQKToEENEuP<lLiXyfdufQpwhM[]p<ioBmjdqM]YlhTTmqO]TVHlkeAVnqLmXyyXrcxrpYxTYsyajHUu=LqBDvJiwDmyoyqxpRVTMxuvqmvrlXfpRVTjguVyumlDQs`r=XJeYwYuytytymuiMv=ArNLnmEjZuNTqv@uxTtOiuyOtL=xtSIpp@pelLpXWadShMTyHOc`rVxUjhrEpxiIT>\\jKdqL\\LSeVD`p>hUk`nWdjYXx@=gsOvTwe<QmL>]_?wpWqBf_khkEarZaZuq^pyvehe<pmAop>GkLf^xFwBOx:^ZQWuiQxwiwiWxP_xtVj=VZBv^KWfmqu?FurHqu?wnNZEAeRob`VvtwuriglW[KFw`Xb=H[Fn^Dg_?Gthi_snjRA\\p^\\kql`_dTarkpnoXnRIuD@goN\\EG\\lXs]vnX?ff_hXHrTA[]W^Maogp_kppp`b]Hp?@\\LXZuqkmY]YWyQ^]t>hLVupWx>NwWIi>NnRIss`mYNd^f[Uqvay[Zikh@neBg?G^qvuqIQmufEXkitPswwgt\\uVwkVpMt]IhMiXHcwu;rvayBSHmQdkIW;kR\\YyT?GNIS?AgPoRTUgfoutmcHUiHot@CFLarL[BQwGq=C<csxgYOkfagUNlwlyxcDT\\yLUtMEdrZ@uoQX]<U_QXeQNimXXuvPPqHxPbINVDjk`XTMph@wqdvhYVbHOvtWPQsZtoceSPMutqkwiq`<Q`xwRpQEHtW]o@mj>ykbEUC`JxpuXUviuOyuk=TLADY^uy]`Tv`nFam;aNMxTs<rN@OKMn>mK=HREdlQXmh\\y\\qox=tVIYYHqndSPerHXQ@AyvIPtDKxiXDMKn]tMEKniM^DJ\\AujHwAaqyeo=at>XSNDMTeK?un_@K=TrdQS=hn_iRpasnDMT\\M_uwvIPxIwylyY@ycijQHqsUyDdx[HPXdQmaOIdmtMMIYo`aV:=KKypZllgYOKHnR`WGTpmTpVqWOIqpPoSeUcQpnUP\\qxOqOqxWnElP@vKxRdaydyoFYPx\\v:TrbTN;QK;mjrIRApkP]P<@mohsJdot@qXiK`uxVUnUqm\\UXm=jrlKJLr=<VoeTmiki]W]\\jZymyYxslKWfcWhZ_PgJOv;IrAQjR>big\\wqjyqaix`y?stV_>qe>XwRA[A?jgOhYIgPgm\\qsOY^hqoP^n;yqPUtwEeUbJMDKyRH;wGqF?eH[se[MC^MFwWVbiViSwnuU?YgJ[h=mGikiEyChsygST=UtvKYrIH`qraYCLGXsKiN?GKMf>mB[[BL]fOCYl?FYDwRdOlaY>`YJyOJ@JnmpJXVlqv`er?=nfqqHdKd<PbATalT\\@O[tJtTTDLnXqQMDMnpjp=osuYKyNhQMN]oC\\Y=]M;PkoLS?\\Jx]kPQM[<nTEMZagIY`mfqQhxoibdgp[nxHy]Hgl<p]c>_XqlrAZB`xyVZPh^kYajPhu^fggn=QtG@k_YuxNZr^ir?jmycHXxrY^]@cw^Z\\nrBv\\=A_Tfc^xgMirjh]>atq`]VPkZwfugjwwZYqrlvnrHiwoj_ildFd^@\\\\FlTpoWWdvWvUVaFn[T_i_Y_]_]sNd]peqXyDhlNxiyP\\y@sr?fCHrhW[K?o=NqdXrowydvw@v\\cWaG_ne>r[vo_guePd;q_=ofi>hqFy>@tiPZB^Zp@woobHhk<G_?pttf^AnnIgbjFwxpmD@tyWmKpZ=ofEOtR>rLp\\[H[SIwpFqnWygon@n^Sh]Uhfd_ftvl^Vc<@d\\`bCTy[CwoC?QVqAYUwxPGwY]fCyDppurxuUtrGMWaLJ]`KtXoKIjH]L;@Mn]nkDVIqQ^MNMxuT@PKMLvASmUWulRpeKHHLRdKDeNiHPn<QFAXwM\\DAZSQglH`@HmchqFacgIwwool>mvyj[ffxObRajgI^Py\\gogXwgkhpd>dDnmr_iRxvIykmAu=Y^:^Z@YbSp_KHkCh[>qbZ@[CHc\\wjKH`A^wdfs`XkFvu\\wuVYhFwcHIxDyke_uX?j^gZkNZfn\\P^`y?xAV]nXu;vesQs>v[y^ea_hNiZByyHIswQxiOe\\y\\Iv[fF`:`g?>sZ>lnPv`v`uvtrp\\VGfKau<Qhf^aqPlMNZfOx>`pvxp:wyMHjB_\\;`gm`kW@_KnrZWcUvsh@`dwk\\W]UhsZWkp?t@ytxOqDabYoc;weA_sWWylYvLitdpm]GsZhk;?cR>oO?eWIe^itqwi>Y`avm_AuvI[doeg`]BOcN@_KOvh?_b^p@Gl^alcOlLatT^ckxcGob:NksIfSoqQG^Y__unbog[dXnkniLx\\PH_?^b^`vZFdLNhoA^NA\\aNo?Wbcogg_ZFwdW_aCFbRFjjAamOyvVxmxZb`dd@ZcWfl>tTg^mEBEWOgVisy;;steTbUfkgGQGiCWhNegQ=UtgyHKIR[v>IeTsixYwm]ewcI<krJaHxcWm_Ru[CceBxcuZ;FFcH@uVseECqfNGV`usrcHaQMrHrkYNa<lPANYAy`XRZYMFHW[UuKlk]EvuqjyLy]hSpmX<lYeypNtvIyk]IYw@leTmDYSU=UCxUn\\QJar:]LxyuBptrIW]yrf\\rq@KgAlTXT?MQL\\OmunL=NuMS]<J@=n?pr;InhLWFDP>xjAqRvHSMpN;Hxc@UOmVVIMHAuIPTmdPxMVXuvP]YMpphUNn`RbElbpJS`LWyl:qldLK?hLbpQlATJuNFHPBENk]WApTahsGipU]UtHyHTyatKj]VxAMXXw_yrN@OKKLHxmToP\\L=lpCML@Xt;pU^eQeMp=YKDMjc\\WsAmWhvMpnIIMiAONupa`J^DQ?\\N>=NF]l<dMT\\SBLONiqYhLRqmZHtp\\XpMUVdmUyrmtSvls]yKwTrsyny@rfasxYQxLkJLLe`kGtwCLpsMxNIxmaoixWjUvTQJQpuuekaqQuxjkHUAhtbXsPuP\\HtD@uRuKSuUHDuVukbuPNDXf=pg=oHLuFlKS]t@dOvPk>qp_dkpqN@mY=hqAxjriky]xEAO_=yeyqhXtb=UBEu<iX=\\QI=PlLP>iwUQkyLy]hNheudMx\\YkMasIyKOHq@dNxEnkARLTJ=HnbIN><UIttreWayRfTs?\\jU@uAPld\\R\\xtoQTPLLHXpdDJcxxNAVjajAalodr;DYBHP@AqZluZ\\P;dUWInduTShX`AYTQQIAK]`WbiKp\\v@Lsb\\Og<LT]vMPKSDLJEU?UknMlDi\\?Fkt@mY@lWybZGcEpcNqfodkqxGWcV;et;sXGsw=YHwdqaWBYWludSAs_KSN?y^KFGUEJMSKkR[KGNIWiGBtMsj?SIKsLSdEGiXEedWeouHHWh@mVcAyWoFVSg`mV]KSIGcmKTZGtSgdbSF=CR<=DFMeV_cK;VCKeGecWee^avcySkIiIuY?OYw]EAIXiAyBevDGxwGR\\EuCmiEuscGxBIwIUF^GvawTy\\wudt`UOD<WWatf`oraOXaKR]qKiV]QQ]APO=J:<L:`N\\@NddN\\<wd]p<doMXx_pPbEPtDwjlPcAPr\\W]AQL@QP\\WfaqC@mXyr=ynHExity_IJH]mj\\ygyuDloYupBTrplpW<vsMKcdOThS=inEmQjPrcYtgmnahU@qrd`TepOLMsyXhVansQ`CyfdVhFOcVyiv>l>AnBfk`>d;Vukq^EOwpnqWIro_e>h^MqZqfjG_u_WZJNZg_[OFe[obHQhRXrF?`Ci[kg]EOeB_^Wft[G`T?vuovu^dFgjqYje``]p^LWeZhbiHtGopgql^Xh?AfQo[<Gj:_\\mQ\\FHZcfZT?]PwpP?eVweZNdKOl^wrYiaJ`lbFd\\`raFZSA`x>fGN``gc\\A_Qf]canmIhxnrE^kF__THaLiZ_`gfo^aVZC?vYH_tPuq^bUP[OIcgObkfjlfnCFaBIc;?dRQtVYjfo_JNdJV]jhqTVf]W`Fwcgi^DXn<QnHGaXxuu_\\eX\\SnrAqnr_xFYtrXviGtCvymVgeI`eX[kV[QQqf^eqIeXOxsNin?jAocHV`t>wLfr^nc<V]dWbLvhJOnf>gpXfvwel`tVafCX_V@ajglavmr^rJAl?Immf\\h^ej@qnGs`gggXjJfefVc[GeTpgQAheqdQF_]ohp_g`wfwnr@aadg`IvtoGtTWvtp_phgYihxwweQug_cSVZN@qi?ijFk;OqDy_J^btNf]>e]g^ROf=woLVk:vrpX\\Yof;Y]R_dDNxLgnJxkWN^MG\\:fbF?g<Of\\arpXj^>TQUnoRZoUAMECqVjGSaKwZccf[FdGdegBN;s;uE;hSxLoyuY`PN^IkFQM^MuBdWoUQ[lJ;=wqyKBlnjIMD]lbJ@DlH\\wMluNTyexJc`rO]Tb@rPhQuhnC]w^HScHy<eT\\PVHHjd<O?LQSewQeMG]p_@KPUv>qR^pXMTJMyln]u]dJCPpZXVMXoElRe]OUQV\\]XVHwkIO:PrDEXs<jYyO^UX_ptTDO;Yor]KrUTVMYQyV]etaEy`PvPipHTUeELHXOrtyFAQYhQyDs^AX_dN@lJn`JKTLR@kgAN\\EYm<VwUUkhpWANDLUfuPPIXV=QoMSl]yr`vCxNfmurUr[ioq`UPtLg]kkIXWAlDeN@MS=qxp=jNpQDepkiYEPYwxRFLWoPMXxlNpQGal<DO_ll_EVUqXxhV?=SDMXJMvx=v;`N@drhtrWet[iq`iNhxXYYnGUKUMSVUssYqOMjulo_Tj?hRUapruTyXsLTkRQu[EQXEnehY>LlRernTn`dOMQrb<TKPRAIKsDwCMt`xNCuLaLmW]VZxtrtrN\\oAeyxtTgXl^PW[\\KeUUe]uXUU^htcEL?ILhiU^yvLdND]lraR;=jZDKxyjWIT`]qs]mRY^rIccOg[?l^^q:_f^@bnQ\\wVks@fuHk;_uJ_jeH`[Qq<gpoONGHJ=wY=XAmY;=VpEuGOYDQRN[RFct@CYrAw=aIl]wK=Fc?RQMv]gRVCEpot=kWWewl_iJiVwESmGiPKF?[Imaxrssv[IHawReC][BLQS\\<P>pn?`PG]OIiVjpWkDooLSHDpm@vZFhXgsDqh>vjIVcH^]j@i[iZAXkQfgPpl<ntPQunWqW_gu^nTgkkgu^>wiqh=_ldAnopsC?jJNZgh`TWg\\@_<ihW_aIYnTgoLwoQImTPmdFs;GkuQkANlR^\\[`cFWdgAtLi[\\G]\\GciFqZO`yFg`P\\:ieOPjvwqK^b`NfUagkXF=tJKwRcfOKBJIW?WBg_X<=CN?swigJovc;eXgEbwfH[xYyFIYIZswB_WpuFugfAQcn_bWuHfQhWQu\\eXeedCIdckrAwrCQeigd=ORCOD_kIcAXgsdCsWDWFXIXXawvobj_FLMs^OiIgS\\uxNoFWsyMQblIYOAiXCUJIf[;UFGCPOV\\qb<aR^IsBiI?;fYQSNWd=?RaCi?cr]QVZkBYycrCXvuIAkxV;VZ=VZyvmiFO?Re;Wo;vTYiu[Hq_CGiECwvDmswcIDyirygIKHkkwKSfB;t>;Gv]H[]u`KTKCdH?T@UdHUvF]sF;F?qHWAxo]yjYWN]u;[hKaRTUbJ_tAgFIeIOeRcOC[=I>qsH=s@qRACF\\[cC]D=cgw]dDGc\\?ej[CcqXu_b[=cLESsHTNDL@HN;=LJtrkTJ=TJv@x<YKFisGivDQRCPLqQMI\\Qk<JJQT]hOGHltdTD\\J\\TUSLyS\\OVPUeMVMtv;hqJiq^qvfPJLhj?hN:Us^HvSMmDduIPjt=lgPR_ERypkEPO<HsguRNTlWQx>`v^EjEEW?UqUQVkeW;HyCHY@yjAYyfaT_LSN@OkIS=mPpIW]HJbXu=OdwFrIodx_kgA]n`cPOg>pcdP\\CFm^IZqi[dIw<FldAg\\i_??pLV\\hPo^>sIHwQgiEptZPf]VpNqbNHl?`wrg]S>k?N^P>wJn[Hi]\\ohlo\\;@cgh__ooRyb?`wuo]T^mZIsmve[QrUxokiy?xlk`mhvcYxm^yqtikSO_]QjoGt_htO_`uF`GqfFWnKVtfgr>Gddgblg^XX^kggS`^qvh=OaWxpsgyGxyMxrHgyHflTA`LQc<Q_;@bTAvRAvtOlDgt]_gFi^MHonpkMPtnHoT?nNToOUnSeGMIWoCK]DKcRKhuhdmHujgiwgmpppprpYwQQ]UV]=YXxTdlJ_lwElMrMVZ]j;UKW@O>DUAUvupMR=qyup]My<dwX=qWhoFyL_ljf@kJuosIU[IWDTymqN`EYoXkFqVN=u\\=t?ToKmSH\\l;=MC<M<@NZUWaujeYKQIQrTXBXrumk^PK?HyiLNvdND]<Ai]]glksMWTIQxQScyMSJiw\\[b<MWC_XFkrHMBb_ifEgCUDAWu@ctHMXCKfGeRVATbsiaeC_wcR[DlYC\\UtYecbcua]DCgubsTE[HTURw=WJwrIuICIrsYRysuiCwMKC[[B@;XfucSGs=]YkYXywRuur\\WVh;X\\IHAGvwoGESIWmHUCFeUW[SgEGFeSc;ccW?EcgCLACJOBSUDNufg]eCSEUYdZ]H[OU`is_wI`EY:iVpMwRkdgAVeUeSOsVStOGUJKBc[FhWFk]Wj;S>?d?odTkNUuoQIwpUqnXugMmGqN;=LZYyxdwpUM[\\J[=MlUv@iKHxMylSwpUiNjLvx?v[NF`bnoGYknwcfXfTIhEveoW[e>`q_o[yvpxmVia^O[Agvq_bY?nYxvH>Zwg]kvhogbhYupgq`ouOWxH`m=VlMhjxioQXkZNd<O\\?Ok`Wq=Qs@Q_GphmVim_fWh]EohJOn>sMLR^TvpAlu\\sSHkAEQqlyVtonlU`XtcUvTtJg@ST\\UTARBLuQarGekhUM\\hW?PWcMvPpRqeXxluaiy`MKOPkF]mTIklLVJhNXtRnaLYQrkHSh@MbTnsTYvaNIxmx]kSHkSqqOmulerqYn<uOh<pftjAyMsEjPUoCQXUinxdYKXmedMPpLvmlhEyf\\UmIeRN\\p_`mY`ONoowlhnjo@a\\Wr>?eppZQGfsNZcfZDqdn?qDilWxaZOdV>b\\Wvbvl=hl]^wgp]Z?bHF`QWu=aegw[ovfZfw_PmO_aCOlJY`BG_kgeQPc_Pj_GefawfAfFH^HXfdhtdfpTgkGisG_iYybegkgwaJG^VGkA^ZI^vSg^LFlH@eAa`<hghvwV_vp?i=vn\\AfCV_gQ]cOl:QeEpaCAyh@uW^uQVqKvwtieI@^^H[?^fuY[kOiK`^^hli^k[xlY?\\QFc;>lCotCw]paiLHbE`uP_^?@rk_gfVof_gPOn>GkLF]lp_qPdBo^dXdvqskxyPhvEV[VOwV_^pN[cQc>XfJppZNuP_ZEFcHFjdWw^_]pFgYXmfxoGoeRN^wxmSyaiA_OOuiw`<G]noiyF^fNbD^]SGvVIwmacHvcKfjKFhNvxOhnfFs;yb=`wvFj^YyxOxCxfsPqxgmeVsiAprqb=hlUG^Qyon?erpw]Pfrnh\\?jYOyTa[UY^<Xok?sDwp=qdfY\\t?fV?Z=HtCFmNXlond<XgvhvYO^HNf^_fKgt=>s:If@oslogvIixf`mIeHp[Y@fBY]@Ypv`nfAaqoywijJ>iXxrBAsBfuhwlPWo?_]AAgW@e`allFywQfMavla\\dFhi@x:O\\=`f:vctw[>N_ZWrYwncP]BQc[QbEWjoeNOevGtC?GRIbl[uS[yMWd=_Gjws]oynyXsMfkGGxkuNkYpcI?IF]sBuOsOOwfMfcKYQUytAF^Ey@CsmAslSfZ_RCOD_kwDCb:IdHscHeI;IiCyvSAiwGr\\UyPcTOErR;CQUVtsd<Kb_?EgGSdsDCaWFsHcUvBaX;or:]DdMvBAFo;IL]f>AFcyVZWFLiBWoE;?t?oRPOB;GdTsf\\UHqKHEWtcOX_iwqAUYMuZOUgOHqsHAqewSYLwxWmRnuIQ;y;qCeUsUaUyuhGqrd=rGWGWmTQSBtgS?axFwr>IvDsuYoxsEiSQV=?Eu=SZIuLOCnae?Cw\\iePAvOMWZuCZMGCCWFOrRcVA_iYqYQWGqkGkydqkyFwfAqe]yTIsyPsCGee[ovH;fKIw<uVyIIJGd=GeSGETegPCN^\\KM`J^ANj\\rk@w]dJ_LSVYSv<m>O[MpyMAwvFZg@uGQdBawaieQhuW_?qWe;tWGi<[xBKrWeT>oyZkiI_VNCS>mRHKH?AFh[g>eVXatfCUssG_wdXQwFMYbCT\\_RCODSKDICYisRfYgAsyKSWWgTxay`yy==V<[eBIVoybWKUqORF]WjUGLSuK?UL=F_EXvmS<[yAwxG;Hx[VMawbkWgsBfkg>CC[=sfAfkcypUfnmWjKGgCISeB]UC@mb@IY`Asa?EhoCmqyuytJQyw;BdehTsRIoE_Isase^]Wf]waAquav\\pTS`NbuKjUxdulGhTYhp_AKMLMHtQk<s:IqTtLHLMTeuPDje=oTqPldSZuwEXLLiJvDlWxLcari=SmQLFhR?aTJQtjXtWqvUYOyIkQuLx]rMYLIIxeunyUlmXXIxn_ISOMlq=ld<SJYNATpmXpnXugmTQuTcup=mXp]PDelk=RCXyAxJT@MZMlLLnkPkKMSoQJcaQrtLceydML?<R:HsT\\mK]kkhSIqwMhv?\\vqpnQ<tqIl=pmt=tAMMLytiiPqTPu@S@HwoYObYN?\\NMhSh@M^dtnLytaM^mX_PL_>?tNFMLPhsIlw_YPmuOkPuXMvuXsYqNNAP_Uuv\\X^PJ<llpLJPqp\\LNgHk\\`nFHo]unE<SDLwT=XZ=t?qMQ`wgXqVMpfluuHt[htg\\smdYdPp;\\Jper@ts:eJHewwdrEtnX]vkiqIMjP\\Jx=jY<yrqYlhqmqsu\\sGisKeoPgOay][dDKrwqRliytmsZcDambrWq_XUiQn=uKkMr[HxNXRuanZUndHtP<UH@rlPkW`puEp<@LCdMgyVE\\NdHlO@oLmlW@USakL=yKulPxu\\yQYQy`LcCN^Yx^qqaM@lCOdUWe;`]BG_Sn]Xnff_gFX]qn\\RAubQtfO]\\Ay]`yxPcvOtjAfMVZBo_Ha_BvyZhlwgmX_qlVctIniQfhnZhibl>l?^vsF\\b>eBPiGPsby^?FasF_LHk<PZJhqPoeO@snytAqcm_[tgcJAcEImPnuaGkLf^D_lbYbIYbHnpnHi^OwkOuKWkBghBftUamSv]ZAxbg[g_[qnlt^_g?yfvg@^uRowl`qXNtfG_\\AuZf[fwo@?y=p_MWlpVh=o_`OuJqeIHqOQxcajtxn:Wwnip_`btOZ@``r>xjIrm^icIoiHxLImi>`^atcopU`j[?kiYynPegnpppprHh]qZEYsEacIwcMgoPWsVWjI@Z?Qv^nl_Gpyow[osVVyvvpiogmHaNabVXhSQahFfJWf^>aHOdG@_coldNxbHb^YkvOZ[V\\L?mnotp>]KP_EN`[vZTQZf>lp`rg@qRqrjhpopsYauvq\\WpcAhxgihX@uqa`MVrM@aPXlYxZSoa]Xvr^tdWnBGa<qv`_mMVZMHuUXiYpw]^y`Vcv_mkAbMVZAQhSNh@@mepw[GuY?f_ne:f^j`pOxobaf_Os>Ot_`_s@gqGluYafwa?gv[wdAOvvH[SGln^vAAmVG\\Zwt`_h[xf;ofsN_^i]^o\\\\`wrVdvg]?wkb^l>An>GkLbuORB_riggGoVvOI;YhmyvRGEbMDSgWHaSFSH^QYbcCDerbEfr_XugrIuuUIvOWcu[ixqT=WWqKinMIkScEIB]gTuCsOUDZQWRtXb]WAaXtHVTyK[dW``WC\\VO=VQiOVIPAHw;IUxUxmxqGyovdx_mnAuVcepT=QXXRuhu@Qpf`qmhWgpT]XtcAvuqyIyxEUy>PrR<Qv=vfDtahKQXuiIpllyw]oMqK\\=u<=K=hwB=SEYuDPRc\\XKPx:TnMpYCm^p^jBosO^b;geJFwxalb>]K@\\HHjTA^UisGoyYYsyOr?xxxOsyAxVyq\\inmve:qoPYdAWby?lihhG@^RfnSaoLIwn@k]Q`J>_kwyjAbKVjfQfCOl>Qld^\\OWq@ah_okK@iFhjbqZLIlZPiWo_GohOv^SYq?`twqu?hdfvaTYdD^c[>naxkZ^\\=xxfXpkfj]OxZnqZWZ\\wtxamR_fxgtvPdKfjLhn`xtKFeE^nJfjDYZsQu?iivqrE_lbFD=dJOUj[b:EE=eitWrSQwG]U@AtRaR@EFj;IpWbJSRVgIJevfIbCkinIgHsGygi<yypywhUx=wwiEf@OdkKIHcCWsUKIWd[Sb=X^;UL[TTmSTqXg]wCUcb=H>mTgmesKXXwuwawySvcWvaAEW[E=AE=AwBAGXWw[YyxKSoQETEUPgbgUuwevdSSVyYnyGhGEnad?]x\\eD]gU^eFWwVgaS_;wacBuoecqG__SDsIEOrIEEK=dCOeZgf<ixV]daGiWai;yExOyuaIp=wkmBeWRwMsQmTOahUidnSeoMvruG[=YscyFcvVyU\\qyZIb\\kBSKh>WVC_rk_MNmnbXy=argAKulpLiTwUt]uwcMJlDw?mVDttsiMDHRKEOJ]LBER;@ORTlALynIL?`s@\\R;eTb<l;`U;<OdXJnYlH`kN\\LTlm[hKLDjgdWfDWw]xY=YCPL_>iZA\\MFp>wbya\\OIwjp]@Aeh^[N__dop=gj:V[AFgVOghxrMy^AH]xy]WoynAylfkG@m;wt<qbJ^g@_pUNkhWe]PZ;`tPOpja`^H[@WaRWrOoshii>x_xNxOoqnAyQGmSFm_pvOAjXgktQgoPsJAtJounP_HXf\\Ae[`dcPZyaaJh^dx_sY[vAiuYyvpusIZhAnM`l=vpFwoSOwhAuUa\\hwhuf[tqxqQ\\<VkS>[CGb?a^JFtb_]Aq^l_\\yNqsiixytyfyY?yaw_xyxVharAeiivLyvINZRIucPpmXpYphuGmqwuWQfiqu`VxmYrsFibFd\\qe[Ij^nZ??[^n_XnkpG`K@seocqIcso^g@e[Od_FjxYwuvyi@lZ_uQ^pai]EXk;wqCYZyO[PFnWQ_<w]S>wMO]BWhA^ciAy<oa<OlyC_GxVUu[]Y^]c]uBHWHwCHM_YhQX^;GKMf>tMBDJ>Dl`QytUmqlUSen_YOdXjPTV]qK]ULhTv]pK=UJhdLAqrL@RO=pauqAYSilSjUwTulGhnJhk_Alj<PriMGUpMDtNIJWIrBtXFqV\\mXVXvuqSl]YhaJI]MrMmaxKyTrVAuX\\WEqsgdSsYYKLNiXSYAWn<wpUqnMQKlqiHTdDQ``KjqwyLpO@Y;@NNINixPx]rqpXxHSVEKcPYO\\jUPo?lLwLXJ`QjtqoDOE<sM<lo@y:pnapVQDVb\\L\\DLcqSCMxtmp[yWhdYUxjqqm_MYrmjSIps`Q;DM>DVBTQulPeTO=]RKaQQxOq@Qmmn?auVAPTUm^DQt`RCXY>xJY@MRDjghMfdW]LVSxTsIwKTJ:aNeXJ@]Lh\\t\\LxEpqAmKtAS;EX_yqZYyIQM[axhywlXMcpmD@pUeKZ@SZLKetK`@xTPOL=wBATk]Q`uN`@a^IepishycxvpJf^s>_KOn>Gku@^CNo^n^XFfugiHxqxqsU^rWWmTAj=giNqfnOs`OiXYfpsRsej=ER[hk]UCGDjCHcQDp]HgiW?wweMeuCD[wgjcXIgiAwvskHkHtkIVXdQvAMapVXlv:Ay[lxFpw_]YbMNYEkP\\x@yvf<rmaQIHxkIXTdk`tPimu`UYu<nUiSBHRcPMv]Rj<VJAK^tPuxtrISaiLhPwE]T@`Q^XO:ILCeP[`O[AqjAqV`KJyw@<t@UjP<K_LyfMruhO>IUVHlq<SGumP=KjeQQhkgiKxhx@yyAaujqMx@y^yoZUUHmytEVb=uVatf\\OB]QiuMQyoq@uTQTBDT`\\oQ@qqAYZDk;@OvYoSiPHpkV@vt=XOPu`AJtLkCXNOpP=TSi<MedtB\\RLEQZqkeAWQ`KRyVYLO@dyY<qSPrgHwElycYuaM[h>\\AhelankfjaikoNtM@upXj]WqRgnYfp>GKEcI;RT[c]=DB]IssSWQyNKFtedogrGMvbgb]QRo=r\\]V<iViIfTSYIcTSOeqEgI?urkgZkcFKUaSbl]DbMRY=hqmybSbasxk=y^YFfYes[rreXVwrqqIGAbq;b_cgXmuUMIxswPUCl[CF[CLugIWvuqEUWeKcwpoGEuSx]RbiV>;MMTxMpvI@qVlq?Po>]tvPK@ItZuNCavuXxDLY?xQLuX:HSV<KX`xj]n==S>xMsIq_AmxtR;dyUmWSmnZPOR\\UIIvOxh:hi]Vys_xJYnfYmx>jCOcWF^_OtkAiggck^avFruywUaohPebfnj`_aFiIhn\\ad\\q][IJ`nlAWl<JumlAqm;hYfIohYV>]kMATU]r;=kg\\W^mTTn^YinCabqWxGnv>A>[uvsfZsUgyGPoCGQBvMxdIRNkYYyDryvdCbSiR\\KC>[fIygRYEB]XV_d=UEX[E[]Y^]eDwT;mdskB_KSN?GkIBBMbyCGLosjWBXaGIcEvQGyWyUqHy=yAuyHWGiii=ufUirI[Wpwh\\ktQOFPqD=mxWkglShQiVb]t@Qh>CVZGdLATeGIFisFExYayMwySWHIseaoIrKdFEF\\Cey]hPAGg?d<mYZmyQETG;TDKIWsdGisKKugErHqS>wwAyXVsU@;q=LXIyq^UQTAvadmYDXUaU=Yor=MUUjg<LpMnP<kflT:`pv=OR=UR=SN]nCTjBtRTaMdpM`Anu=kUIvgmO>xWZPRO`LyDsfxr?HqxxQaAT^hvIYtl`ntDpFtWAiKhlurUlYlqmYJpiSY<JnlJ;axnhsxiyHlrBlpqhKieqOEvDiLCUnKTPtLwNxvFEkuMkATlR\\LZdj?erhPP`qSjxpl=je?koAf?F_g^nBQZxWZ@?jnfqLOf^HkBAhQvgZfauUFKvmiTvad>[VW?HoGu_?EnYd<_gYERPIHMaDtWEUOF[;G`CSe=Tk;S]UXvAvCmsVsY>Oy:eEEMUsaRNMSBgFD]dbFb[?kc`d@>i`IpYWf`OiXx`XaiMxtYWycvdXii=@^TIfuwfWprUXefpor`wuNdaArKHddh`CnbLag>^tAxbrovfyolAwSxfchdAVd_?^sogE?eyVh?G^_``GpZVQqo^jaiskQseVkVFalPsCYluAhWQdGnqY@`cyag_\\y>utq_QWrEAyHxcGio<hgLW[KFs<NNSCN[HDGDe]bmOxkmcEWdvursYGhSgEAuLqvBgYNWxPyfreswedE_U^[TKMu?CexgR<mXsGCtmt^QRSKXg=h^?V]ghHYyEESA_WucGiUIwcwj]vBwr:Ab^KcfKvrMbqkuj[itQW>YSicTKQEfOXGAh>iI<YBC]C>ciHAb@Sb_[GdqsjpTpYpTaU\\E_pno_Qf^hdBnpMOdZfcYPgJx_`AmFo_fiebPbM@pyqqLQn`@\\bYlqg_PQoR>yaVeYWvlftUymG^\\wFgKa\\^nr^qqPGc_NnTxd]at[Xtv^h^a[oPw:Ob@Nt^inL@]N@?fuZHk?iZnHykNdfHvsp_Anx>^kOyrsFina]EXga>\\kqeXqiuQ^WpwpFnTqrIx\\shigq\\]XvXNtL`pUN]yht\\QyGyhJO_@?[SX_?fbOIyaG]AheQOdgPqrpwjVweyZRIusWmhw`@WgGOlkQe\\qi[VpYvb`NvWqw?OmlHjnXlVPZMX\\<`cg>cEWjaHZ<X_Wob^A[]aCEFKORJCgJwh<wHSUcQPLf@LAHLbPVf<pUQjVprADuwQR_URnMf`GcAhs@q^QpgWonSIgl>eW^ZL@nYQpF>nRV]mAakOn@ptKvgvHnsvhhNfj?t@^bc`]N@qa>iZFk;oZg_hH_[@^o;oxPo[jGokGlrX]]_e=nd;yraXi^@rBquZoe^nZTAg\\gmPImPoZUAuBg_MXjDp`Zhe^AnA?ZLAnyVd?N[UpcCPb\\w[\\xt;Gamx_ON\\PP`sOul`_@xZA@aw?y[ocYniBPkQGsYyxhqZbf^D_lbFxCwbpnMaiC[yoKTvaDcMu:[TVscdAynSF]cDpqEn[rDyV`mw[;ca=WpOeVmYyYYvAw<YyBEefOtpMuToX]WcpyWLkR[Mv@es@yuYGnOhMdhp;MS;eo`ATixKjEv<aK[=q<PTpLScLyaXvl]Yyxlj\\nmuqk<ydXrOAvllqfAVslTLtK^`jZxkN<RhUUpikIiLwqOUmVUhtreL]]KTEWherqDUjTK>IRFPTtDYgPVKMlr@RLLVlev:dVtmk=PJk=p>hRa<wjqy\\iTxMXsiXXpQwmKQIXk`OR\\MN`SIUUrlk^YsYmpR=UJ\\qyqY>YwixRvtyvhkPIk_IoV=PfDx[Ex:U\\?QljWfOHhHacvnr_pvU_eVqi=f]RN^KF^WGkJA^fVZPsHKcXaFL_raQeDgU[Mhp[ca[I>GDfwhPIwrien;eiiFJsDi;YWsDOMb\\CEZwYEOt^gf<MHLiEGqsnmf@?RfgDmSfM_EUyYNGwCGG@KW=;snePPQPw`RCPL_>jv_`qnjRpZTxw:T?StZkr;QDkKt:kVKsR@]CO]YTQydSHAkSZQck`WQEub?hiV[<veMvb@phmnnMQ`r`r^Hh_yjuwjcYen`_CXvr`_gf[\\fvFVsEQlOitPvZINi_AuxwqJpiqIlHFeIvdSOkiW\\QCCIuEQbcaHh;DseH=avkKDCUUqGi^mG\\gsU=eBKh\\CF[]E\\MF=GctiWCIUXMfPmBMcFESb@exM_BW]TQ[d;Ug^myQEh\\eWeeeqsgxGr]wrYSrp_E^_bCGCUWDa[Ih]uJaEukVBOFUwitYG?yevIS:Ix]qH]WfpkgeKsm=g>yb@YbE]Cloh[Iw?YUquRrkHtMc=WWA=ekmvRQcp;cF=c]]E^oB]EdBmbPugCIUtaHc?FZGxfQCmgtSmrVGXV[UXQCYafeYyR?IhISyebvSbfQfiYF?CDwKhJCevUsuSEQSSSgDlEEDgCKMh;KWhMYXWhasslcIkcbeAi:cIEcT[Sfg_E>KSN?oM`kXerS@KYaq=ptiML@TmnUVE@rdETm]KoTs?il==Q<Qr\\HrZhvMapxYLUhuq@qwpWR=uxHrRan=UVELJYUtd]r>mqGxPXurlPLeprApYYpNC=RhepFTWe=L@XLvPxDujMunp<Qr=Xv`xDxua\\VayRQeXsuqoejhHwZ]NBEOt]RZxy;dyIhPZ]lbiPpdNCxQ^LL]\\KT]LdpLOtm]tpJtnkHRN?mBOqixfqn`Cwc>f[k_obaZW^kKAwn`utAuRhr]xkP?qlgbkqsunjUv`^vliV]hfedQhxaq`irQVwrpoWOuCPcv?gv>q>An:`ScTgQGI_SvkSmKWjyTEyY;ioG]W[Uno@w_tLS=V>@RBquL<lklJ?PrlaW@hvBtRvXnF@sklTWiTp\\r@DVVDV\\ap;MUK`LNdl<@oaEMDIS;mVWLkMtyZmu>dNgMkPyTh`PU=x<UVSMl;Pu:tkW`YFxOymve`sGmw;UWGptTDN>lTsTXN@OKM^W?`RNftFxoogf`ojgxwhfpn`[PdAHkcvlkI[YHttQa=hdIPk_If]HorX\\>OhUPsjwl;Id=AfePjYi[CxtOfsW@j[IrkomsOwQ@]V>oavojI^PWfm@jGA];_\\;wnMNtgq[kgvD`vdid:@]cvaPVdly_VN`\\?tPg_XIgW?fmneAqb\\^jW`yGWt\\x]wWkmgqAvx?YySqaM?uj>^Df[FajCOwCfvOn[Epg<`hkAdAonJVanaoDQ\\BVrHvwXWqF_\\A_[Oa_>@jsHaUx_xGh:xayYxWne[nfyIj:>ZZ>ZC_b;_dug[Pxlofk@P^HXfxiyyxkrVh`?j[Ifu`^?f^x^`X>uK??[RSiBY_F>CSHktI?vAqIQmXhChO[WLkBxKRC[WQQrRmFIMHLKhQedbSFtIVq[Vagh=qbXARSmb:yxmiDyegFKFeSUtWi<ATxEhqaT<cUZSCweYGKcoecEgTJ_b:CVJAWdoXGGxdaB]kuRkXfQhv?iFQulQE@AEddP@pj@@oOQWNMOOPTg<OKM^LFot__FxrBhiXxwWgy`v_ywvGoliGyNybe^deOlCH]AHuwo]mXid^cHGiFn[SAuH`bU>hvVm[I\\Qhwo@mBy`nnpv_hfGpiwsKomuovE@aHxlqflvAp]ooknZgh\\@A_fWq@QwdhsOYoHfk@pnXwCQThOyXyEB;sm=S:Ob=csZ[CZ]RTSTNkYY]ws;dOWHIqYhkw]wRLKhlWvwweMaI<?GEGDniu]ebrCwyGvuqIQkGW=VuGh=AsZAGPgVKEgBHu]QpiuULawfeYWun_yW_tuyqYQxYmyWPDywxuU@vCxN@@tTLsPxR_ly[@YZEk;EL?aRVIsdaLt]xNtN@xM\\epmPruhoqHlp@r`pjKpJ]dSdPM^Hk@Eym=STLo;YUWyprpvXUro`QTdm@dUYyRAmvHqy>DX;`N>qJWHS<HTtPLJhUjQkVeLrXpPHXtlOC`pMQn?LQn\\tvHJHdkWdnwpt[YYyUxw`nmPNZdOCasnaKuqxgYv:Ij=\\SGeSOPw;EkLdNxDxB]O[HksXrOTxfymtaM]ixOmue]q@QuLqKXer\\Ew`xrgyx=mnqajFyMjAmSYw_hSGaNdlSLtPWQk>ywdLqWdr[YJITxcyVy`rVasxYY<=K>MwYuoOaJmYxHLTDlN`LOF]SN=uSIkrqtqpXrQwQuRKPthtLvmwULlm]NqHNaXxl@O><x<LYCN`L>lHytRVlaYZpad=puvoeVxvmij:Qj_?aEycNIdiW`[OfkNsuo]c?tkpnOIgKVorF_lPgLVsjgqhFixIydvutqlZXuGoxcf^SquP`y?yen@asOt]wsXvlSH]IfnLNhJomEg^xodv>x>AnQgebFqJh_fojwHdXhmwa[L?c\\YuKVg[Q`Wwq=hgu>cEOn]abeY\\l@lb?Z>A_\\_\\[w^<O[CPkON_PiiWXkuQsHhfDIbP`iNvxmxyvH]TOon>puXtkOmna^fFbRvbZhZ]Xj]_wYVa>Iswx[k^wGvvONknptJFrDQsDfwpWmhwpEwnMIfhogHPegpxKpiai^D_lbFxEhjfXqw>j?Ik=x_JQai?^TfvaxawWj@Wh=hp_wmGhphVsEn\\EwpvnxYf]ZohYgjtAkGhgEOnjFwlVkJa]RyhVxvXpyDvvX`yvnpgavkOvAH[lPpApteq\\avcP?pgWksIiQxrXVo[QqWnqsis@vkynwlVau>keQes?`ROvXVN]f]sgB;eFyr@STvqsMUI;GH?WvLQX`iiZyijwIEyDNiyiGtQIDs?gV[b?SSKmtJcGp;f?kh_UF__wsWFF[TdKdQsUV;v<iB;ixeafw]H^KRR]GhKrYmy_UbCISCyDx?H@AuRWedsB_MHlEcYgCI[QJHNu@YnLmThU]IoSXxN]oDTSGiJxMqSLpOQu^PwS=SEQR]XT\\=lH]N?DUKAM=]oOlRU`YOEnR`XV]OUMoElP\\hu_ISmdnZ@uoDQY\\jLxPV`qf`LCMrK<VEujwUlA<Qoxvntnqym@AW=xMrAOO@yBdlL]XtdMPqtPAxwumbLkRlMXlqehnb`MBLSN@OkIk<@JFFn=Af__jaymti`pacYPfhoxI>igixYVpn`p<wpeYvq`\\Ex`\\OeGpZgqfFatfgj;HNOCucOqPJaqmrQJYPYlylSHmXyjkLQgIVjIVOTj^Ix=XjLXrAhQdiXCav^\\QoaLnPULxuyiYCypyhq?yly`U[]YVQSYTx[pUl`rW<PRdoElLYUlNhPQEMc`SEQmqqKyXX?yqZpJ^QS;mLryxoMQpDYxDVitnj@Ly\\RCXR:ajwhj>UnM@q<qr`]oxlj]EQs]oZ\\JrlKVHQ]QxjYrKtwyxKeUWPLNGYnNLr_YUYQu[<KvMoO=y<yL`Dxv`nFTVCmKD]yf<yRAL=PNFlJC`VvPPCIqcySkhwiEXoUvwLJgYnfAMAqX;=Kn@PsYNlYmvUL?hT;Pj_<oRiyrtsk<uOXYJ]NKlnA]JLTj]MOUMSChN^DVJDtcQyFikHYX\\mw^tqnAuQDQpdY<HJu=lbLkBTrJ@QHHK=Alj\\KcwpcgpT_j[?slQxlV_eV_rnk=AxjAxAgyovlbFd\\`ri^[FF`Th_ZyZBNaBGfm?w:@fxwwMaicYsYXvAxiugm`qp<Wg?qrPicXoy[ymm`h=G\\AHZ=Yfknk]g^OAkTheTiugNrrXZcwpVYiSNdSolBgd=v\\J_ggG_tf]EhtOWkyAxYntrvhh_mkH`q`[^qw_NtcneegkY^hBXrBv^pXxsPeDGlJfZLIys@dh`pQoin@\\=^n?obb^^GvxKpjVI_:wuiacpxqZWaPIi_WbJNeJvj@HlTA_y`yfy\\Sf]XfsUNqDFl>a^LOrmxs<YuiW]h`eK^ddn_Wqg:>eRVvjQxEicpv`u^[GFqVxay^coPgOhthPcvacjpqxixixiwyvwq^hi^lVcKO^>>cdox:fwjhsPwfEF^^Nee`h]FgtolW_rSOjjouDaqZG]Dw_VOn<F^b^lcfsCQrhQ`^Hwgo`:a^D^bdhgR>kOHb\\GdkX_vninI_xVyBY[vowKylrNqqA]OPc?Pc_PjaIisiiQihk_]AVupHgoPe>Fb:gqXwfZ?f:Hn[Hnn?vjvx>y[UOn>GkLvqRAwg`wdO^\\WhK@lyi]Qx]\\FqF^e@nu@?kEa[rwtSPmc?pyAv>vjIvm_IvMv_kImawq@AtZA`eW]q>uc_g\\_p=wnSVppPp=atbIdHnwuVrNarX`hFgyjQk;>lPwn=fnFvtixZVgqd?wn_]Pod\\n_X_e_qxgi`@vZWov`Q_F_crFoI_qVVsy^aLHiKGg=w^DFyCWxONfuNb^hdbWx@AfSI_O?mAYiPYnWWhwG^aA`m@ZOV_Nn^HOZtod]Asna\\<@rZXZtod\\@_Eh^>FdanfJq]\\IwmvcmAycx^j_mFg`Bqs;GrBA[f_gbogYq`fwgU_j[_cP^qRV\\Mag@_qpQuHVxmi\\`pnVOgoV__f\\_IqNOviyrAqck>sTqmU^[ovn@qutqixVpii^`PoMayZGw_ouVwyCvpUw`JObKghLvgxHZFptw`b]VdBNxmIZ[x`R>pUhyQNoI^\\XAcT`dFoyTFeWYfGp^DPfTfmhV`=WtVPmynsQxswGmQv]wQZ]Vj]@uLqrlh_^`lCOxKH`bgok_]AvtoWhL@\\@H^Gpb=phuhuQyuZ`^?f^D_lrafZF]Sg`e>]h>fmG\\OpkkPbR^_>n\\pNbRn^digtNqCwdgXnoIe@QwuI]rh]]WqJvpFfgOVtgA_TgkRvqU`hlhuw^oy?]^ohJ>jdgdlIyIy[jGv<wl?ib??]@?yxWmZ>[sYvyneaOitPbwpgmVaeqlWfgiIZlVokgspHax^aDAs<gZyNg\\Pb=h^Mvx:`j^pdbOuwAmvoc_xlE?tQxfRPe:P[sqjfQhG^ugHwcodLaqRXhb_hpaetFdH>\\rnkMyf_V_Xy]V^lv@x<hjiY]xAxIFvavacP\\?G`JNZXnqiHiuiwJxiuygQFwpg[inqrNsNu\\_dCUgOCcLqfPMv=CxkYF@CudGIZcb?erp?um[hIOgOUVJigmcTUovASCYYVkgYEobYASQut;MV_SbAME^yxvWbw_r[_ypqGmgRPaHgwXeKDUADZMtlYXDAG\\AI<MECAV_=dwYvAGYbus=aeukxnscWcYLGekGUZCChYGOOCDeFCurGeu^;C<_ymIC[Kd^_F[;ttCFGcFD]dbXl>TlwyW:ApG=ohUtgqwjhtS<RrpjDxJotr@Yp^lP@Tk:TNPAk?QLgeYMpVmMmHtwLeMD<xtlKgqRFUo[@wn`KdlOnErvxjBQjuut?XpaUoFqstaUv@oSquHHP`LJNtwvXt[ysxaWEHoctkipYo]LUqOuluy=UR\\JDao<@YUHmTiJHht>Tux@nM<MfTsnQSGPSjLdBpu>vmOg^TieS?oixkKodW@`]fZwgdEFw_a^hQpVvvOHlLwh<p[oNtBnbeY^VVuy__c>m\\nwPwhN?h^Ak?yvxvnS?eJ__f>ufggO?xwA]gXfFHtbf\\miuiqpchtPApfFrEw_GP`pnl_NtapsDPxvO_kw\\v_wBHZJXsg?]=Hbm^vOIouWrfy]s>s[Ht]@g_Hy;iwiIpTAe?F^j`n>Ypv^_[gxCwjCF[jFyxFlQAa`xln`_C_xCfmLPZcNdl>fJPeZ^nBGk;H^JIZWApEgtdH`xNaHyvHwiPxvIgi@xfIoaIgrgp^;pqCOmRHuphcgpd=?[;wnMIbegma>^aOw:otfacNnZHPx<w_KOn>y^<njNyyi>kopfownEYuQo`R?ecOdgXc@orfnbAge@wjVojdp[OWu?qlXnlMNnGYqfOoQGtO>]VftnV]HVmeHZgpbFPkfnj@vrchdAVd[yxXikcHu<_pNPj[IfUXnAg^iyqi@eTOtrnk^^[]_pP_iqYqgnn`pprfiTYv^Is;Qbm_pL`]vyl]@\\VYfB^s_NfmyjF>uQAih_u\\iq?Vm@x]\\AuChjBWmNGvQ@flhbw`aaApZq[JofQF`Z@tRal<WvlpmL@tmx\\oq]uwbcYd?FhJVdkXoV^my>ssX`aIxVww=vyXQdDnxfIjQven^uthZiwqWGvPi_GWpSHuD@rRVmiwiuhj_GjaIrsXhoo^afafWe^aZ[`aYPcfqrAq_AAfqnhYPxp`pS@oGOpq?iyvZAo[m^vPIrR^yByrIhi\\g]a^^:_^_OrLXeSXyuaZS?vIoym`\\\\vgjpbDOZFH`bfnBNn:@`DFdDG`Lg][Av>I^XXasIexvi`ylsatCycm_hpA]oQujnlnPlAyfP^^tOs:^^CWdSoe;_\\?`wfa`CP^?AtJA_]Wf]_cHokaIsCgfHHbCP\\_naS>cBHbe>e_ixExolyiwyuYQvdYm@XmiihR?qhYpt`]JAgA@y>ah_sE?e:SbKkGhWH:]DDmXpOVpst\\mHPURpkTu[CG[cjYwYUyiAImMyVkdOYwc;XisrNeeh[FSqh[QwOeruuw??bIuhugb_ERVSYfeWSKugueQkURkSLWVmQGPcv<;tIQCG=S^kUAUciITMkEmmSGwHPKeVQwrarH;Ucgyr?U:_FeoRRYGqkGZcUsyfZOEbahFEI?oU@ES\\EhHMYN[b@cEdqUXERJ]sK]SmuC\\;Dk[BW?cCItSkIwara=y_yvy?y;wvXmRjSgOEsvai^uwXeRNCCPytgmhqgFDEG^_cKKR\\EUPSSEEFQkGfUtcaXsSX`CSBhQAqwMEovtpD]YfHk;mLZTmnyM<\\QuPrVAvXlfGY`y^pAPkOGbDV_K@[GHbSflX?]wvsxHb]?`bWfDVgJ^vsF[sywDhgHF\\BGf[AeXVjhA^]gpkokHw]aIp=vclImMwm]Im]ym\\AyVI[@qjL@jXoxKvkXAfZfflGfefnbo`U`huhe<@raWiuHcRNgdixKorAyrRPmTvwU^bDYku`bCP\\Yvh^f\\U_ZhhdAgjOn\\hwuZy^ihe[huFHgfGgPyl\\olhoZf__A_hUOmj^`>Hn`>[NniqFuTXekVkQYuVaqTArLh\\xIwiwyenmt_y?Nw=WnCYgVyZ\\?lwftRAm^giWAheql`wfAAtcebew][ROoWQ=hr?i@isUwTsSYpMe;IRqqivwdIMBNocceBQ?w>uWJuXV[WUQVBIDn[TFicH=eFIe`uTsMXWYiigD>QI`[TK[R:]GtQCK?D=ocnugsGWR?G@KIG]HpCBbAd^qYbMyg;SK;ejCYW?IJ]IwAxskYeYcyAe=WYHKfooyuuvmUs<GgcScSGERKEl?Wo_WhuuPGWOKF?wv;AvZgb]AUf]W>[HTcUdgT=AtJgS_OXaEg\\OxVQGkIh`kB?]v;qXtUWEUe[sgHaYwuGAqrH=Xb]xBSvOIX\\cE\\_c@ycvMBO;D>qI;]DJ[r;CbD;T`CS@kd<=fnOFLEB;]vasrAqIkOcK;CdoXOGtdAEawVYkvcWbIAxSWvi;x\\YRY=v?WtiCX^MyRSV=WvrkhMydi;x;=hfSGcSh`YynUiWk`[Wf]hbqXoSn]H_t<HmSPlR^lbFd\\Yl=PflvoNn`Ovh>Hp[iynXqu^huhcThkPfs@wjPW`^Hqg@gpNfthoR@`JarKH^ji\\;wrJQg@`jWvkcHtM_qnIwYIv?xvxPs^arVnhtnaYYwkapradHX^R>]J^Z;@v\\ib=xwq?dDyZ@F``PbqXq=ioUwg\\YykVhmgh`n^@NksGp_AayIjRil>>g>fkhi_ThmE_kNQZ^@xRnxd`[rNlh_]lgpK>fEPZk>_bhZk_oSnhea]UFa;Io[XdfwZUAyWAZWf^dFbPatNwfGVs<WteoePN]n?lfo^_V[^P_=F\\cgp\\>bCNqx?rXHww`icYtYovQomyQ\\OQcL_]_ywLg[lhyHX^Rn]P^wWY_SN]<pdE?pmXvJfb<Pc?A`j>ZoP]rnk^XuO_`TFZTwrNO_LPeGqwepdNhvcoyW?_IYqIx`xnlsnZuHlcpZsWrl^[H`hj_n=Ajm>s>ghLHsTa\\MhpCo^dWdf`pP@egwoj`uV_fAyu;Gwrv_oNuGVanWrHfoZhkeAeNQoM^dgQ]H@hCPnJPoWgffPaHav:a`MWjm^wSFuAaujq]`wjaAmhxsjFeY`_nWeqfa?@bVIw_g_Pp]gpde`kIxkMAgn@k]i\\tf]?wpU`o:H_Ooe^h^D_lra^[@\\r@[Japcp[n@awOgL@mIAxhil]_ewPiEhj?hZpxpQIgnvdSgqg@kvAlhW[TYxDHr[W]F@nMQkkhmDVxAv[kIyQniWHmciqRodPAffqyHho@A[Hf]lHyfyf[iqqa\\yWxqVtf`OMrJYrRsbj[hR=UbExYsy]YERqh^ytyey[kEt=WtcYfMxw[d;MUKSiLobkCYsGUEasLsBAGUUIy;SdoIFdqwbscGOinSvBwhq<udUOftT\\dw>yUM@QuUl?<RUYXRYwgivBewRttqmWjXxyYpqqVkLXWEWXxuiamuprXDlKXKmEvL`ShLL?EobhU_DoNMwTAtWUTWqwhPwcIwpuXIAYF\\k[UMp\\w;lJx=mapP`IsITJRArv`s=UM=\\KTdK]mJgUrjuWOeoTQqd`TOMUDUM_LTVImFiQ]TVyHXQYXvAX]LNMPLe`ndpn>mNsuY<MP>AV@]uoamuiYaYyxxyQdXJEj<]Nc]vZqnBErBIMRDsLpkVdjKeq;AqJHYb<W<qoF@wKXJA=QtTq>muh<nNn_<o[Qn[igdYO`hisdHnJ?lff_c_cMAnR_psIxIhcXqiUOpsHg:na`H][QqDvuQ_eyp]\\GeWNrjNvRIp\\VtMIafV[VvrDgvKGybYiywggXf@iq?ii[A]v?lK`mcA_k>sNp\\mfjSo^mYdvof`I`@Fx:pvZHsUXwiHpLIe`Nc\\^ccO^?Hroime`eSIQqy`IIDqS?WvoYDVkgWcfXwe^wwqAGugTHotQ?UfwGk?Tw[dPqEBUBMMe]IrwKetoWgoHjUWVsr[mV`mbWgepKSS]xuQcXuG`;CZCSxCbM_dKGdKGXQMHLYFLAG@;fU?Gh?f>iBfsXMwrYSskAs=uSjUVsIDh[UVUvDitU[UyGXSSspEhfCRVsWloQSPXyDrn`NwqWFArmInLTPSum;MS=xKQunWqUpQMnmpgDYjIRMxYlySVMMGHW@TjxTQulKCMV<lK<=QVEqLavIyyviK:LK?Tm?irdqmTXjFIQRiXB\\xrpTZdYO<Wg@lLMlmpK\\AkAAUXayCdtvPRTmJMlX;xRddLXhmbMxqUWwLr>Ejc<Rd]jN<NLQJ[IRYyVuhtZ`Mgenexy=Ujy]Ue=LgQQ:TNa@NG`Lb`xwHlVHwGesJqjEhl<ULM@Tg\\Tr<TRXNdaNVXQymkLEq>PSNdxtemLEo>hVSupnlrAElm`pheRj=yj`V`mr\\Ioa`Litqf<YoiT=XwQiOvuY:XvF<s_aJ@HnSIuCHQqmo=xvs]OgdLbdlZPTCIlIyvJPT\\Uupisa=YrhwKXvJHXiQXYAQ@TvOAyKAYtAVIIJ:AL`ljj<pFTMAAXKtJX@VcMv>LS_TrT<JCUXtujWto;qTiUJQaskDURPnPXoM=pE\\jk=keMqNMXoLosPOsUqjIn;`yEaLtawwyPgHReUjbLs]YyOMjZUjZ<kCPNWpPeUMX\\rA]R:TPlLPllxwTR;HS<mo;tu<avo]SPIT>]NDANaaLr=vrQNEUkE]XwyvBXvyQmlXY>dlbmYrQwyMvily`yY]\\kv]UQQVZirreqRpS[xRV`rRyMoHxUAkNHw<qSgpNrmvSTmeutFmtQyKk<M>aK@DLCMvL`N<TtnEqnEWAxQuYpQIK<@myexipma`Tl=PGEQN<oRimrywytN[uotAl<ULL@P:EwBDl^AlLqReUk<XQ;eNyAKQqTYDnq<q:hVH>[MHu\\@vqqkOIubgrvhtT>vEgjcG[N`tZNd]iq_yprqimYivwevw[]N`qWkAX\\o^d\\Ncuy[biacXbd^d]q^aWn`Hod?yDP]pWtPPZgF^BX^XfmyOlth`Cirqq_lGvVYyrpgH`^C?idIoa@i^IlA?mXpmXveUYe?w[^`ffa_`Qh<XvAiZancR^isYs`vowpfmQsen\\EYs<VtnIpgA]QiZMajxwa\\Qyoq^oQq@YxF_gUAbDWjdgpl^l>wd]qeDObBNoOQ_PhfGXwYvxlwyWYiqq^qik]?x;ob?pqJp[lfjTnqiFp>Hj_WuNv^Dw]taEabRer>ISF_D<Stj?H>GxmuTyiHtqFaAFOEItAYfiHlYthEeJkbhkeQUrqYX>EdI]D_gUncxj?vs]xuGurasBAsrwXK;W<]HYar^yr:ub>sDM]vj[CECbGoTq;D\\QD`WGcmCD;Ulyi\\CCa=cnqH`WDJcbJsRCcyh]Sr;HBMFs[cP[Yt_cFKilEUjixiWr@qb=yUxifGIimEDwqY;CFl]FCuB[[GPmTvky]yYvecqsuvOsy_yQwGjatMubc_TlUvOQvuyXXySYwYKSEbkY>wsIEWAWUfuWWkrHoSjSUy]cdEwBcd\\aIasCwYXh_uryUkkC@[tDMB=cS?AHsEFQwv@Qx:WE<EdNKtnWV^qgJCcJQDg?FKMWqGcSAU??WRUWJ;gnKUjwfUGxhuu<GfnIi:[FBUtZ[c==RlatkyfrigAuYUGs<aDC]eJkb[CRJ;teixrUxGyHKMSkarMsSJugQyIlaSFow;GTuUfcIW=wGxETlAy]qFQqgSaHTCB=GR:AVZId^SBDcb>StF?SL_bXuSGSYZ;GPqtPurHCrBMGwCSL[C=AReesFasFSSEUSF]SF]uxYsSGXAEiieE=wC\\CyjGVi_xXqr[UiPMiccSFEHFsHE_xYalUxsmLw]@PL`MWYw>`yd`k@<wZ=VLaWP@K=QKTur>HN>ETl\\uhtPwpV^]V^]uU]k`IV?PnA]s?]yZXSa\\KjIKbdvF]Umlr[lrLPL;hk=PnVxuZXmvyUfpwBmX\\hV`pVgLUUQkhUQ;Ywc\\yxpreijq]oS]VTYl@UPsDWjiki?mSHtvWwUo\\yNyKgj@WfLfn\\>rA^\\Xx\\loxfqZyqyYyiYhogxrroysYvf^_NwrHnjPIooI_>iymPjeH\\b?^`ifFfyWOxfVn^PfMQe_yZyfyXfnvI^HvsXHfxOwcondvkJ^byXc^pqC?\\i?^gVZUA`r^a]QhdQqEwqeItJN_OQyQOmkQlUqm`ynFXAYYuqDFStCorwkC@gSFqRw=d>AhyKb@SrlCEniYDGiDssx;xvsywyTyyRdmSG?FBCCvAbZ;CjaIIoWqWsdQwdcc@UbgiwgMwoQIDEgk_csyBSYe\\oHdWUj[CBiv>khg;GQWX>Cb=]DcKfbORNcRbcvMsrxKT`;GOSD@GB=Gr:ssmASL_bbKcBWvR?IHGC=Adj[CcyxuaggggKIwn=Y[ibQkrciRSueGWY=_sk;v=YdayGd?sQWF]wYNKtUsR>komLVfqMVqlwatTUvsMl@Ur`<Kd=OOTpxpQZUWexSNDOfTsZ]PY]wdpTVqlGuV^]V^]uO=Og@uS\\xs@XhhsTqnAMVbMWoTlCHKUPUSqnNxXjeWETtJ<V:]s_MVe<rd\\KbtTgMyW@jrLtnYQ[Ll<dj<aJPhxcmNLdnfQwCYKFTJHxMqDOO@VlMTKuoQHyxyxI=plPVKdRU<m`uKMakJMO[awSYM^Yx_LnbtrmtsBmLP\\WlIYaqNopnuuUWmVqAyNDNktvJ`o[UnbLM@TX_@MceWjExTQQGpvOMmAxOkdlUeVtMxBdkPaMk]uZpPKLN_@nJmPrLUjHUSuKbqp]MjCDjcdKJMM_`xrXJlAq@=ViuL]iQH@rb@or]U<LPFaxLLQO@LGum]INOQr>tmudxsmyjirylvmxKyTSJ\\JnPugLQW`PiyuphWFUt^XtcAJJ\\J;yrxTOqPqfpnc<ON\\KDdjK]TFIM@UJlark]QFEMDUn=DRJ<L@HNK]LKywqIMFlZHGjaIiBF^bo`U`euphGhlOh\\Hn]v>yKPwDH]uyjFI`riZv_m\\Af;iwOPpuA_vvcmHqcHcLPak_oswvWXoFwcq>xv@m\\Gd\\?]YvqZHa]V^]VfyH`X_xJq`WpuNv_yaxoo_Xxu<Q`gOooWlCHgMHmswjcIeUPy^hbk@g[Au`Ncb_uv`nRGpjx`\\^l<voQ@vsG\\EVpA>ak_wm>uPXhA_tPoxD?lTqp^Ax[?_O@ftOaIaxnI`XOiCIvtix<Fbjpj[_pjhw:>]jGylWkLGo;ptsnkWVkr>h:inLG_LO_O>hVXmupvxaq]IqQ^t__pP_^d>nUf`bFmDvrjGp>pfpve\\InAV^ThkgopTxt;Qu`QergjAnkxQawIbQHsCaZ=i[jX[s^j[>mbNeV>[^VwU@pPF_ngc]^`B^vROsNg^uO^@Vv\\OfwWpJolVfn\\Fg>p\\bf[dFdbfoKPblfdXHvsXlIYxuxswYfx@h`YcBF^jWhhf^OO^DP^vwuYV_LFm`Hk_GeyPpLotXA_<Awo_\\GO`FVZ=Alrnsgh]\\a`w@oAwpUinYyw]YyxnmaIvtpwrwaQwdQGmUXmuIqK_kFhyAovR^u<xkeVtoIhywypI^R^[nVuUI[LovKQqDxwQ>xwWl^FkKQu>nawa]SakF`kFxcAFZb`t`Q^IGbyVbqWya`_Y_q;_]@?eH@roGnxVfmvqRXvZIpVVpAf]df`MVsPHoKwj@ap?Fji@wnfiVVp>IwAvm\\IwAyqj^u@qgwptaPi^WnX`[=alZPeGOxVYhPvfHads^hBivUxufXh[QbWvuypkcogZOmkfj<XcNFevXyhWkqvuvwlcIw;v[v>hJX\\ankjfawFk_Ge^QhhAuB^]Svg]xdghxW^iXhyd@wwvihqqO`j<hsW`ZKOcbnlFIfDv_v>hfvsDQe;XsQh^K?[@hhXxdXYq:pdsov=V]q`maG`i?jP>msFcKalNWm@fmHhjqAbBPpL^nJ?[gnhu_]FbmCF@Gw>qrhqcBce`gH[gHTufdWRjKieeHoOv^syrIwYyvqseriWX[UrcXM_DcEhR]E`_CI;WpSe>ETTWyYsrCCSlyCEUXugTdEuAEcO?E@GRk?U>MSskw__HtwdfUu`kc]]hPuESCeDAuY]VHGri?rW_ercYYEtfmFBEe=MsD;T]kcmHq<pPYlScMqUyNsakF`kFxUHDJBDVk]VdYsveyeHK`tYHyKy=yWLugqOxANAunMLpopMkHpVDX^aVXHy]lK?Qk>ap>DXNPOGavELL=aPsQsQpyJxurQtyEs;ij]AWg@Ly`jF`xalXvUYV`jLESjySyIWHxVYhm[iuqUovXyhQJiaqmUjGhke`vleLfUu;iXG]K]`rsYxaIUXmqDYMi]qHepTxnVmOl]yrISfUu\\_xnfnLG[Ma`c^\\Dv`sF[Y^dQHuY^kdFiMGdIVuf>tWqm\\vnhHdIyrRqbW^hKPlRGv>Ix:pmYVpwp\\l_x>gmpW_<?[?N^^gn[?dXHcLqi:OcZfgGad_@s[vv;o[fnm[ywuvu\\Qbea]X?w[WcUVcTAc[F`>HZ<?n?ApiFjRnbL^Z^Fh<_m>A_O@vAHZpn[mfv=^i`oyKoiyYpy_s]XkI?dCyd@irhYigOk\\GpBatNa\\UWeU_[@VZ\\@_`?`bIpppt^IlKvwKi^:>ZZRLCTJXNYpqwIPlmK>@LnXugIXDHTL`N=urlqsIxlFXuEmvR\\w]\\jBeLBpJ=dRVTWNPpJPXLhsGuleytw]SMINQXpmPy<`kF`ku]lKeLa<W\\]jj<YbarE\\vmiTHumt]mqmux@rSyxXUNBLQreqhtLYywlhqgMpwHU`Av\\Ek\\Eu<MS;uqUTvsiYxew?yUaijaoZEVxEWbaW^oNhhav\\ysXicaH_@GgN^vRI`EHuSWjavmnHuVa_moyva]Wqo`^[M^jB>llO=IY^_w\\[R>ugQYfYywkghogc[=EVsIx]eSGeS[YYyVgeWg]U>QIocH?QtLQDAmcVCuAkC<AgXwWN_iIMilsgNkb[=TEiYPoYyeegovOmvaSV:yRZATY?Xs;HaUtd]RVmIYyflCVK]gR_xuGHeUgXkf=crdGby;cKKUJcrxKIbUxowbxUcIYUiKxPqvIAYuUva]UhmU^Eioee^CccibwKvrKSueFFOeOgCMacfCVM]hD=S=AvmyrX?vmwRysrcGuMaSPsfR=er;SXIGZ=S]YRWecAEd=_Yxss<Qr<SuUYUrqYTUSbcvpkiYCvtwhi?tqcyrysyqcwGW`mgeQXZAr;Ghm=D>CD;=dpCUWiywashAiQ;sVSbuoeWIRacF^QX@cdDgr`qFnMILCGe[ghOSXIYAyfVmsmcIwuV<AvSCESCEY_EuecIoICSgbmu=AVAOR;=XvAgIaTw_rCYfIQxRYVAAC@kCEyHPGuVQU@=sB?ITqV]qR=oY_CrkeSvIRFww?Ae`GSc`ShtT:XqFET_]vN\\kpEsoEroeNMTLpTKElPApK_IwoQL@Tjj=qDXU^HunDlLYRctmZ<MJywqAK<@VfDQSaWpDxwumPUoolUoiMclunQYwlSWPQoIn@qTqUMcimJ<vehV>ps[MTAMKM\\j`mYtIVh]WWUnOIwJeOn<O^QWBLRV>f\\pgMGmB>qjqhYHrZnFqGK]fcqh]KbZwrkWT?KfZcGnkhgUddmgHQvFQDPWVk=hl=emSHIWhXYU_uVJAV_giFih`iDtERISRR;G_Wt<aV_GDDMHSwe`atFIWfCWm]WllkGumZMonTj[txBUmEXm_UtqQVSm\\av^S@mRpvwxxPAuXq[bht\\ahuvm\\Vnnv^BW^AflDgjcHoCOugq\\wqi:xvcNjZ_n@hlsfZqQ[SXfjx[RFgNWupHr;YjhvcxFe`yZy>[RweI?\\<ivlif?YciFyFysA_mtf`DfjaW^nV^]VvX?fiXdZ@[sPbBypkHi=Vjh>g?XfTasNYwFgcVNvNYbooZ;a\\eWoE_`U>\\@Pkmx\\xXruwdxHcRFy^YhhniJF\\F^^Qp_yxc]Itgo\\IV_FFgVih?@qY^uGHlkifUA`qvf[hp?pthFc\\@xwQ\\;?d=?kNohl>[vOywqyjvbwfdTH[<@ZQihk_]A@^BnrHOrdQwdFcL@hnAwKYmtVuXi_aIfqpoZNbeqZTxhC^xu^xwwlJYmAorM`cPq\\c`la>x=yfRIwfApSaypvjWp_LOgF?nJx`c`tg^n>X]QObtfoR`eXO\\?PmGhl:PcGa^Hh`<o^F_cFWxBIpaHhWv\\c?]FylHN`U_mAGg?`\\Lhvpi`PXeQAx\\pa@@]Xy`t?qDxk^pmYPv;HmM?mLacWHZcF\\BnghIgnIvmWqqpu:ihm_\\EXprqyuaxtgc\\@giYhwYtf^kYiuaVupHaj?fPXgQqtbqhObUOS`wV_kBqqDSWVjuDmKTd?EGKiNucRMHkCV\\Uu[;FjgwVSb;ov\\iRMgsGUBYytRmDRkRPawfSF]SVyYhUMWd;ccAtOugJyTyyGMKH;=s\\kbJ;Cg?RiWFREroSD<[C`qcvcsKgrQCxAcT@KyVsdPeC@kY<MD_Gt<GRI=tXqU[GudMDAIH@gYqufKacDwRMyv;oEh;E_OYoQTT;UP_fNMXx;xSguCyiYxnUiwLYwoAK=ALYySWtjlEqFqtPqLGqVM@NBlWdxQrXxbIxepJNdSLlY:`vyIrNXUnXj:XkQiSTYwE\\ms=ve]sGeQ<EqrtSRdYPhwPiT`PoaAsaQSRMt:IP_Dy<`nTuPSUq\\EpvhLKxOAAMPMRqhLMump@mXXXb\\Lm]sPuSjat]uUDUW:\\p@UlPinRPt>=NrLTwLsKPwKyko]JDUokmxMyrytociXHTrdDVrDjiywJ\\JCyRy]wMTVnuMcMK?PKTuTcixfWqxFfbN`AAvXV^m_[pI]Long_s?@c=Wi_PlE@\\PV]UF[GpjCwpeHoNOdaN^]V^]VvXA^o`o@Nywnpwxpb?igOusQ__vta@g<X_D@u\\Pj?G[;WmLHt_HoXOf_?x]nhpovRqxYynpfZn^gtiw>piqFfaWqIIoMvklV`ovj]WaYfp=vhWvqfhwXxsaIpgW]AIhRAuRArj^[FWt>IhVNhs`uRo]mqw>?nC?krPb:ymMO>;T^mgdUhX=u^yoyQLiqUrqOIxQxaPatvyUm\\HYTPVhYofpWWEvjaU<HVe\\ScDpfDkMxtVPYrAM?UxnToeutstYkiLvIj^hpcEPmTU^arKXPV\\mriXHlsW`uMaonuOcXnjXu:dxPYOimjBuM<yMAmxvqniutuxQgpl^<K`Ak]iM\\AyhAUSxk\\dSixT]xuiHL>lMK]XaMm<lVvMX^mk;qQ]dXB\\P<]nWaKIhMm@oOaMfTSkHpKLxqnr]irQVhf^_R_wg_rPHlKHlkx_KYvy>k<`jUvlwnutvp=oaa@_PHnTW`S@osadeheDGaEvtnG`>_kl^[fvr=a_Wxnt?r]Ouq@[wajhqcBxtQ_xtH^EVpAA_OVo]q^OX^O@muHmUg\\FpiVWjKA`FN[?PZoQiWhlOh\\\\Aa`FcLHfmWoIVcQpuG?gg@kO_kaPfDpn?@t<PnjFatfe`Y`IprvAwuVafpgVXfggwYIfcX^FatQ@hDXdrhloNk@`bDGk_WcFWs^WpqWjavmsiixPxsya^?vqIkM@m\\Gu^venFhfP[hhdAa`MaldhqIAdGpZWpt?>]YvtZy\\YnhgnaXIx<wnMVpwhe=YxH>nNP^BNZlIimwcP>raxyvwtTGtfOqrouFFbj>vVIqoOnbF^YxsfgkugjFI`RyZfigxWlEI[`v^_noe>s_a^AokR^]t^fL?_:ipeGZYYyX?sLQlCgqhFhWW\\[^xXfl\\`gZqf^_ffybLIqevgXn^hi_jGwW@mpWh=PdSqnJO`bhcT`cIIuV>mq?mVpsK__R>up@bCfZ@_jUx\\Rok>GgjaqRvoQFlqOsVHirIi`VwmXiL_hpy^YfnhVpuYi<VtnF_QXsnPecwlWA`FFk]ajrndqgxs>dD^q;pf]x\\MwmlGL;ER[SPcUXKIPMvdir;CRJKvrgS\\CIZQuPQHluF;EeTwBIgSZmvG[fJ;upGSuWhGqV]QEAqCyCs[YRI;fNMb[Mswcr:QvPOhoOBkIgSQvTufGcSqohfmHpkFrOYowreygYAvmtYVTrRlweiMt]niuW=qsHekrlxrTYpEmHuNZ`TDIN_qWwLR@qy_TXFlx;TYU]ui\\OR]QyaYKxwxuP`eV_DVpmTmMx^pVtMUjevD`vWxX^tVIqrFmSDmLQdkkYJiqoG@La]V^]VvQN><n_<nk]sSmnEykMUswalqxUwqUTiLPqPblLgLWMmKmTKHTKAUJ`mvMqn`mpetjWQW?LT:]MclJwAMEAOjawMxq@IoAlMa`TfpnUHqAikShq?]n]dtUpXuhspqxplmQ<thujnTmXdnLEMAIqMyKF`P<XPdxnJAlp=LHPKnUmA<WaqtcpLD<mLQrk`JmexRXTaMKVEYYyrl`KlEYGxwoDSNPvtQo?epTXV\\Mu<EOj\\n^lk=mOWEYEhr?xNR=muDjPQXIXNjuvE<tAEo>mmaHWn\\LUTM?MXsDsIxYVIvsxvNlnsuNixkZhtD=uVas[hxNloUArmQNL`RgYkBXU@yRMHQ@tXwtPiPKNTk@TXmmL?Qn>MsR@QPaj[pND`JWpk;Qg=x`Yaks>h:O`yvokfsuWy[wlKHlkwg]>]THkTW^>HrKHyAAi[ImYyf_gfWhxGhhvIjIqdy>nkh\\lPhGYfoQm=Iv]Ia`w[sttgbgASL?U[GS=ugs_UKgrsyRrYbYiyY;eX_eygVMGguedwos;ehTeVlMXLgxoiStcEYgtOucEydqCeV_g[Uu]_HTWIkwdtusIAH]wUe]f[CsSuBBYxfSEGyi:ihncRQaRdERXqhrkYl?r@QWBuiUCVSCI`mVd?eh]r_WxgkggwHkiCQcfZkcOkfcMhtoXWgsGihkOtJAcKeU;ie\\uWNqFFCfUicbuhWktPaWXqYuwciyF=aW:CxcScE?wkQF]gVC[IIAfUiGmcIw=eGisBGysaBEQHlCrMWY:SvImy^`yCimXIkFxkIptT@QPaYaYQwmOX]kS@mBYnNhRaXNrUvGdrOYoD`NC<oPePamsr<qh`MA]MhyjAtU@mR@iQB@t=iLWeShtlaAv<IPX@Y\\YXRpk<YxvLqWqKwpUApWAYVeUpAUoS<L?LKn`NH`P;xojQqCdyX]sLIvaDyWxoxySv\\YdIMFTrRln^]uciLlYQ=Xwt`PUhQXIYaEmEtLp=OQXWfdOGQTddv:`TkAwMqRiIXD<NGuuKL^qIgShZDHq]^ogwqIG_YAroOb>`Z_Nf\\We[ybDhp_Ajgik:F^OndHWtTIkbww>a^DWfTPl@qf>wp_@uVWwmVawOjAvcxF`hx^:XayamVFa@Nc;YuiWivPydxs`qnZ>[VNrJQvqvimvbs`g[?]]pfvwmvqaGpPcBpgGb]HNsvHiFvawaECWocEeg`YX\\aRKOWocw;GXakwU_cUyRPCHRyHbIfakGj]ECIx]qHQqgcKUg?erkccgtfMIW_LqiteHPixqXTxwxwS\\msTl]EXKIRc`xu\\nvXxMtU@mbFxeHFj`?ZVXZPI`GfsVanCy`xphTx\\XXiJXhaqhrPisHZTArpHf_gywohtw\\SoqVQfdAj<qh_Fd:fqHxcHp`=vqC^kM`dhYuhx_PhvZffG@_dHvsWg^p^;i]p^kCHdVW^[ii\\f]mHqMyrPVxNWxAI_rXprpc;PjmibTguW^_mWkDGt:AbZ?^b`tFO_oVloXwWoli`xr^ivvjeQunxhLquHnkgWfSq`;_u_at=xm]avkyjkh_a_u?Nyh?bDats>pgGrQwqTGvipyDyfogdJXsOHpgWlioimNvUvuJ_sHqneXxYpl<FvXGwnG__Nd`xiCVrLvgwh^bwpG^nNAgwwqHpnuwjFI`rXsSFujQemntgphVFscXdpV]UNmQqeEHgoP^tiiUpiYWl^NkGhk>xpXQkSPmLAA;eYwhAQYQIwqiV?IRSCESsXuCg[Ifn=SZwWJ?ciMvjEDMoUtseSoFoOXBEgJwfPmhr=v^eBgoS\\AeaCxtiYHiUvIDiaUvYEPyTIQTgodBORbah=]U[IvGKyuWerww`OrKMXPMyFExwQDwqyn`vTiMQ`rN=RFYMZxqA`vw\\JjXLp@qvqqCmuVMvbQrM`Mbxm[mYtYPfaXiXv?xQ:ikq@PGuLATJAqlNLs@lk]EpPQjeuvNlWshRmUsa@qc=jfDPkdvJ]ON@UtLXTXJMyjKPT\\PtOXpu`vs@quamhxtG]WU=Tc@Mv\\yjhscYtpt_?GxFY`TPiWGfUQhI@qBynsxkDfoOnk]O`wfe_Quo>iai];Qr<PftOuVVudvh?IwFAy_HsVVjw_rbGb=?[rFilfkJ^MybnQYDoUIKb[UIq=HRauF=ypyhA[SF=EFysU[Et[vLUgSwXbMDCAsBAsrivJYR]iHKYBtCtU]B\\ywb;egMx<ArNKBcgB<Ccg=uFutVKsOqDX]EZ[X;OSvSR]ww\\qg:=ic?woMV<sEtgwR_iK;vIKbwWEtwSWWBJMSKiwTaHUgXnoe][CoAuBmynAEsMF<cS>]ru;SXur[uBECSosu_WwoCinoY;gcgYxV_Ut?s;OxE;Ww]eP]XO_FSuVhMI;aRagYD[UbgtE;uAqvS]eyMcOiwqCh]qDsQf^ovP;eY_GkSxRITPovx?r^eYX;iuSTYMt?=R;eg`CgQiBEWcjIuIQSxiwyghsqtq_YlIYUwbXKXrahhmuwobxeg`CGQgF_ODvmvmCIFUDXYYiKvRIh>GsCEYYqf`iue[VHGrxGViEDloVpmlKYnTPWo<VmUT[IYT@OTdQ[aNWqoZxtEOxEiidflRx\\Y_ojOx^om<Gr:A`>NccaohA^]V^]q__?erOooFbRivtqre`Z@Qa?vdLohlavg>hGGk]feF^^L@[;Q[k@iIv_spcaX`EqtZQ`Dae]@dBIvqY\\tiEiXOCSSarlcuu[YvuXAKU=uhESUUeR<AxbSgegItiyr=UZ_ycyg@UGOKDbgWFCtAid_[G[;INEXrKhZGUYuu^ay_wTC]seagRuHRGgxCSR?ENKS`chT=cjcGfSG<AH[sUjCecsE\\yhx?xi;YyQvU[XugWV_e^MVDqfLUsmcTt]cVWT?MSmqcQSEy=dNmevcSWkhfCr\\QfGQxlMRVsFBCBgqh;yUviRYGgc?e=ybGKc?atFWE_OEyMtuqBj=yjgsVaeGEgNSX`ac^Ax[ErEuG?_yryr[ScEOcSIUqSdCuuAaVHGrxcFQWHboTMKwoeShsfb]HL[dL;Sc=fN?ReEbPQdQuUgYhlOt<AHnCyv?VcEgj[XF;EPYEVIw]CsBAsBTKn@ReeRaXu\\itQuYD]Ot@q?DRcPPZPTm<mbHUNMkxdREaro\\OFEW]QsTDloejhUwG\\XhDnlDK;=VMYWuaxuHLk=WJUOIQXbAvC<juLo?tYq=NbqXOTmUpNCMp:yXyXyttUuQUYXvAYLfUQglxXdyXiwaYrsTSdDjHxnj`KGEqJpyuhJv<Xv@r`qS?xxHqxJ=yVuWxyuVUUuYYVTYLHysUktUUkTPkDjNXJfUu<YxUaWfmq@ikoyXs]yFyvj]mvMYNtPg`VYiqGUMnpj^DJMajMxNgluxUUkEwL]sIxYFTQuLkoix>xwyuY:YrITUvdynEXfpLnIsdLJCHXPQr<Qj?auVHShtLKUocllP`KxYry=tVAq[IPkDNsYnyLS]DMcey=mlt`qYAsVVy>hqopZTwn=^pNOlv>yZhrpq`fxoA@[[>pgWjj^`BOln^mQyw=Qwd_seyoqAaj?r^ohPirowhavrffpbV^]Vvh_begj:?vRX\\NgsaGyEyquYdL`^`@dFIdbF[dyZfovIVaV>mqGoIGeNVk`np_FbTalDW\\FNg;fm@xbL`b>Gl^HufY`SWaBIwMwck_gkI^ZYj@PvwIsZ?nSQu<vuq@_Qx\\kiiQ`^sapMIkL_cSXriycLNs<Fdh?j_V[Zh^Mnc<Ik]HitXjBhsO@jsUW?GJ?WWAf_IGxmXPXlIAQ>HXl\\lYhtnXQGmsY=YOhr=ukZMUHTnHqtcYpHmuOiNaQRfqLOtQuaWHxXYitvixYUWHqmOaXuHKCMVjypyUu_pUI=YbINQPTCayNeV<eMAMPytWldP_=xTYWKdoP`nWqPsPYOlymyYpAQwMu^ItAUO]QR^gikxqBavDwxSViOHZ:^nNa`TNmqxuH@k\\VZjFk]A[gXl[Pg:_kPI[k_]]QqjuJEVI_tSMU>ohq=t`mewmR@mrWwV^=TB[S=qV\\OIAifEwdsOYsebGixHcuPofkoEmGhTKtRaCcqXLKbJED@Qcj;Trqi\\;Eb[iXMR]UF^QvsoD=oYFYtI]YSwDYwyi;eYgUVSwsyuIYXX]EekUxEiIYSicxcyxG]YYQVhmCHkEn?eTOXAqr`iwwsR]CILiuiatTUfN]cNkBwuGZwIRuFDwgKEGN=BQcGL[hW?v]?uReCJQSKUgF=TcOi^KI[GhgIbK?FFcSqgEMAuBCuSQCSmipgs]wcv?S__TAAHF]BuUiUsuGysuCHHEXleUCiteGDiiiQSthUifmW`[RK=ciyRrqY>GV^[ItAWx]YisYlwb^GEO?ffmW`[Ut_DkmyvoBVkGWMcb]HvMvr[rkMDXGY`?ccMsI=vxIsrafCaE=gYDMgl[BhWGcqXoSsEIHk]WL[B@CVR?d^Cgd=RdWxZ?C=ADIYcbaX\\]SM=X^ASx]ywsPGqJjmR@mrW=rjMOl\\KEPT[MjvXU_XtkAuXqWJQWoHwpxJnMU[duP]SihM]ixNDT^Hk=ekiyNrYJ?xtEHwoXLvqUKXPIdyTtUrEveamt=vk]UatQXXwhyxstwWyXwmUwetahup<s_QObemj=wJHrkYvPlnsLU[uqwqJaPN;Uw>dk<hQHMm:inUYgOiqFax>OjNN\\gNfLV``>^[XtCHuTW[BPbC``oFkDHgqVZpop=_uvHjiI_pop<OqggbV^\\rGvSyu\\pdSPbDGahIekwpu^juW`>^[=?tca^fdDWCQ[B=Gb^[C=]dD=xv?dgggXkcMSXjAVH_Uh]tUAvpyEUquwMEwyYegfsEy_ec[=ifog@AYX]RNcRnUi;sRH?EFeSS=IH_E`OIWiiaYI]qVlsrZTViAYq\\Kb\\L^DVbHwoQLtiY=hmW`xiIS\\@TdDRB`tk<xwAlXuO^UYu\\rl`NmXpHlnclrG<tpqYqiuvDV`]V^]ui\\kttu`<Nt]sIqTBivF=LDdnolkWxrnLXF\\qBpYilVJyTF\\qRdnnDTbHKALKixmj<xNdJumlYayDyYEImMysMEOI]nW`XApj\\iy@ASDTX^]Xhho?]mutLkPp\\DQmmVL`N;HkC`j=yj?TLMlsg]kT\\khxn<Et@EXX@me\\x=YwnPye]R[Mj_MqrlXC@PN`XuiOFTv<DYQ=N_PNLDKxDW^=W_QW:QsoqPwqy:`NK=y=dstikBPw>hjL=theJFLY<hrsyVrMykyoJ]ONmjAqqyqoq@LcuS=ts=xtXUkR\\Kf]YyLRc`jj\\KSQulGylWmAq]eF`off]OmlY\\f^bXik^_vmIgWVveyo=woaAtb_^>Hf<_\\?_pTGZWqoIQtLXbwpg\\OmY^wffmkw`MHa@Ba]Fcmhj?Vjoh`;ivEUMsrL_F[uSNAF;=CGMd^[XtCBWqW<qr@]rnahGIr=owr?fbSTK;sBAsrWhfqvCmfeGsw=VM?UyWbLsgjSIIsrQocl]xBYFVKUr=dCOsvKEGgVs?Ul_bQiSBKr;CS<CTBcyh]SqgEM_R@sGxSyuasFeETYhl]YyusmESLoIykXpMDhcUDGYyiYGyIuyV_MgOUeHuF>EgBwbYksIWWTqy[ET=GdM=fKAy>]i@OtymRByhRAwwiIaqTxMrTic`CyvEEEaXBIIM?elOsOgdQGehWWVSRJSC?wgLKY[MRaGDkew<wSmUI\\[COCS^GWf]RNqbe[t;wE\\OfvsSXoy@SSAmE;qhV;VyeIUqxDYbPOScGhyquuEDeUWPSb;OFCMVZCFCMDPuTuWr<?VQOWOQy:MSKiwEoxFoxCEG@GW<MbXuSjqxUIWwSVVsr=yE?IymiI`ofZmYXqV\\MFWyfWEsoiymeEhyRlsrZpNOuMl`O;Eqf<WqHnYytrqq>yxMqOBQUaxQ<]^tf[oXyxPfaw^<Ih^nl_>_PfcVvbHxZwqgGVbP?aNHlKHxcWl`ymA__MFxq@_xycVne;?xPNjm`\\mylR?mgIh\\Au;nkW`a<YxIqyXvybYsyQjQvmui]`onQFiaiuQHk\\@lbNtFNyCfup_ciX\\kat]xyBPy>a]@`cePamVv^fmUYj:Wh]qb<Y_i`^vItYflbhtFosXh[RweIHyvyvgOhsVxphnMFgnF`ea[ryukGu>ib]fkRpbyWlyPyUywjWfey^niyo^eu`bg@i<vrw^b\\vu:Q`=^nN>yCObu?\\mXpWinLXa;GsxFjYismWv@Q[EydU>g<Ok_WkCIk=_]Why\\vevowyH^Yx_[vx;OyJys]_\\kHllfsL>auodl>]BNnbF]tvZkNb>ayfyfG_gU?hrApEatNhcNFw[WdMYuYpZpNpO^eQn^aFvAvaBHwqi^;?nBVrnwmNPkrIuIqpKN^[GhKiftOu`Fc@OgBXyiQaVyc^ok;qaa_tLfuk_Zphocn\\oV]UNlWhmn^xb`lXYvV^nsoi=Hj`Wf]>nSacjaq>XfAaedihEVrJv`On`iqvZqu[XjEAsBAqI@uOprF_dFqcnytngtYAfRVmRNZ^@\\RNr;Ar;A\\KNdXwZaaalvu:qs_AhfQ]B@jmx<WFFOR\\?Fo]CteuR_Fn?yVYHYuVdoIy[TgGiYicM_HW[RBCb_ER]GfrqtqOyVoIWmVmUTjqvUgWhkUVIFDORX_YlOb[=cUQdH]fK]Fn?CrqDHCC`KDE=eRMTLQCMkdi_hB[xDSeGyhs_Y_aE<]dRaWfGv^QyREiR?C;uHFGuTUxkYy`sCy;x_kirIiykv[yBY=FiqtsCYvITX_YryXsSX\\yxR]eumcdEY`uUucB][hP;up?V\\MRLIwbmgYuSYUd^cgMAD\\kFFSDhwUqIwoQDHcElEIj=rxGWKwwpuExAS\\ctk]BqkW>]UwOGbehLqfsEWTSX<]EA_urGvKIw>]Et[d]Ar;SYV]ivweiwrwoS`AEfYRx[ud]IW_vGUTJ=GB[UQ=F_?fSad>GF>Gf@=CGMUB_ITGG^CT^;WqWDPmT@[wfab^QXcyX^QX@ybNyclGRVGdKGxcEfL?cUcsiUhPQY?sGDCxooFNKeRMCn?EOiEb[bV;dBiG@KYOoRyQDqkHYQVugXC?ID=CveSiWEMYw>ab=;YkIyiWHwchJGI@SR@ubiEU<geW_bYkyJYRDQFeUWksTh_wjUv@qHgqhIYvIwTboTG]SM]y=WXQidL]C<iEPUIyES;QSjgf;_D<SsLAU_Ud_iv;CTl;FFWUnMye]XtYwfaXp=HWuevmu:Me`ceJyfoggREUhMTDism]YkICH]GwksFat;mcike[AtVYfNYGE]vWIC^_y^QckuIgkRuoWRCwmiiTetfeWcMeGERywCCMdTCvZ?wnMDTccRoSakroeBMSD`kcMouiyhmowZ]dS=Hl]GEefNMxpgtL[C@Kbj[c@WyNSteiRfeW?_XtCCEWcsKs_UVv?CSgxKCiuCsVSbw]sAcE>stGUTDOGO_TsEVuUUl;E:ugqKdAWt=Qe=;D<AVj;TfuWA]Ux_w[IYkctd_FQWdNSccaRlUgJwuxmeZUHlKHhqUpqhUOTC]ssWSy[vWyxYQVwUt]UgSKtfibnYrJsU?]R<EdBUDg[Fk?wk;te]wFkGloioEcb[cCcYGuiM?tXIcjQYDOTkMci[YxYwFetaqwCSVkqX\\[bZ=HJ]GisRVEi\\EhmWDlgiWaVauVAoWq[BlasGIeNUg@kd_sYCOUncIh_GBuyA=foorqYivwiliWDcBIstlCh>WcNoHsQX<UhYCtiifYCXEGD=?XOcW>;GKSVsoFpmsZwvA[XUMeewdpCS<QBmSdE]GWCY>Oy>aDMchs[Ua_bJSidMSYsWYuwhmRuwG_[sFACfUEvsSLAW^Gd=_x>sfIqxpUUkewTwspqX:Eg^CgQiGDcbWuvZ=yGwh?AFYcxU=eSGdRkBnKE<gho_HeCRccHnmCnceH]sOYgxKScmvaiEDeF]]G_Me__GYiY^mc;iI<qU_EfvmUJ]GDKwoERRKCpsH_KSCKvrctEoSCeTs[C=ARBCRNCWpohvMvrCrl_Dsai;mGa]Cm]DqUxVsxuaBUGdKGXQSHVoeNoTvgYpiTXeycYev`wPToQMNPqTvmpqMRTqUBuQCDK>xRZLJ<]NDDm@MLn\\xtLkhUQ\\HqWDtd]RBewlayauqDYtI]YSPXcpJ^UxRyJeIsFTJlEQ;YsitrnUqCdmHUMIYwJdRDxmxaLH\\Mj<Ql]r`pUIeTymQt@kNuwseugml`<l^DPf`Wf@LSutkeMBImo]nhPN?u[Z@uXq[BnZTPh?InLWsMOoCNqw@lZnk;Qtb`ZThkRhkUfi^Pok?flIZPpkVpbcfZ=yfN`uaNp^xqfNbB^[=?h^AkZvmQ`pToZeV_L@`VFcMxnoIaXxZaysqAuSI[RxmqHmXppkfsWYhkWaN>[qq\\qV]@@fpodJIwbooVGtromknok_]WwiIYjY`y^hsNal?axnhb_Pf\\?]uhZCyyJiyCAqw_fHHrw>rXIcxfwx_m`X\\OWo<fnZNk>NbbOvR?\\AIwuOee^[=OfT@fSGoaqaR^nsQkK_lpvbMPd]Gecge<Oo^IZuhcc_xXhwaWjsV^]VvpAnNOj[?mnPmwnuuwxlv_yAxGnZWVkGX]KV?IBeuTwmXpSF@SBG=gZ;cMKbBED@OerKt>kY<qvd=sDitxce`]s[gb]aYe;UBSI:;BB;RLCTJctisymyy;av>IbfKUjUCLQFLErnahCYGi_bf]WbKeGqExwu;=cBcff[IIkSX_skAr=kGuuTruYkIYVcHkSEoStN;F:aHWkFEwfssivQHDmWMmGC]W[CS>oR_QFtUbRgegAcPUF>iGR[vDkBUUWKSwekIwqU<Egd=hooDLqW@aWfoxj;GmAyamIIgVsCWwCrreHvquvor]_uxYrAgBAkCBKEGCs@qbVkIUYTKGDMadNMGhSUUEBUWeX;djSH]ETc?uY?s<ueL=vr;ThSGfSSkOh\\;xvSej[SgMcKiiZ_d;IumgIvsG^oUq;eYwXj[CSgGvku_]VHGrwkrb=tUoFNQWcmwYeihGTDUvsMbHur^[C?Atk;TRmd@iXMaD\\srk;wpUFPytwkB=?BgWVDefniYQiHAUUrgrpSh;aeKGdkyC]]tGoD[GDBKG_ISfSHAqxHQIeYEQAEriY\\?H;Ywa[wfurnohOkYYUD@GWqWvZ=dZYYCkiiGwfaRnOECSCmsCmYYyWxYIx:IcAqbKIt[qdlGIE;isKWZ[bZCSNsvIYSpsH=KvrWSVsxj[CUoVMAV]Uf=GVraexcU\\cHpyXysXmKYR?idIDeYCnMdYKvAgE>kH`_s;KEUqXCSBE?IVQrJYENMx@;v]IDK[FDotH]rDiHYoV=yrl_S\\?DTYIkSbxMRooW]ix>SeUcWdcr][Y`atQ;YjarMSR;gcuutkYuUgD:CWWCV_OBEWcTOVkCrqiGtcE=?GLAIHMb]AWDeFEcfncc@Ab@UV:mGaGGQgs[UvtWUYWfYmvViYjueDgRCaxn[TdKcpUuZgtl;C<CHHUGl[cNqeRauF;UUUxjcS?IcMcrIctT[yDytiuW[]vAIukacUMdskBqADuuwoEGMyen?HB=vtGWb?E^KTDKvRMVTWf\\UvNmXfcTpKBUqdBECk]gjiyB_FK=e`MywqfsIvVgsIkC\\eyksBaiirCYa]V^]yd?wkMGBoR[UUPcdDecSIe=_SF]tS?gX[BgCc\\?ej;ccmwn=WfexMIIdkSoEy=Gb\\;EbMEUeIdgr][IwAwQAyVpyPDyVExX`SgDqw]ncdMoPmZaysesdQWFuqiYL@hM>@sKtr_lXpM]pvdjfs:Xdap[Vayciaaade?kr@c>YcR^q>?_XwfghyXv\\ihqGQy`if^H]]Quo_g]O\\Yyu;WoOOg_IZL?]>^^rGd<s>]wf]Rf_UO]WgwXR;Y;ciH]Rj;LO]SJHLWqX:Ir=tSjImAtqFasNIVnpt]YWvuolxph@TB<pgaxThOf<SddLMtsM`XuPLghNhXoblLMyVu`lJdRCdqX=jaiKJQQ@Qp^lloIVADv`YWsUwaEyGysyYmE\\nmIY;asF@VcESL`NLpSA=tiYk[]d\\vlEwiIG_GwoQFtei[b^\\^FqVisG@txGtpvxfAftQpefhnIlkO^gh`]Fg^huf?ouwxXHyO?sVVju_kwXjNWwn^bVWo_X_Efvl@rj^^LOc\\@sRvc\\poe@hVfk]AgDfZM`iXAbc>]FNfthu:>cjhgGhfCHn]?nAYuthauamGNsF`kui\\ghxjHxO>[[@tn?tVxbBxxbnvq>mYh\\f^sU`_f^_lf`oVrVauKo[Fw_[>pBYqM@ccQ\\AG`[?\\Lvr<vuMaggghRHoy>r]w[yGk]ybYreqSAyE?qU=UhVmdfuWa[ghOCpkH\\MfbWSL_v:OG;=t\\UYuQGUWeeateiV`mVD?IHMECmE_Ob:;GLKFXERkyy[AcE?CKqfMkgkmwlYYVwijmcXwhHMRASuR?rJgVFUH<aHPGXgERb[DwAH[WtE?wp_H[uX<sRHYblGwpWR@cyROVCIVlMg@eijAHIkGxeb_WrI=dmUcFOF;ux=iHXYU];VUAHocFSGeK_tdEg=?vtoBJOgwcvl=dIYSfSC<?F`;C<Kd^KB\\]C]cSSkc\\?C__tr]cbegAqS;igHyvgwuEuUGUDdcDCQtL_fR]SW?bbKHBOF=;t^QXTOTCMvtOdj[cc]H@;ScGD<eCMUeMUI_YfpGIXyinyGcaC\\_DTeFbefKQSWQxa]e`mx;UVcyvVstwAS`AEVYrfiiaiGecgs;Iv=Ul]vB_vJIfnMvBKbn?BSaHMEuksr;stOavlMbvmuRsHxSEFKFvsGZwuY;D>kIk]EHcxMgrrsWqcuPyGy;rlGrRGdkuyjIrO=snIdXoDckFF;CnycKQviERyuErIGLAYQOUoGr<aY?WDasCkAxcysjMvRYfFaShCxBYRIQvtCYTewgkXTWeB[Gvoi\\GujAhGGC`yfY[vBIvMYRu;vXiSmCiw[f@eh]AWtiY=gsGeSywEL[B<cgEAC[ID>SwfwgYAv<ibpSSEUDFmS`yrl=e]SbEEDHSIUsi<WbGGSX_ee=tbMYV=ilorOWgiQHJwWM;YD_iu=EMaXcuCXyfN=wMSC;uIK]hTIFWqD^ieSmexasq;gQmD;eDjgsLSxmwbrkYnICHuEwqBEuBYWfLMe@[xwUvN[crGi:?IwmiY_Ic;IoMsZmV@arl_GfUUFcE=cSxsC?QVTGGJsrKCVbYd^kI<]rFkBwIhm=fNOFFSR<AH^CSLGxuESL?BvQRASYqoh]cU>]UR=bsIYCeg`=VSmFCMVZUuZAIT_YXUTb[fDuTgqhIuiiYBkkhGkbKoF]GG_oYxgS[gXdaB>IDCuh==imGsZew@kydiH\\ortCvPQE[qvTMytgh@=hsoRjgiHoc\\[TNKfM_BcMUFoxrqv]Aiymw]WU[mYnyg^]wAmxtcB<=c[GfiGIj=B`uV?sbISc[ut<ES]GVJ[B@KUU;E@=cgurRqh@aHMIsp=HJ]wfarbeELkbc]h[[CgMfBqFQWcjgWu]IJ_hPAe`GccmuvUWGoBq_dl]ymwxmsxuARFAsrwdKAwUoy`?Tb=r:AEOOhLSwRoYl_sTOyq]T>uBQsBcgW>SBfEEZlqEXWD]L@dncYNv@Quyrrlr=\\qxqkEqSiiUplOWXrlLx>HVF=vS\\Ux`YSHuCxPsaumtu:IXVYQl]uuijwxsExJX<psYjy<lNTkOlynySIDtiyUaLk^LSS@K[UL>LjYdybQNyqvYAWxixypYKxoveVCTrJ@O_HlldW@iL^LlBUKDml<dmJ=LLxJQPsnTqCtQsIVUdl>`y^awYPXhQxIDmdxM`PQcEVQUyNPX_]K==VTqNCpxRmUuu\\xfyIIy<Y[YwrkX[>Gh:hfS>]@hj[foK@[qNdvayN^luGmwHtXfnLa`Zin_Fs\\Qn;ygvqj?Y]i?mVGq\\QptPuaXtkApf@ZcVn[Ooj^pTG\\TwhkfcG`l@nncO^>OeM>\\AI`hXwLxsayrK_jlGqFgnLGqcIyxIvN_nWgtdVuP`msV^sfiTOxuvq]?xgygU`iaYapv`h_x;v[EQ[k`oRVslFgoP\\HymiWtdghRXmm@mYxoFVt[hclIyvFqVogqNl[BC]C=oICUXUovIqYFUwwweKYIyqDKQulkh]QF@OtfQUE[DT_Re]d[ETwMx?[esWR^qCgCHkAum=e?OFLqhMQEaGvquyd<QiiNltrZosbNePP_KfniilEIgn>nLG\\vFy^`vlifCQytHspqponxVicmNbDA][^\\@HnkfsNAjINj>peIGZkFhfItiyxkfcm_aJ`pPYv;_a<Wgwneo?hVvZQUVsrswWAcU@mrwQsBIRJ?SNAxyWG=<qP\\U`EuyPr_uwWmueyU>IlLTREmyymxXaxCmoeaSmYyWXXq`UeTOmpX:dJNlX:`NrXl\\@oo]nXmnWQwX@t>=W<YVAajalr]IyZuS>xyATu[uYlUuHHpy<qgIXrLQ`XnUmwcqTqukNYnG`lbDk^@OD]NB=l:Dp]@TuQmSEqViyVXvItx`mT<\\nNQL_lWZmQFXsF]uFQs_qvwxvvxssumqIYOMokhl^AYkMkMdltlohUPQ]SR=o?\\wbyyK@qumlopuG]VcektaR?@pQPLnaKGiWYXvAmw]arKyjjeUIdoOAnkHuBtQYLR^epTtJH<UvmxmhRPtL_TWeMkpUq:MmP<P@iRcDj_elrtYxejyLy]xvrHYmUkYyywYtf\\OF=JZXLRquGEw^DNoHYUtKADj=aR?lSh\\RfxW@`whmnVLQLuNGmtSaWiPp]YKtEpAYtI`k]=lBENJpLnUqgmoVuYOXrAlsktPmlk_EU=`KoHr^iJeYns]JXqnDHnLElvlyrEjmuvVMrj`SuhMmpqXYNeQlVYRB@JQikklN_xtEHSL`VJHNJMSKpncDWTPl^DKCMlJpnc<JIdQnALatSX`Vf]WfyltaSSXkL@VtMu\\yKxARlIoIEuV]qbEXkQn?qr@mxS\\MaLrphL<=WLalVaJ_<rl@sCTk?hO_LQIhNJpL\\\\hQq\\cqutPjr`xDnsgXcrfqw^eEqb>fuu^yMf[@fgFNsBNqIiiWplj@`?Q`EXtA>hIvmZowEve\\piyYnNNwMFy;^`jI`_VmjN^@vxvnjgHstYZbhf_GotHwcGb_PlK^jPWs\\hup?wn_]tf]IvuI@cL@][N\\fV_?IhNnmQHeKHj`FcnnqiH[=GmyxrxOuihuhw[BQby?lcy[rnpgWvso]OQgOHxkIhdixti]L_nKnbRFvXQbypj:NpO>q`Op=QdnWk?av@vt]Ysf`rE`gbh`TQq??o=NqHPsPWyn>]KHiMy_AVwv`uUib>I`]QZH>qpVlX`vRghUNkCVlMI_[?vkPtC@[tOmHWa;Ok\\fvLAepPZtYcqfvtAy\\xib_n>vtO^]wN_rYry^pS_efHxDY_XV]UVf>HfO>xJQuJvrjQyeYgnOawngYqu\\yewYoI?hrAx^opdamX>fiHiJXg?y`rftr^jEA]H`hRpmBHako`^itQVub`ZVvdJWmBqryipo@l?YbW^ml>__?\\:hfColPxgLiwo?lLOfFYu_Qb]xunVrUigBW`C?h[@fKWoS_cF?uFwcu`fmyxRnr^`xun^AHfBxwuYZL>\\>FZK_\\KvrkFdNb[=STofnMIWkGV=i:eiXufLEgvausWyHer<Ci^AIU]df_T>chTEbMwFgMIWOH@affuo;@M[LNfTO>iXMLl^dNFTTL@Q@EW=ll?Pk]MlrLRceSTtr^hqHDncLNauSkTueIPgxWJ=S<]pJxXKTjfTKZ`k[dtDDoLMtH]STYWMIUS]ryHYSPwwykmdycxOlTx>ynKplOxtg\\YvtsiHLk<yR<Vrpr@LpEhtRDlQiM:AyrhjklX`qNK@Y>Dj`eWgLnSaKcix\\MjZ<NHXRvtk[LXJPl^DwWLM>qyPyUc=MXeXbYl=dnNlk]ATixtS=UR=nTeo\\UuplloLUGYM[]jueKuOk;W]?YexYmvPuuGkEGteaoShfPatlFZwNf\\^p_HpgwZcQe^giK`[bFjHg[uGh>qc^Yno@b@Ahsh_bH^sNdlImon[?g[c@jnNtnvhu`dEYlVvatAZmyjH?ZYvsCiyWQny?odhd;YbIFevYxyoe^AykWmQnebXhcQtffoPq`Tww\\fn[XtK_ewpp=Pt[no]>yVyvHWxBYnma`dvncqZYpfgWwPVf_p[GPj=h^>neKO`q?r]GhTIsta\\N`gdW\\Hnk]>eiqxrpimhsNamE_]d_dDnoeQpr`hWhqpqwUQpxVnYaxgAquVgJyuQh\\cVcVwtGyxP>Zm>iXOl^VjTPjnfcCVrJpgqXkiYy>Gd>?\\>^htF]sVuWiu_wfawjSIuSOc_PtYYd^`ypys]Ge<PiWqnXwpJQu?WgRiuoAddfbc`jnfs^qc@Ag\\@`Z^k]OrXwkZHq=HpW^gi@jHPbNH`>qpAOdP`xVQ`HquHfpHq`ohq:`rl@lsyxU^xYq`SoiCOePNu:hnGNdc^cqwkjioWOrGi`<hkO^yGhd`pmra`_Ios^_AIs^psYVp?YsKF`rAm\\?y<h]x@ggWeLO_Cn[V>xR@mjHcLfbTplKOc_q[@N[]OpEx`COvuN[MPy^>^FVb<A`vXfYwa_FuiNgTGeSG]fPdVfat_lSIuSyhxAn]^kjNrAO\\wac;OgLOadwkUHvOoqOqyUoeDni:Q_E?[QN[Xxj_fgDPpB@sQgxnpsmhZS`aWF_?npN>fU?gAAn\\fcVNgPOicVsUnjkg\\mf]EOoxH^ni`wpcFYdI_a@YdI_iKXnAos<^fGxo@Gh^y_?hyFIjZ_iVOx_x_s^mxf[mYxOoqsis=amyv]lHpkW[cVmFgcuasYf[ch`t^ieImgNawp_<OaVhamVbGYiVhswx`rpqsQZcahDgpR?^Opj\\Gs\\AvKPZipofIpuX\\M>yHftkwjnFjUwd=>ZVvtDYafVgNHdbai;Ng^vZuivJydB^uW>miyxf@^qg^FqoMwtowjBWZbgocqhu``UhctgqXnk]avSV]=WoOQfqwhQphuhaZnZyw]CW]hhjRykqNpHHsPhfRHmSno;NseA[F^bK?cNnjnpgVGfeqt?_vFI^^Ir?NttAi@?evw]yXt@yuTIrIXfL`d]W[;P^eap[OhMfrV_]NHd>VlKnZCHrPP\\vv[cA]<iqWohx_xgohh`qCwgqWm?x_xGklaw;_n]QrAaoHNh>_[xnjrXx\\a]fi]Nf[So\\rpoGwynA`sijNhtd>wVItZV[lywHa\\nYtJHePH^X>gMVy^@nyP\\KqgqxZIioOQgFwcIwkL_r]^kjw[Zxq<@mO>]eOucWkYvpy?ryiqmyqlHggP^wFsRXe?OeLV^lP^^_jSy]a_n:Ao[vyEqiQad]?`P>[A?vRFkGHbEWbeXllXnL_qNWdmNkkIxcoauaxQ@ak_x;HraIwuvpF@xeHrRFjkNjMx^mprRWxmYtvgwegZxpyYNgNOoQ?yIoqnGjYqyAwpch]bQxgxqM`wgh\\soxsHhhoufGh^Ac>GifYlVoqnQ`LQcRHmGamd_k:Pe=InTWhRGqOYf_GpEatVGjdgp:qrD_bk`fmfaaGvtPZ[gnvoymxe\\AxvI;QhkkV>mCXiChqFDsYY[GEQfPUgKcRKciXqi]EdJKbncTnSegKIWoCmWhmwilGYBYIr_bXIRRMyhAURcbaQi^WWE]rykyhcuy?yq_tHwe[_xsyI:muyaBcaxFCfYifgIiVqinqB?ife_DTYuBOfG_t`=TwMV@KEe_ef;Fl_W<myxOD=_rZQIhkR`_xPydrUvyAyY?dPgkY]ywMOmuj:UPb@oxAQ>iN]LVjIPAiulTnxlwFeRhyKbDUkyl:qpWLK?PRxauwQr]UVltS^AOD@wn?[=AhZXeFXvFolN?_N>pfVkXwoAqsHq[wpeI``GwZH@[]^kjjGdk@=NRqSpHyKUySlyIimyIMYiw\\AYHllgDrl<McxuXToaeNF=kx]wa=Jg<P<aV>HrDym]eV^DJU\\q<hZ[ncoVwEnjApsX`f[qyAFgNyn;xkAabxqe[?uvPf\\ObliriNqV@aKwvnIm\\vbH_qFYfIvolBdAD\\GXyOhGyxyWxo=ShCXeUYPWcQMwNguc=gVkRBYW>ESFav>Ec\\WGkeEEOxRov:au<csGOBuWGUaWuSgfeg@=y[Ue]wfWmV`QEvCxJydrQraoycStMsbA]vhYB:ar>aBcMeLYwoqBomBDEWnodRSty?SyxqCYuhDtv@rrhYgQLExyxyy_UwuxYGXoODxoyPkxtQDlYhy=Lqaum^qt`qPidY]yokpWYEv>EUmDUkHSFysyaR<pQs<siYKJpNuhL@UVCEkaIYbLVXAyymyqLv:yvrywyejTay<mySpQXLl\\HLk<i?ysUX_iqs^^qwf^ShhQ`sD>mYIi_qrogevvsU^Zyqqiy[vnnuIM?UfKDAIHwoUi=dk=ESqdH?H<yRUkrRGBc;UIPxfquYIxoqsY=toMurloG`p_<U^Upm`NeyO:<jBYpLHufpWJ<NlHx:avuQywDkFmoSpLltsZ<u:hJPEr<at>tLutlrYtYpyCDkPaQx]xC]jVdkctw@Tr=EpNPJ[\\K_PlZAukDsyMyIeNXeVCHxluk\\XW]AJAyVe\\UVHwk`XuQLPexPTV_QMUXkGLkdPsDitdLUiIlXDKR@mb<vrLLUIj@aVSHqtYj>iqdtOYxyulvaxrrLPyTsKYjomvI`MZmqkiR`PMmAupXPLPjwxRriRmmo_EUnLMGLYwpMUUUU]J;xSixlL\\J@`u^@wQaYi=MHTvGmogmPTUpq@YWXWymyyEttEwuAsb<rl]ODml^unWIvgxWyUl?yww@RmxLlHqrUlYqmnEmkUKBENBeXP<w=uqOTwIiYqIrm\\RxIU>Hs@xNQIXBXjhttxHxQ\\Rk]sSxOyyvNyvQlQpdJCYN\\=P<YQ\\ytstw_`lrlk=EoNMReekiYyuQu[MpEPOeMo`UvtpOPhVw]wTXtF@P<iq@HVqInGAWGxVTuuZYqWyomUuVurcLQBUU`mK:PPMXKGLv;`YxmsLqyFtsQyXF]wwyr?Aj^\\VElLTMmfiPgDj_QK<TOZYuQxqCetStnP=okMwZIMnHtBmRWxkYiO@xKUEn:tJHLOpUlw\\pOTJplpJ\\tWQJamSQ=uSqu`dtgmreIK@mPCUqM\\j[=r@QXFMmdMtRlV`YKrpo=qXvXkYiU]@VT\\sNqMa`ThLXZHX>XVmxrslQy]ktexbll_aKyMlqYyexYfHVFHrmaQTdktdk@UjOitoMUg`jcHoYaKk<qeiulXM;LOCHUuItq=Wxaxs]sHqJ_QjAErL\\pO\\qPISr`tshsH]nkeJv<UlHYZ]s]PwRAouprGXqCHrWdp@\\uwlq^]vQ]v=UleUufiOYQV_iriYTs\\pJHL=HjtHtvQY;MtA`M]LVjLrW<qUHryQQjhWUPVk@SgpT=AM==L>tXr`L_Em<hYgEXYywr]jKlRrAW;avXyuDannMlptuUIyPtufuYGXM\\QKHEt@MUL\\vxQWyimy]QnUVhQu@pnhyXVeyEyltaRHmKJ@TddLSQeCyxi`a=acsojcQuFftLAePHijvxxQgYygPVrTPtvVf]HbeVkGqnGPo`@qOVjExjaf]Hw]ePpn`]lPqPF^^pvJI`?Wgag\\]`_vwa_ggCG\\AAvO_^pXvJqwhWpm`llfdSvvrQr]^bCwknN_Jvxd>q\\o`]fZwguAAkN^iZ?oNorRPmTh^DpoLQg_@yxp^i_jvY]=weL`m@FZgXwQ@urquQIluWuN^]UVeDOaCOs_qcFirHcMSWvCGrkTkEywWBOmfVCc>[dkCeN=sB_ijAYygh\\GwQCFqifIiYqOf[yy_yh<_Y;Wtl?wVqi;isiyYEGiAmI;eYxASPUw\\[rwcYpkYv[BMUFvqrJyUSyy?UUyIYPgV[IYXSV]UVNSc?]fNWBcCT`eUdWXwOvxYwqIC<YuEWnjLrBtMP]xmeJ;PKrIuhYSvYqoxQ`QUtEMAYXJpp?HwiPwIdNDljC<jcyT<luG]KhquixwvyvjDYJDqb=U[@MUTOm@utprqxurykVxqkQw:IxBaxWtSxqMKHrB<xHxrbtlumLWPL[uxJTUWUkPML^EjLHOjlwN<QmuU?HkSTmXUU]<XbxSN<Qn]u[pQ[Dwo]LqtOuaur`t]lkGllN<uHHnllNsLYfAPMYtM\\wptpr@YciKhmuvpswhMxeYN<l_xvVtr;Yx@Ik]ISTiWBLJmYm]lJ=YlxpPrYwe\\OxyjiPLvHxmLs`dnZQQfqRCtQeejv`uF<SnHrMLj=dRAxSnLkV@OSAKBYYcxV_<S@AMFpPuYr@HsXtt`uqbAYjHPv\\sfYl=TnOlkaQlpUufty^yRvpxoxQ]\\WiIVFpvXuKLmR>AV>xxNLT`muCitdeXJasfLk\\`qRDqihTntxliPpLrBtxv\\RxyuXMt^yWptqDUsSirhLURmm>=Q@DvB`oZ@u`iwmpSX<xYIpc`uh`pYIpw=m:=WjLufyrgpVy>mg`x_W[NFnHHqrPiKxow`xoNvnFbD`ofAtZH][yl?HiUyqnHtZFfd`xsOqgYrf``MOq>?_\\_[@HocvlcIeI^j[gfKynJ_hcflwNsovZUq\\foo>_qtaiUhrenacOfK^bgoghne^`ekGmUXa:Ij=VxNWo]whf>]G@x;QbcVbJ>anOaA@cMI`Lat<G_mYmGxk?`b_F[xQsgNmi^iQHxLGllXfmPwAaqnX]jqvX_jUX_Dn[NfgXV]qAij_s]NtZAc;X^:Q\\uix<nm]GfUGuZWtiWkl^aNAm[Xu[OpZxZYybZ_l@qhV>c\\oovwxU^pqntKQcYYtlN^RF\\=H\\XYZFvndYySXj\\GpBAyrAa_PdCVslPhL?l\\Yy@`^sAZy^wBV^FtT=t`SeXUUCqGi]XYevoaxa?s\\;u?SEV_sX]TTQB[UC^gdM[bv?BSAVJqRaYGv=foGF[cFPCHDAGJ]V^CRS_WMIuPyFACuUUe;CWBeh[WD_?C[GoNDtrayrQxm`ygYkYenSIuCyNyqYb<lw@qS\\W]@SnqW^EQP@KG]jLIN@arBDlKXo=TTaEMqmQGUWqAJQmpPIuMDNxDK<qjtaj=UVDinUqTVEY]hrd?jjxnKNdZPdRWqWFhgQnIqwP_kgGaNOc]AqXG\\[^ZXxvL^Z;VcEWs^xqsG^uuu?bk;D?MbOitDCSlsSVSY^GgtIihobyOteUB@uVe;BwgvU_wxOx<KXeedlWwjUtIEiViccufTOggCt@kCOcWxSISMvMcc\\cFU=VC_cR;uP_sEsbgmrQkDR?yisyUKwYwyg]iCGGnMe`UwGCYZygGGshYdoURPmrVIRLkxiYefwY=oTnoWYAvdycXgfwghHSRoSdqQF@eH@SFvwGbYiNcteiHTgsWmtPqhbqXMKYwcSL?EFGiqGErAC][ue?wuOCgoREairwx=KIHqEOug<_X>Kr@CN=Pn]qYNDNlAVXQpf\\nk@tcpNkDOp`pslf@ajoFsD?p<QmypbLv^=`w;wisxsFNpDF]C?dDAnOHn\\Aev^aYov[Hklf[Aq^HVd\\@ujnauiiTOn?_]X@nZncLGhQ>pgXqaxa;H]TG^yWyB`xkG]]PyTYw:fghWZiFlJPpSI[SigD_]wvrvaw]`lEVpV>gvOljWgEhkGh`Vvp?gp\\Il\\?hvFsRgu@Ih_vdXagkHqh>]i?i>Ip:Gg?xwa`bEI_pXml_fxA:uvxccgcELaFGQIXqRCcwpudncTsWyWuuoOw=cIjsEe]rk?VsEULcRA=ipeWOWUqOuvCy^OrpWHqMrYUwqIsSkRnGi@]X]QHXGTfobcshvabw_R[UCjeGCaba;YvoU^aSOifhAUSUY;_iGERygt:?dLsroExdYvROTkSwQOVtIU=SHBqE^]fZuIE=fGGsqyvSibxew]mxgAtK=sDibQ=IxaxaAgY;eIyR=oyrEXieeRWF\\=H<`Jwao;qYm]pfTXZAQO]OepjiYUnUqTtuQancAW:yM[]jIPM@>g[>coOsd_p>ijjyfrfZuv^?Fep?bBaaE?`^Wbi_[R?eVvlaF]QVvfPsOogUXurnr`ahka[a`wm`q^xe^W^RAbapZ[hbp`ua@rnYpBNuZ^`^Fo;iblvemGinHd`ItcIhXnmcF`P?\\>ObKi`D@biNtFvlSiwGIdmx]AqlYPnfvnJA_NN[jAlFHfKgsyhuxG`>iu_ysqqohiiZhs<AfJ_o]@yhn`IIZDvagQh]W^`wf_HrSXvQImW@iJPekaZ]qw=awfiuZQuGyfr^`Ywrl_ZCOfjge;gn`GfknjlYongbF?]q?dc`b\\Gl`njLGfTXfmyclav]xeZnk^FhLvvGY`OFbZxbLVtIf[>FhFVoeP[gxncgpT__gF_\\@_;Ih@XmH`yDd[]SXuTh;TcMRlgh@Mhp?ckgUhmx\\kxLcb>=TJOBQMCXCEi;xjeg:erHQUNGCMgygoFeKIPEYo]Ytwt^[Ys`ReUWbtqQhx:EM\\tJDxXBaMJhLiTwxqPnaMJ<SUqV]QwU]XqupkLU]\\nvXokTuwXjKDPRDvwERpEJC\\jbTnoeLYyXbix>DRZ@SMIvKyYrqywlXohkjLrw`jv@UiTog<Wk`MgLpcmtb\\LDDYiEJ=dYcAtZxV;AriyKUMuvDWwdrv@Q<Yx`yJfTo_<SlHStlTkDoLUJSDLtTN>TJCETTHl>dm<Lsj]oT]vEYKM]y]YLm<ULQRKDtMILW`P_hMa\\XwalnltRdX;TuUuNLUON@Q;]SB=R>Pto\\ntLkgpk[IuG\\Ue`S`xXDQj<Tludl^uxqYJ;XQQYKy\\u]il[iwKmxuTlVDjpLkNXu^\\YQtlNtKEHmkDsgQVIxmh`uZqxTysrlpjuQAmNyujCPw=\\tVxRs`XcIU>HKbtTg]pP\\rkpnJMLVHQuMj?HuIApUau`EXsijGlKN=J:<L:`N\\@NdPN?Ho>`VV\\OcEXpat]`YdIoYYvbQrcmtQytSmUp\\j[]SqXmFDQ^iYrxkeyr?DS\\=uXqT^DkAXvFIpuXUZhtD=oNMKiQQU=lOIy`uYVdppEKPxWJ\\oi@tlLlHMl^eX=lT`tLTXxfmQKAOL]ptYWoQNiIY<ArV=RBDkLQmrUYU@xutu\\DRJPKC`p^LTaMv;IJs<sm^tZqqsXbh_`RyL]sLQhSqiwUcwgxoKf:yfJmoaUYidkBHrBtwsLy=pjk<tgQKThSQ@NRtNDPY>ET:MlbMtNAvrtYyYWG@P<AKYlMb]PPlLQYYQHqbyq@xWoAoUiXj`K<mwqaMrUYvuloULTeVShQT]oShLFPt>PO\\ImHyXrmTyul^<SCUvnTmnYXL=nMamN\\vLPnp=llmWf@symXlMjidOFYN?IN<lTSitglpuENuTqCTYuHOk=osLQMMvbatVdklhk_tsM@x\\lQTpKClqp@wneQTXmOlSplyelv@ym`@wNEt^DqFIt@QLHAvUuusPQtuO@toT`tbLR]=OEUM[_tfGscYj]aoYyosoyuhc`nfhVxLine_`DwkkvawAarynR_qtq\\oIgUvso?xuOknFtbGt^ItAom\\GvZYfb`d[_cPWgZ^Zrpc;vrkG\\<Oh^AsKndQwdrpiwgkWiuRVsTFmL_iR?^>ov`i\\@PkHw^_Fcd^qvQ`v@x<wkyOxIOo=pn:ywdnbPQ]fVkHYeiXtv`y@Vmgq_eNr=Il\\?p\\waeIuvf`K_nfWkunovpqNybBnZONb@>`<?fVw[[_[PwuLfeR^`<fnmXxDG]JOiY`[^XZL@tIA_RXavA\\FomOAuSge\\Xpmhb[`e[ie_GcxNZRF\\=H<iC@ARiwBgqh=wwQIC<oHxwi=qsH=r`qVAGisGHDgRaqe_Ev][cjug;QFMGDfgbe[g?YGRqcOgtM[CBAbrWHM=HNaifCTcsGcyD;UC\\aHDYb:URTsfR_t^Eu:SFlQVQagJAu^QX\\ceRKvRUXh]u]yUVOI<yf`mcZ[RC_bOkXoqEEYU;SsEEBUYEkkd@wfHitSwed=Th;URCeJqRLQSWKu;OViWWBSRGgG\\kfAaHHWxaAFxwSFWS:MRIcRTssLeDYGffee?Idoag=UxjurP=sEsEF;FAOB^wC`]EehVOIYr`lwaM=eKXaS@MwtIMY`osXtJyxKQjX=VRux]MOMPJI=YB<nklvjuycPPqtooEPDqnxDWKpnQ@YeevdlX?YVmUN[LKOdrLmlClxu<XuEwttQuewu`lDTlVlQjmL]]PLMUsIqjxYVdjJ\\TeXX>EtGLUgNc_qmp_jvAs:A]=`l<XZA^]xAxIvrrYoyP[BOl\\VeUgZh_ujA:qSZui`YE_GHx=EKqcM[g\\lLSDPr<UnEaOifx`v^oo]_fiipi^iEQjrG>Abp;eVagfsiGieFGd@[Gc;TtSgmMHnIS;mRBKTwwyiahyUgm_c<KT\\yhu]gXei<UXgeccGy?_SL]VWYYXkI]KVjKruMc[UIm_sSARMiwT=yxUbhuh?UigUX_QSMGgcgDDiVQOR;IyoqTYkRRCV>wxVkBm;csUvnkV_KiGqRlOcW=XJQRaaYZ=W?eyWkg_UVFcUWiENKDYItu?fiqH>Gi=qgnwyRoSGCWfGImSU_avRebkuC\\UhAUSiAhrou]Qy_qEeUG[cFAqvfIgkmcFuHbsDDAGSStKICUEVBqXmCVuUI;=Wb]TVmv@iI`KgXkcfUbOIfAtTa\\XMdRi<qFqVrekLHqIpRcaPMdpc]KCDoK@uVLr`ML;XlAttuIrhqqQIkvuS_qRwuyoekX\\JsQJ;`MRtK`esaapLYjIuVUmSxIolxvpin[mr^uo[dx^DlyMlotyOmvDpP?DT^@VCmvTDKI\\QPev@inJ`PKalEqMOPTCTuE=WpdJuTMCllOPNg`oiErXUtaUWuem:yw`eqf]S`axLhMHXQgtO]Aq@]Lo<K=iO\\@wXiXwEyb@RBlJpHpXxNRHmK@UP@vbIt\\dk@Em_iV=YmimrVPQ_Ivrtw`@RVaKCaxltTk`TULKLMlberfEr`aV?ivJEs;qLuyTJAN]=PZ<K\\=RH\\VhLmMHQc<MdiYB`sLdlweV]l^XPkxF_BI[;pwMhjVYqFAj<?ldgbLvrbftqWstx`=`lKF`RFvwgbTP]<@bjxpQ?nUioKfbMahtn\\gqh:OmxqjUG_H@`<A[iIaNF_wfu[>`;opL^uAAhaVpxQpWiee>rLAsvxd;qiA^x[yvFn\\OnZiXlSOMURC=SXCebGtjaGncEtGWIgdwoEQqGqEYwidHKGo[ItuUSWyIgSLEGN=t\\Cf]ORPQI;shQQYfoG?=cNkcW[gj=Yv_sNegBXWK<Llxl@`w?EKgAN?yKOLrn=x^UL]tPjlvTLsF=lB@MYDJtmMK`s]LtSLkPIPDejkIND]NAPKhXxJlvWTVCxXY<VfyXjeMrynJPWGuNWYVeDuBaNNlRmpMf@tFxXKQU]AMAhjdIXV\\UDpTCPqmDRGiMAUMG`L<DNgLKpaM_EyntPPuYDXXbLVl@v\\dj^@wSaMyDU\\eYclriarrLTLAmbTNwhQDdNCqrDPNF\\PLMK<uUMLyLhtOhLpmXqPPLIN^ATP=yHywWIwR=yxaLK]pGMmD`uetuv=vS<mK<roeJmXpplpgDQqms[AuktjbLSrQwQeYxixyplF]SRAUsXJJYQYXvytOwYlK`RylwJln;lln@X^\\LfUk]dNAHq<hS[tlODU\\tWlPQrerFPYauoZlJthV]]KL]VoPJ<=jnDUPHR^irHiyIyl_mJFAjJ<OMXL?TVJMQy]OIAMnyMAMsumUKAP\\lJ]\\qi@TDAL?=tfMUnXuO=vZLS;PTd=PkmkjLrBtMW<K>lp_AVUmLCTRxXx=Eqxiy<ytVhMFdPhTPRxp_mLsiJUHsMhLout[au>mlg<kFxsHxwmew@=sUuvu`qpEn=IuMeTPlKGHPslUCQMnDt`eqWYvTQnIQvOumWiw>XXaPWVPQjlr;IoDLK;=VLlpN=rPqUFqshMRJitrplZmoPmvZAYCHp<PRTuTBhS<usbLqDEtEhW\\tYFDMXTV<iyglKrtVKlXVhJflVFDS?TkDLJe=wR\\KWlnVMRoYo>tq=ij>iYSATdMLtPo=uToHWcpNqTre]UnyUAUkNdVNtTTylRExQ@tDEvdukAUwY@rOqMMltNtrEynrLTDAk<aTkmjTxT]@vp<mftQ;in?YnftlQEPMXYFHqXLS<epdUPu=s_QsUDPeTsg]YyD^@O^_`^GGfiw`_fcFFg\\?[vGrTQu@foPobD_guwqR`c^IbVw]gqp\\htd?tgqsJiwp@eYwgk_xba^<?e]`[lyZ>pykw_O`^InaR?nR_xS?e:xrXV\\V?q:vitynKverQj?YvIxlb`dtIe=H^SOuWWxtYawqkuGvDVggYcnQng_ecAvB?aR?hRx_t^lg`mN>ck>sygxeo\\m`oR>g[oxmwesFlNnfY`bBpy]QbZVhCVed_[KP`^NiYIlbxmc>]fO]LVZCp`^`fS`Z_hsJW\\nXiMV^\\?@qe<=cFmD>Ceu?rkWV?mHqcCyCyCubbKGL_Fm[WhmxRuUQ_RKmX;sy@]xDWFF?H<xK@aK^aO=hoyxuFTYYAm;=XyuReLtxxlZALs<wEmxGuqSHUY@M^iSHajN<Q<=N>PnUpNftWA`UuUnAYoaYQf`w>]yxyWW\\vkXp]ARBHp<lp\\@kexpvmuvtu[uWudv>IoLtmw]YTHskPP@TRfMRp]XBQxp=slisJhug`jtEu`IlAmNr\\UiHN?XRD]RQAKTPs\\hM`\\XuHO[=mZDuZPViML_xtC`xSLTP=kkHrVHrPuVcPkaDX^aLL=YiAnUxwY<pwEuIAxMmwpmKTlKn`SxypkpkRAkPEykuvA`qKdq<inbiXPetLlqcIn>mVsAwSiJfIPATn[\\SvmyhXxQVnRv`kA_dP`X_e^Apm_ky^avi\\xFaqI]H^dHFde`slOi`yejghsyi[F`U_]v>d;Q\\<`dUn^agePvoTaey`pAioeg_HqaRWZf_gEOnLWbiXn:AenPmWomr?ynvZ`q\\jhgUfoONdTwh?vkSioiY_pxpwn`pNw^HoIypxhhKxipysXPff__moqk`oKarjqi]xyuflEQlAn]b>`pnfjiiGqxpHfuWu\\Wf]@sYgyO?sFakEIoModxy`=yfjHq]VbnxitQ]Fpt>FdIxdPxyRhpgygZXloOkpxbCQ\\VPot`kSu^yI=MW>qycUhImCtQVroIs;sYsEXQXC<slpKcHJYEM<dlcanN\\KCEklLpJ@MBMxuiytUj>awepMuyu[qU>AkR\\kjqM=]KW=s@HwculsHQ?@LW]YYINFdQPqtFTsEQkXuOmpJMPxHIJ^]RLlRRDv=iKMyKjywb=RPhvkiJ^EPiAXo@vZ<sYyo=MP@aKoAOZxW\\lqI=N@TyS<lEDK>]nfup]mlhujflUI<YwQYQxswMWLxJIutcLYHDkHHWEaleYkxttiDyR@ujAwMdPXpY^MkkQSCDOZLN`uNH<qxpu]isYhXRAUEDQttU`InMTvV\\oOELN@Kk@WdqMUqYUhwWdsHqT>PS[Ax^El?HwdTv_tKChJPiTLML\\UlLYTeAyxYX>iuyHn`tQ;aW_YtNYOaDL<QrZXPLaNV`QU@ty<k=iXDtwfAY^Xx=@NJ`oAYovAowaKyeutYXp\\rDLsH=tXHrKpKoETYyyw]sxEJqHpGlomlkc<jHhPdlP>plIinZQJqx_CyuWQyeoasfxSoqjvyu^]y^y>VsUwcjHqva]Dwpc_cN?dTGnort_VfoT^EytMssyEiIvNcY<ogZ;x?CVZ?C<ADQIxrCYvIB`mfICBvQRSkRJ;r`qVDqr@eBIYIB]DoiU[oRrAf[cV@mCHuep=UYubHuRmOiTGIOcYoYgxsrHGRs_I@ayvwHbWDVkd;GGW?VnOsOsITCGgMrbWr_iriMhSkIEwTBCD?ODp?CSgGT=YL]C@OcywwF;iuQGKswjGRP;xp]h[WdbKYcoEnQGBuBlEFm;F:CchYd<oyyGsCGrjesNiismWH?c;ACiYGlGr<[YYAtcAC<?r\\qxgQB]YvTgeWcSRkfNSchAcF[cjKrAEC`swi;tYesQAVn?sw[BiQeTYy;MWykChyTrivm_xZSRZGEfUbhsr=oe@kByCSS]wnEd?sbWqXFQyl=stQWBoLYPY\\pscYV_\\jNardlV]XMlewLuljXoSXmgTX\\Gh`Vs?^]E^\\CVik_rgh[Yx`XggmxtFGavve\\aucQaAof`>p_G\\gNZTO_^gpSIvpQd:qrD_kgW[XNaWgvBafWPek`knh`;Vifi^CfwJGtpY\\vA^?f[]qeDGuG@hVXubnnC?j:fbZ`[\\FaFGkm_dwXtROtXNxiyshgsj?iNXci`bxxyAViYIvsqum`qK`q<Qpm@kkh`Lqls`f\\weEfuynnba_JW`wiyson<An;AcnHdnWjpvgpqe]gouPr_hoq>ywhjy_rnarM_ohg`SgqoQ^k_t=IhgObyVfeWdmf``xrHSOqslgutGrtqrDSGtebLERmMvbYBf[ExcsMyerybF]H`UhiEFxmiEWcPIUPAfWqXREUSSvSyVq;ylyd=MgOuBEQh@euIwIZ[xeyYfUUjuuwmCyKyKMr`qVF=D^EEZgwgUrYgySUdCGC=yTxOH;wvSUBL=D`cSTgiq?udui<UgmOcjkHk]E]UsTcRqGReWXWgr_gUDYSKSTxof[IkultUQRhyXtIuAlNUuwn@Xy\\ecvsf^bTWpOfnnP\\G_mEOjtqx^H_uip@Fe@A^]nZkp`>qZ\\W^BPdBXvNftixjvxb_ys]NfjNruQkFWdDFhf?k\\VbVVrXqmAQwd@vDi\\GIr=H[AqksVjNHxbO\\RFf>x[s^[bqiIHj[ps>Qb`GZvofWNfXq`Kwf;Pwxoh:Ao[@Zpv^DnnyWa>_\\>HZg@fi>cr@qMYnTo_Mqga`whw^nQiDPfWqvbU\\Mf`UdD_bHOSRmUECUUMcRSgr[Er;UZMXv?ba[E:UvU?eooV:itegIPwg@_uqAVOwBHmck]Wp]clXjlL[MYf_wn=itehaPpg@`nKHv[Xy@Iatf`?gqvnk@?tKigpXv:ho`Pfaw^`fkFVf?vj=hk\\fklXbSYg]GaiOt]Q\\WglLYcMOq;H^GP]FHeq>p^yfbPim?_]@d^@]D>cdAunnjHfp[ntkVqCq`igjQ>y@WyYYx`Oydf]uw[UipkhgqV_x`\\uIgSHj]>ojvhTaa`iZYAgJnp:Ogj_pGp`SWjshlXigpotpHuTYu\\YlMxc\\qp=OnJqnaypb_cN@c]WbVFjkF[_Qp?Yraqa=H`YPfqHqCqvpQ]RVrCXfaAmUhaFax^IbvPbkigp@ow_xqgmvFeZpeqIcMgrhqo=ijEf`hguDHmXptNWowAfm_`c^qY@wEoh:^nN^awah;X[QN\\pn`FFcLyiPhreyoa^imYmWnkVFhsaxaxrJNbjhqmHs?YgYYf_wxu?klihFht@ywR^yX_[d`jgNgrimRXkQQiFguHG_q_^?wt<i\\\\xqx?taYriAms>]pv^rij[NihqonXmbOmkp^BiuspZ>Ab_Qh[NpTOj;F_jFak>tJF]=HhfO_GH[Dhldqy;IqAF`\\nZ]ru[cCQcJgdLAWgGC=QBuSIpsvIYW`qvLkCYkuIaGF_WEuRRCv];bN;S:aFSCRJWRWocuIraSbO?Xm;dKcxmkB@exiUy>CVbSBkqhAYhg[cosgfOyF=YPCWmCFDcHKgChUr@YGB]GcGcoofScFfoG?_hpWDDgBEstO[dVEb_USLMVTEVFQvdwslicJOb_EXyIwkkSV;E]]soEH^[r>]gqaYh_mmeygtmnLtVTQLEv[XvM`tDTTZ\\Jwdt[UPfAXuUNZeWkDriunFeku]MVpOkMYppK<LV\\MQdLnOdxRYKL]y:Ej@T[NGfQ`lg_[E^r>aZ>_^tPjJwjKFxKNcHIbVwnHOgFV_;Q^yNuuolaQriWh=_e`fh]_aQYZEAf^HsC>j:VluPqqY^ZFmaw]lOn`^nBaqXifPakHF[@Q`ZG]Vvs;QtpFlHFy[Qwm`eUGq:IeuOk=PtJ?uE@k=`cEowqGfqwp?W_wPbvoo=YrI^iXVulGdTG^>@rkhu;GjkysafZuQhMyjXN_m?v:w\\AIkJNnB^drgxOgSab\\OTScX:ayZ?tyicFGHvCy^EdaqMRMUL\\Xu`vH]VL@QpEy[yKwMoOeR]HNrdYt`sexowAlyAyfymjhtxIMAqsPHQn@T_XpQ@teAO<ApE=wiTpuHllPqhHkqEvj]wZUUpmu:`sZUKjlR^ynfmSfuwl=QuXmJ\\VyqLsUxm`wYMs:qUdHUITTtMS]PxAQyWmkMuS^Eu<`NeAxVpKMTJMhVTLjNEVQ\\Q`qkWTnkTQUHs^twKAv^]RFlRruUKhL]TM^`tRqp:AMAPUg@s>ajEQtL=roXW@xSvMN[pUqHXVTwHhtDXYnQMVDV>xk`LyQiNLttN<XLulrDK[dNI<Tmyrg`UtPN@pybttuXtQHKoYJxalfXpkMmaUKlYu;DVJ=nM=LDLK<Mxlisw\\ViDvBMW[]NnQS@`tO\\n<UlTdSRpnfaX\\MUUIKuTuCdmpMsvaXKxnIqS:HT>`nf]P=mTPPRLpo`IvAmrcLYhlPpLJ=]S<UPC<qkUuaQvsqKdltv\\yjekYQyVaOGToH<QraWjXMgEXeeN^QseIJeXs;tjaUSV@QMevFayN<tZ\\VUhWO<pSIKRIuGEuUISjLKPlnEaOFePR@oRAKkEkRxmKiPTpoC=w_PjXus_uWUYvbeyy@Vh]wcmpL@jieWyemyUqmyq]ToJmOOHxVuK]eV;pQ=YKcDqmTK^]UZ=TILQNhPbYQ@pV>Dj;el`HL@TNolk]UPSAmZuVaXssqWApPXtNVPN[=LZQY<`NP\\XTEKdLu_qrgYKVyXtYlrlpAXVu<K[DtTEN>mvP]xEaJKmpWhJZhnLhr^aVShj?PPilqrXsMuScmKWLt=DQKAvmxkjqQ:aK`IVghJoPm=YlIMOhhUm\\OiTWDdJA@NJ@j?QsDMsYayGukbLKsywxYyCmqkimyDvOxTyMjLMmWhxBhwmljdes[<wcLlRANguk\\Es[MpKTvealwhQJISp\\TFLSF@Jc]K@=kVxuTHJcisxdujyNoDY_pSh<rEAu;dqNUXgxLmhMe`kM=kVErbMxkQvfXkPqJoPmL`o`\\ndtlIdvLMnBEM\\`T]eLDaSW\\akpr^>Z<oyvGeVybSV^\\?`<Yy>V`JyjtpoZPeO^lEQlhwt`oix@rfaoEquXOsLQl[giwFrogZoQqvXgL>]GaZ]^kjIf<Pb[Quhvn@qsl?qm_kQXiyNnJ?_FndhXpSOaq`ZSnqvwwp_]LWy>>ZOh`jV`=W]sFfR^gsFljYb?YkQYuVw`PNpa?gDgk_H^Zf^>A\\`Nlhqm`xtCGc\\gsHQiDQu\\_jKO]V@mppkSAuHHuXwcbiZD`rO?e\\Vgjink>ydRguRvGxDuBgYrwuxIGxBYBGKgl?B`KRCgITGhIihUIDQkYPIVsqTBIumgVxSxBaGAyCHQB_KTpGuOiWPmh=kWYQxSaUGGDTkIqAu^sbamrcSYPKU^?yR]w`gBTqYDqUU=D>KCUmFFmcSKCHyUL?eiYx\\UiCyunog[qTVMC?sC[UbCiF<UbhgSiab[OCFyUbSchYI:avWAfF_tbEd?sY[MgsotDEWqWiVsxV]w<mVGMucUGJICeSGE]fcMHNUCZ;hfwUg[rBaUcaH_Od[ausCry_yQObyky]QBycyc]rnaHVOIOmENkhH?xxYfy]uyCyNWsOYG@wTYEs^aR[=wZgXF;InsXOsswst`ycxism[Gh_U@QhM]bnACvAeEuv]mFa]UL?U]AILGcSsclAe^CcgKb\\ofgYEpUTGahl;GKgDtQSpISggFlKhJygyiwYOswQF\\IbKGRxwSB;xOoVwkSSACM]SXaEKUG=OSlwxjyst_fa]E>eT<qd\\Cif;SYECiasR;GG]DAaet=xKMwmSHrkeqqyX;yqIE]KVjKj?dyEltl`JGpjGYNI`LcaXntvIYKhYqIlMs]RlmyvEjZ<SrEv?`JjHoQyRSQjKlRr_by@yoxgO>ib`h>hj<I[XgwxajnNdSxjrHZcwvoGZwAnoxiWVwwGkKArcvb__ZZ?mN^fqYpfFrWYyoOgJNsJnb@hn:Gf<`oZ?lN?tFNdpNvJ@an^hTI[cOlgpbuno:?uJ@nK?unhiGWoS@tdo^fxo>_qpQfUx^PN]rNtJ@[?W_FHeXo[RgqSFtR@hbxct^dDp[p@p:ann?kshqK>hwQkIWimFv>IkLvkVytZAvnGm<XoB?gKatgn\\QYiVOqJifwGa^PdjHivIj@vb`xrcFihNc``po_sP?\\jHqMVpwH]]^kZOgFivJWnBabOirOPmYn`iXxvwfQppgYvtp[RofYYkkig`pnni\\UWyqicYimbwiU>wrxu;_nWho?afcpZ[G[>h^Bf_GQaDPdA?dRY\\b`Ztgq>PnQ_nZitJPbXIbvnisGo?Hbc>hWGs=x[t_eyp]]^bDauV>jGytxpp<xvs_sIYaNVkhoxQVn<_vqA\\Sykbhsxw^gOhe?`]__dikNxZXFe^IlIoprGwAv[Jiwt^bKhkkn[CO]mpqh?yexyiAZAwwu?jlAe>O]iI\\rq`bfbmWa;gn@voZ>_Og^MyZDAoRWpOacRq\\Dh_[GxJ@\\>PuZfb`VcNhiqWrFG\\qwZuh`DGfnpbEGk<ofoVZson[f`jPwa`eigr>PuZ^_ZOs<_`^ndkV`A?kAaZ;_oKpq;_\\[Fmq?cQW\\NQh<_mdO^[N`qN^g>avOyxNooQihG]v^t;YyXVrB@]Fda?wI[uTuVUgV_ecLmCX[Xb]HlSsuGeS;IsMTjOidUhlOfsIrIKFdehRWRA_B_QhGWwpyFUGT[IuBSFv=eJyWs[HQMI:Id\\ITDCSC?uI=XFgc>=foGsPehuiHASbLSb[CGKAbR[vqgY<;d^Qt\\_rFkHWOEnMVjCYwSRPut:CSfPLGlNmeps`X]xrValAEuO`XTIOZ<XwDSk`W]TK<@Rb]NLpXQuVtuVYEtSYSS]qT<NN<K[@KNMrHuP`eYsLViuP[MyZXS_PVM]Xg\\J@`T^`wrIPqtWtaWh`RNXSptnHeTR=mgPTh<ubMRtEW:QSEWmihhRaeG@]iHaVyhlprSYnoO_?v[gV\\tN_ZgoW>prPlOn`UQbjOwjgj]XlOo^dhfDnoEioZwlaYau_eCObfPJocBqViUSFKw=;buKbuqi?EwZEynwuaKFYyHjebdYd>Gvayu?MDFme?=HH[Bh[G?CHMgECgdR=yxMcn;TgstKOrT;i`cylWVouU`Odg[E;IumoEaysUkWYqtvGy`[wfabV]iRivUyuhQXvAY;wusiM=]nZ]PY\\y`HPVyN==JTUowiR:`yqdWuyPjxrxHs;Yle`lXEoJukITpuXvKdrklr>aRKhsLQvVllqYqVTQ]QTh`yN@QTqRcTrMtKyqPOQW=hloYOf]PIYN_EmXuRKYuM]rkpvPhoB]O;ENi`lI]p;AKjHPR=lomvHyQUll>QoGXVfUMvuMMdR=XXVQJp]Y?QmL]p`hNXIl<ls>hjOupjmnD<UOTk^lSJHSD=VFDWd=K]dSN]tnMoSAROPWB=sVYkDYV]auyaxa=MYPmCYpOTredMqqL@]rZsHCGmCIKps`=NAIPNTkSponuXQ=xDYOTHoc@lMtNLmkYtO]IYhAOm=P<AKYlP^ir?AMbHqomKQpkl=tXxvduwg\\OSHuGLMGLR_UOHiyOiwFXvYitj`O_uqPAvh@vyuQM=rZumCyMQISpaUNHR`Qm^aNPaqvQUUHklhscYr_\\kPASUETbDKL@UM\\NKTwWtm@hVKqWa\\j[pMFxOCMnC=Tb<NB]KGqX<Uh<xuO_whorb@\\vVcZHdra^fxw@__inj>pq\\oynGl=V`?Oo?w\\UO]<W\\mhwA`ewp]j`ho>ff_u`qqmVfv^i`pcWq_\\_k<y`[VguoaQqgoAqsgrawgqFv[Yy@eIick=X\\ObpkHgeVrmXqGs??GZWvR[i<gBh;SU]VEyf=iX?sX>CyVIYFWxGcG@kGIUbFgsJYxAwhu;C<?Fe;Up=VAQtRMCDEh@qhE[sFeE`Ay<iYrkcqqG=efwQB^YfAeUHcEDEYoiT?YxIYWPytu_xtEHyCyC]sVauhscvKH;Uf[evwqW@Uc?uiS]wesxoGTrIt@cwXQC[]u@qdXcv<aC?sg@icOwdrGhviStEvDcrdeEUQyDCWTufOQGJ_FC;d:KdOgrA?xDkHMYX?KtnyfrouTsUrayQGIt=yfsgwGyvsswAiAwwiOtXYTNcECGWBktO[Uiqfvkvt=G]MHcAEseCG;fSywX]GVsBs]y>[sWKRYEi>]XmqBx=EM_vwwSPgIGUwZgcq]u`oXyEDqMs@IGR]DEiC>_Xbuxp?X<_bnKt>gIGufWOf\\SRm]UL?IZWFBed\\?Td?XYYTYOvnYvIMTSsgm;wIQXIOV>]C@=YY=HVIBsOTK_ewSwkEylGfR]CSIuk[UuoFReU?geW;uUYHvgxPMsEsG^_tdeBTccV]TrKrBSFv=WJyeTcDDSST]EcoE]IgCwslqroytb;u?aSQ[glSGF]gFIy`=uq]uLKdDEfDOTD?FC;c]AIEQE^WySOBW?EF]InUYAiYw;YFuxe]DnGrm]FQognAGCCCkGvJahEEgfEHXAhCUDGufa?ik_t]CXncgp=SLSWfUSLMGU]DEmD;_SB;hciRToSUUvqUT\\?TmEwOoGIweDCDaaCD_d`ocSuUECWherb=flCVkkUoAXWSC]STtCX<Qtp=s_YCW[G>srHodsKHMmf\\[U:Uf>=sP=mtQVIXsi]XSYuCEUR=OlavsHK`UMO]J<@traUpYYveYmhr`xnjUkPLPQXRCTqIMK>qyjAmM@jxuPcasTitZ\\k:Qlpmv>Qld`SphPNYu:dVhApIhPq=P>lJkQnJDyuIuLhUUEvseJHaMvTrQlQuiVxdxNyQFYQTtquXxcxQy\\Mt\\vl=yj]J>aUupnbqXw]pH@UUUSsmysAlammcAxuxqUenTeplUUeILs<yOEPVhLrUy]Mk^dKbqjeaOiaYIXUUtuaHuX]rPXvFqkyls^AyCmOVmyXtOy@Y=XWieWL]oxYMvtp:apxYJFpWjXuFEP`dRBdRLDMhxUv=koin=`SGaOj]yfyUldQsts[IyM`teiXdeKExqwmvy=nVelV@qilVWasv<J:<<CTJ`jkhJgXUKtsVxKrTfS@_^wvfpseod>oc@F\\LFoONn^QrKX^^vkxOmwpmIQuoX]f`p<NaC>dJ^hYPxjpaSOfhAmAGpZF\\@A^jHhoGmbhwJYuWAbU`\\^olK_oOi]^`\\>nq\\WwT_cTYcJ@[H^_VfvEyyoyiEav;XjBWoYiusquwvv@_rZ_jqiZ=qlnglD`vVIq<v\\innFhkcn`qf`Qn_Rn\\QFnSasf`cixeIGixIiGYjIn^VFa\\q[s^\\SHreikjNrBBICeeAU`YGA=yVxu\\yOhhyuLlXMjKQLe@V_IM=`SH]PZlJ<ATflLryrmyU;IPXtOfhyJxTwym;]Nluv[HNsAtJDOjdYl<LU\\X^=tcim;ioPEm]ElHeKydqjxReHWrimaxSlIsmumZUnkUk<IqM\\kQmLb<QGMmUxu]xtCDrRLK?uj<ET[`p\\UOBDOcpOg@P_xtGaxJqke<PTMn?pNkLM_hOThqNpvHMReuP;ywblTaTKFxQ`UN?pN\\dVqXMk`qV<ps`Mm=y^ElTAq=EqZQvRMLGMRU`jUUSxtTilxjDp[yMvEV<xrHqPbHu_]NShldqXVYvShtglX_PRP\\NpXmC=klLpo\\TuHxyYpqqV;MlWuxSxuiamuhvXhpiiTWitWeqqLq;pWf\\Jk@XYaRJPLcLsL`Q[HxplpfAx>pv;yS]uqjir[IX>XR[yJA=u[ej]MrVDsN`PNQRD@nbLTVANJ<NPpJJAwwuwhhYIiQiqYHxMhmVPmTM\\nBMJ>uP;ay\\LoePQeTOmquUHYimyyXxyqqyyt@PJ[Mjc\\S>PjJykJEX>AWd]kATta@k]AmqLoi=p\\ioZTVsXVtqWamR>aX@ErnmWeElFpXBilZDYXusBHy:YtY=vqyQryJVlmuDxH`UMXLYHjZAx[UkMyn]lmymuImu]MT[>levdd_yUyiuwZAIm^YZY>w]xoIQwB?lt?ys?tXxuMig>GZ[^^GwgUHyoyvsvpryiLVp;_\\?aZk^leVeFy_Wxb?He`you__iNqb@u:apVObxi]ponCoqrIi<AgLPc_hoWW[JOc]Yq=a`dv]]HdTNrqwZJGp\\xqrnskXbI?pNOiDvdYhfZ_r^>h[Ql<x`hGqvWoLAv]Q`E?oZgrEFsRpZmgic^mp?ySp\\ZP^nYoy^v<YhiN`y`pHqvPGmGw_\\g`FH]sAdKHkIpfSpmEI`NphJpZNibBsDCikUydSEekIlgDb;GGCb[mFlcF=MrXWFS[xv]slQyPSb?ICXkyjybs[ybYvRkbkYW[SUbID=oEXiXRofZSeo;EV[HR_eN;yxoV[EF`_TL;YXoB^SEUKemyv=mYjYbtkd_GIoMGIMIgCTDUF_?yo=IqSYbIvQUBggRvSSTasPsvryWH_yKsUtGxa[tTgD^OS^wFR_wFWt^CGE]YO;hVMU\\wIo;RN[RJ;c^?yIGR?Mg]sDTIF<KWA?D>cWsIdhESJOdOGX\\afhgHGUb`UraUXEqftOYJOrKwVB_c_mBuyfS_EYyR`sEMMXIKtbcYSOYpmenEf;mfKKvp[GhauJAepeCIYccmtOKRD]WAAS^wcH?rMOBcOtNYsOMEo?e:ytfuW>_usotF]uHoT:UFH;ub?yf]g>[HeEHPWFBqfG]EMmFuqg=mtUoIQuGq;rAgiMGU@yRLavFsFS_i\\KBDmYMWW_oFQMgxKGi;Dp?SvcB@uDc;wxoDd=CG?d=qrKkSCwbkadAyXoyIloDgWTjOcVKHHGDLKXGAi@]EAAsRmwDqbRivoAWWSuWCCLSIx=DGkBLobD;G?cCTOI<qhMhT>Hx]]S_yVvUKopy>mpt<NAlKR?xAh\\ifqNn^la^[F\\\\>^HhZUV]SoqlilGov`QtnixS@tpQpBpu<HtIWbuGdgh]Lv^Ty^hWgvgo:Nnr^fg`hPXcExiDnt@NdCOr`^`dH^oPp<igT@yXxbNfj^PtJfj`Fje@l@gkwyZY_njOx^VeeWisGyO`]eXoTfoeAcSFfS?fTHgThpMaicYcGoaoIsGo]s_f:vrCQ`J?uEioGxtSquB>[wV^[Nv?VjialwnZdPlbHorptB>`^@vGho`vn@VtfIsu^fGWZynkrhqsprshk`fxjN^Hf\\Lq\\nyaRHfIyrtAuy?`Aadyo\\EFsWhwtvthwtSGejIeXxxb`gA@]<?fUQ\\af_jOt@ncDOfUQ\\=ql^pfGnrEY^V`arIhXpyvyq:a`uPs_yxrYyfxbFNIiDfqs];DRqhZ=YRAvBIDEgcG;uRATnKECAyu;S<WTPsDosGv?t^Se?GxkUekIXUsrKggHsXiWXJYRIsx=KuMKc^?dnII=[Y\\usaEImGxLsVpwU<Ycw[EAqRSKCc=cHEFeGtrqYBYGmygJoHMadTcVNWud;yiQxS[hucBDyw\\cB[qwjWhpEVECStSWf[Ds_XPGvnAE`UfYWCi]g\\ybxSwSgDpotNSTMUVFwSwwe]YHSkBlsWjoUR]fsCFBEEM]sGqE^kDa=gpsuZKce?up?FUwDNYgkSw_QIqmhDaxOcDOOhI=NBDK@H]ma^xajnfhyNnVGkc`g?`dDG^QwsPIinAr:nk[>k?_bgN[S_eoAuRoxc^fgnZA_gLonCh^F?\\DvdA^_Q_EYShSck]bjgV\\IGBMh^?DlWun]ucCxJARTmfCIcVUy?IrJkB_AhFYWtiD\\?G\\OvQGdDmuo]yRIE=SEgauPqFWewJKIWQthUW_GD<MXxqxsksYQIAIw=ucZmhPgwYqStCXuWGVyui=XnAgGYBI[bv_ylMCcceHyw<At\\IiaQGFuSqCywwuU_v>IcKMu;oTwCUKyIICF>cCiectwhD=EOId<AFBcIDCuSKfbGstexoMsGYG^QCHKSCMvREtfGGpkT\\MEo_reWVa_ClGYG=w=wuNaB[]rFac?YyHUuJSEFkCs[YeYUpSEUCGZob_EiRod<ce]QuOAcNMg<eiXShquUBgfaGgfMS<eT]kCGKEOAEMADfsfZYYx=SY=E]Qi[kgPaWuEHoATkMGJ]EdKIROTjoTmAUcWY>KU]=FJWr`SDY;Gj]vjEbcGbfCfeGivufDYCamhrGYmGR_eG^KW^st]CdK[BxOFOGd^QC`CeVGRdcWZUI@KsHGwukI@at=uRRceWWiQyGUYiDoEk;w[iU?uhC?Yv]u\\IwaWhvuyuqFmYxD?IPcUqIHkiyRwtXUCj_g`SypIuRkBfiuUowVyfqeyiIfAWy=KR^[v:qdpStsiIvMWtyhjURQWCOWhrIX:gVS_rLUFpevS[rVIgIYbPAS_CDgEWE]tG]CTeu<?FKWDcqHc;wRgdMCsEMh^IeNSskCHT;IrCXBwRamuAaSxMcDeg<OTTOUgGrPqtPSEUSwBkSm=vZyFR;sWSft[h<oT@cbFaD=cbw_gOyVjQe<OXpyRrgrtSR]GW>CF[=tAqTccRZSGNUWxKU;gWU[fmoFPmRLetxduAeuO\\teMKqHM]YYDXQQeUvqRF`lD@RcMSx=rdQpAEWmDKtTx]dRTQSFdpK@kc@qxtXp`QhhWs`t@hPcTTJ`JFQkWDU``uw@P\\<J=UMfEwglscyPkUVQtOpCNObgmUCkY>OCOCfUCVZCTgCiJcuAaiE_Db?CpeBIiXqeDNorn[SPkthAXeev@CVNKVSwWyCergi:_VTObCIS=wVXGhSMUL_tdEI<?f<=E`CDTYsEQci_Y_QD`GU@AH>srHgcpeIDygqCIRIxI[wpmceeC[=EjOisEdlwy@cHyQEhwU[kc^kgUafySYJ?FF;UVUIEayLeE==WLEU;?DTgwGuc?WUo]u@oVfMG=miIAFWgHBORj_ECeh`=Hn[I>Iv=iB`kRGKXsUBQYu`icmoIOOh?GGG]WEYrnSRnoDFysA;Cd_TdKb;IdS]cZIRdecE]tUcFdidB?tQ]Ho=s?UUlMViaH=eXMgwEydCcTBeFF?x]?ejkTfYsu;ik[TOorGcH@GfcyGT[Et]fBqu;_CxwBaqGO=YhibGkuvUh<eiNCdKQd[IREoykSEDOdteG@qh?CgF_rlgF<CRVcF`wvrsCdsCTADqeEGyxpKY>AfAWY@Gb;CskWVpsVHAGvsS[_d;UYRIYLOecCgN]HQoGsaYgYWU=ih]b]aFCYcS_cKIU[KbXuvZwbXkwoKuWWBn[Y`uyiUBJsUIGY]UwOMvReX?;XcqS:EdCGuc[H]eftcRdMvk;VA?EnoRMOgh_F^etd[TUYxpib>cfnCdDGeR;e\\YfIsY<wCYSyRCXNSvAkExwv]QihMRFktqCYoitQ=eTOe\\=XZAG=Gi]ggw?S>eD]irI;bl;dtcR@qiHAT;MTYSDFecW[FicHOiwyMrqUF>_BacGj_E;wD@aGP_Ingt^OTqAWpKFNOtRmh>erTcFnCd@?FP[ddIH_isJgwGAdGgh:Gd;sbI[In[C>AYt[Vm_vmsi[IhbybJGWouBt?C;qgDafe]BfGb^EGT]VXxjBUN]UJ;`R?Qkb\\kMLJZpXD]mpxkZuTr]UudYtlWa=SfqS_pWYTY;`NFXVdhsTdvTEkFMOmqpthJWhuceywAvZ`vmtmCEXsQX:enLyRwpU`Lkd<WgIN_mjUupD]YsYse@yx=syHyqtwa]YvtkPayTqSeLwp\\LeqS<@VuqLC=M@`ofpsmikaqyi\\T`iPV`YSdoMHXwhs@=KdyJrhP=hkO@l_XQhdplemCiqcMyA`SdiT?Un\\=LrIPUYM;lpgAlg<MniKRavDlLUXmKDwv]kLIN=TJLxnX`tNiqmaL@ulshY]uMohoSMRydStdKc`TFXvR@qhPV[ER]`tNTv?xu?atIYnwXK>PXWTufPVmHkK]Ojdy>yRRpl]`Of]yYatqllKLTlqV?ynXLOTHRFeQL]t]dRg<TRppZ=NgDQnTm]dVElUxtpGyPxXpHIuQMOJTWlEY=XRuMPFqMCAPjxr;TUneSZQt>lq\\pUGMQ]dpDhRgPp?EolpRRDYRpVhqMvPoqqJwLVJYbOroOiR]dFisS]VmoI[=E]=EpKR^CtdIsDsb:UWCieukEmYxUaB;=sNadCIv=IYlGU=?IXIep]xH]YZcxJYRIswF[B<wVpyYX_cSgrySwmQttYxFkv@WUsiBCEr\\?BnOuKIhqWdIWU?;gDsXDctpCVZWSl[Ru?SPAVRGSjGdYCy^gensyOyWvytvmxwye]=IqKrTQuTCTNCvsmEGoR=_XtcSdcd\\eYwee`UhCEhR=RTKDggDL=EnWgcGhxwrSkGv[ct;DpoWL;ELqVuGYXWCEWeBSxuAEHUdnmuAag>[TDqFQkUYKbAuhccT=[IqkrJODacGkcSCoS?aBlccQ[fcgTdaHdED;wgRAUH;UW?xKOS=CBoKBPyhvmhPYBvEfKockWRDkY@WSV?T<STS?f:eXHktHax\\oxr?upYroWxF[XFqsr;uhoC<cg:Gi^yyuky=STT_TTgCHiUwssIsurmeYIyRyw\\_h<MCsqTkUWysDTirTMIgCyRyr^stiwDSAubYFDOE>CbA]Ea=HF_Gqmwf=x_yGyoSwoEkyry]q^Xt`qkCMyQqwmAVaarbuvE@N:upTMWUUue\\ywypyalydyExyBAs>hr;Xnw]kHenKPLvPW>]MA]lq`QdhvjDMe\\o[PpW<TetRFqsv<s]tqkAOqtWYXvAxOxuJYiKr=ycHNHeQO]NY]PsHYolnp`p@eptHkDhPpXNrDX<An[aYSHuM<ps@y;lLipYJ@nx=lfmTJhsr`nMqOphMJ\\JxTj=tjRPmRyRhtvMdr_lLPpoluVkQL@`PslyZyjRYQxtj[aVrYmyiyYIn=AL;^ujGqjHq@qqxa]xPtrOc[PbbX_?WrFHuFNZx?yDq\\QosQAk=gc`V_sFxxPZApcaIsQfcJO]c^ZPhf[YikFfJFfRPjNorZxiRWdeVcPyl:IhF_dQFmxih:Hx?y_xGxExxtW^t?yoYbUO[^OmCxm:Wg;gn\\?dc@bRNw^^d?wrBFnJN^KVq`WpZ^j\\OgdfsrAyhAclqmkaoAp]hEgEgE?D<GfnACMGicmTDYsVquxGSVcJnhjJQNSejhUY?LRZhWplwf@UMILHywTtoblXx=PTMRuQqeYVEaPYDQkIVxyvyEyyPxNIkIDPTyPDhVT=ScDWpTm>HVB]L?]j[=kaIY>HVBIp]urBivleokTmuDxFQnWpNf\\KFDW]=MpuV[QrpTkFlvHHPJxQ>uYxmlkInA<uyTxbtNIpYNxrI]ya]lTxLSQuXunXWvqfZXxnbpl=NyAa_lXr@FjjAeXoolHpfYpwH\\<NjSiycocYpw=q`D^opfahoudXhgWs_G_e@d]FsRocco^@YvHxq:hmKHpWIg@AgKIa`gu`HvHAeLq_=qh<_rTQd[p`k>nMH\\[xwLHhcppQY^:Fn?ne]^f^@`<Io=xnrFhZa^DgpBHrUAqPVkhxtQWgRN]D_yboqiGpr@wJwoU@[KHbeIi>@o]YyKVcEg^hxeYq^Wp`cywIWlHWe>IxHQfKYiuYn[XqbglrpypVw_Yhfngx@rdqtsNmXgjrN\\Fy_VIvivy`yyZpubVvuOmdGa^PeD>xVgbsW_^HdEOaZolgFbENr:WfTO]=OeV`ata\\yhySxa^IlApaBGolHbfVc^Qy\\nr`VtF`kt^lqh\\QpuVobAGa@wj`Gwen[[OmsnsW_iKhwDi\\^hhSVamoZ[ng\\^kU@acicDfZ;wiYolfo`@O]G_cEYrnN^FWs^vmU^fl_y:Vl]wZj^j=gqPwb`OhFfwy^s^YjI@`sAv=axgIuA_gR__fpoKakNNeD_lL>yDGtFA[BIcHqqNgfeg^ZOfIXr]y]W>vZIkVfy=p\\cap;o^M@mGXg_AkGihYPioNreO_vvdKNyCxj@?sBfn=^pP^cIhmfa]_yxtgoKYwR^xjqo[Xi@Ha:HfB^[=?x:YZ@nma>eWgtfxo=XvR>__?nN`bBVZjFdDafkG`^yjy^_m?xZokkHpNVj=p\\HXtgYcbIsDPibIvXObBFtdNvMFfKGtcNhd_xKoyOIsygsmxtyQmmYmiOpPAe;Yk=^ccGf\\o^avgV@gtWamWx[he]x^syZT?nJA[gVed_^G_\\AAi;xkNq^Ap^HNx>IjaHynIwa?ifAv]AuPXtcNmmGqVwn]?\\?GsDAwWyclYvQa[WQ[kNuwpxgHtRobPPb`waHhtIADcRNcRb?UZMEcKcsGT\\QtaIcWywKkHi?vqshB[YU[d?ehd=hvoTasTJ_HdEHTUCfad>IC;Ue<OSNSVRIUdixDch@OfhcDXmB^UW[;UqMH?[B<EBLotBISkWXVQuDKdh?BsoSjEeTIUCwtWucQIigWtsGOXpvh@RsdqMiSbuuihwkAWYUYYIpqITliUD=s^]NaxSE\\ld<VTpKyexQEJUYuKLUqYnoqN[=UaeWGiveyUy`slQxptqyYyaDybyRI<Pv\\mAEOOISBmYi\\Yh<wPYktXt[tWUqs?dt@QOUixE\\WOyuZUqkEk@xpCUpXDppUO=]vHLtfMqfulQHTk\\nLQJMaLNQo[TMeeK\\AUMhs`@MXtpCuVMHs:mqaMVa`LKxWZUucmJAlRCenLayPYPyIQYQYxHRbmUZlkNdtD]jQat>DV=XwqpuZQr_ylRYPm=jVmXBHlxxJshYaQMUTuq@NhHtBllJETTPSmTjWpQ?Ikcysj]vJISdhpg]WulrJHLK]LJ<WG`L@DXNDvspM;=LZ`l<IMTDJIYrqiYLmTTHVMINBTRPyOX]rqaQ>HNKYoktOyivTTO_ukteP^]WTIv:YJslkXPsk<Tj@wIAQrITFQY?yVoEuaEwPxRgPL;<VTMJEQLRpT\\yPJQUJmoYIvdimiQPuDxRTN=Xyj\\KeiQi@TbiXFLYrxNbqQaPTc<pf<UWetNQWTPYWASL<S=qlmlKO@mpQjBPS?YnKATrmm`mV`dR[@VhQYfpUaAnA^uU_^WVjpIab>hFa\\MhjcobmXvFfnAHcSFg\\g\\]qZG_yJYbcftSvlBpc`X]CqcKou`nyCGvSV_?_]aNuwWdR`\\VP^avfHGxUv[wojIaalYmv^pia`Hhvn_fmNbB^nN@uphcRnjNYwoOgoP]GqfMPiWYvrIx]`vlGqPwpZwxdgxWanZhqigg<AfSFaLqxZFuNA`SasJFmNw]@`pCWe]^ngIflGoKNksH[@VyqQpyOyw_sFo]aVlGAvti\\DgnLngMGvuP[Qi[kf]?Ar>Hc`x_GQsTgl_iv@VkK?s`G\\^oc`Fj`gwhGjRIuJGtonkbXa_AqMI^JgeyywF?]dgiiGs<phxoguO[bQwJ^h?Vs?N]gYjDNluYkR?voNZ@Qk]aal_vKocV>aCptdh`T_xgye=Xu?fqPQjnOej^`^?tYygMagt^oiX]>Ih=fnd@gWaZ>nmaIptPe@yxw_gU?db>a^YxHNdDq\\[guS_ldaqPxa=nhcwxopbegt[nethliAtx?fkXyYxhFvgO>cPquxg[bf\\kgi_IehagxVsdGy?ntEwtRoeXGf_GiGxtYGq;isUxtB>e`_fLAnSAd^Op@FoF>c[Gbr>j]gvcOqGOh?Gb[xshAlBw^_F[=FsnAuKo]tFxNnpWPnRx]^Gi]ih<FpBon:ngWGpop]LG_?_lpXwZh]Hfsw^bhVe:f^sHhmQ]QooVAnLO[jguDfs`QaGwh?hamVfv?wcy[m?yJa]Sak?wiYojvoaEOagAvrn[cahT`htfjgWaCoi:>fTo\\LA`LhiPP\\[wnbnvl`[tn[Sqy;^[Uq^fOinvp]O_ogkSh`SYinVr=v[O>arxp:AgpvbhfglPq`IhpixDvvIatRoq]IdXQcpxqTOkLps;xnCfi?Pk?Bt=iXeeJytFmcWSrpOtustQwxbgCswtk;w[iUAiuWWbfmTjCIcCY^IDGUf;SUUMBYyHkiYEcf\\KdqGgCwwEMrJkUyeIsAFbywq?YrIvvSXmEwPMW`ut:uWt]B[wbXkw_KuMOcJAdlStvkHsaBasrHUXoUwLssi[YYwDPkY:isgYWrGfE=EA_rdkRBEbDgTAyHcWiHiv^ehXarpSh^ig<SdsIG`uBqYxKYVY_vNquAGEDycZ_hdaYRuhuwDCAY^Ue[Iv[Ms_QHeWge_HUoIoQi`kcyIuw?YEYULggdeb>eXDoh>_H^gwkkfAsRSswyMDyMhFwEPAG`mVJKTloUuEcUSWyUS`cy=MC?ADy=C\\?r>ebpScE;TVSU\\_TkAC=?Ec_Fb?IcKCO?w^=CBoxr?TCKUoeWYudn=SqEd<cuoiYAmW^wXC]kVykHiwuxr@?op`qbNqeXeZPaA^vWvjJFcrGeVVb[@ZI`a<nk]Fk\\``awsHHpr@q;goPAbBp^c`\\Rpn\\asSHivwqCgnLgvMvmrnsbAgK`hTIrj^vhvw;ycDwyWIiwGjWNsTQl`GohXihQfSVqXywuxx[imta]DouiGfNa^D`aFWr;Q`m>_g@oNy\\s`huygRW_WX^F^`hgt^qxofbZY[dVe<v^_@]Vf\\Vfib@mnO[dNk@Wr?qpE`]wFx^Vr=Wvvvx<yu\\Pvg_[MNp?V`sv\\OPnPokbx`d`deXu^Wp?^[=QnyxiBPgVhnKW_]Yq@fpl?k>QncidRxevvsoYmaA]by]`oh`a^uqnYFv<ijE`_iw_:n`@HgjNavFrKYbIV`qxybnj;Vj=hjY@qQqoeQdc`dbpdd>y;?jeQqNYwoo`qppB`aY`yfa]IwapA[X?\\lWxTid`y_XX^HVbVWt^v`cI`q_r_AvxVlcagKVsf>heWf?xtHalsItINcNop]NyA`?aD>oi\\Gv_StFKCxoR?mBK]fkcGjQeUaybicyOv;WRYOFWOGZEeHuxUUvwsbXCHbhY;PR;=xNYTL@NJ]mutnbxt_lmaAvuIPk]M[hp;`lP<Lm`pNDvthTThSbht\\mnahMVtRp@s;qkyEnApMt=qq@LgHx=MUeMVWTvRlKalRXLvBAtkmQq=wqEYxmyu]qp`yltvQycwpqDN]PO_Eabk_ucngWFvjNmW@rINZ`Wy`GasFhDxjqaaHYyqyaCouCYfTpdAoaMqeS_qU`]:^fmHetYyA>`Gi^pxpWO_O@qmN^swpn@wa?uippAFvhxaKuCYCROH?GeTsFUOms=wK`yuAsRULFlVIMpR=YG`omEk]TyaAMcyQ<MqRannpxGMmGPQb=P?`R@Exh`P\\Mv>QRZLumUy?uTOLYQurZunM=nupM]XsbiuwumYTNMdWLHtOhN[YoWmr^eoTykuqTwhlqmL@HJDEKlEQ;YVIHWlDmBxqvYsxlqkikSmoWUtBDPI@L_]SMUN_\\UsPp@QxlQMqtWh<xUxqsAKAykiInR]soMqJ<Jd>sYi`lipeyfOQmaQ__E^gup=s@CCs=D^sYAqC;CycaB[yrCMshmu\\GTdKFFWefodHIhSMi<Ajxmr@lSLToJXOqxyXxPYAqDisehTVQq^\\k\\lPQURfTOkuvaMxpll_=VT=xJYyE`OVaxs`y`XkNEWH]My]mamQkyOJ<mV=qsiTvuYMHpC`M`aJNxpOTSqmtrPXwiSHamwmkIukgINWpSmDPl]m?hpQAqmUvHDWa@So`L[IqDdSFxMQHUWaqHPtY\\rkMtv=xCxsMPpmay]yhOvpQnojxfhvrADyueAySwqDcsFMQHAUcY?yt[VlCE^_dbegCOS_[GEQrk]ElGeFcsfmbogxomrXGyfSdMSDvCfNCVZIf;Cgm[WrwsLSsiGTBiu@Ihl]suoDYQYhUbaqykUbTESm]yK_EAuEDYVuKbdEI`UWg;fTmcjMtLsF_SULOG?=vcKvjos<Qt_kBtqFcYGFsiagChiI\\=t=iY:Cb[=WDcB;Ir=ObIwYVkYnYF;IumoBUYuPkgeUfoMV@mb>UeUugekGYmxsQwQuhR]UnAYfIhvsFImvRkEpGSagCNOB[kYW]saeInAXyURZ;H>MTbCGLSbdAX`=eI]wymbakfy;R];g]yRXcDiOrmuPQtOlAtDUNK`K`xJsMWYyjk\\j;MuDAlmMX^amvDWeTtTPo]Xls\\Ogil;xp:UYk@NBLPNMOSlpp`PoQYB=M@AO_HWkIkq=KWYukXmj=K[=lGeSkTQlIU`tJx\\r=UyT@SKprpTpbEvlhtv<jYuyLdsDiVtYMhTJx@V]LPJHLBpTrHUupJyIpJHVGuTAAnoipEAWFqk[AqoiYQiWgao<hU[qVgLlJdXo]KtXq?DN>qY\\TxfquUyU@LUdlO:lKWLPsYry\\skxYyqMxpxo`QamsFDL?upjdso]SmHRtdok]MGYmimsmHpkHrCXLM]MulP?qqwULfIumdk_EugDkKySxmq^@MODkceQB<UshX=XMauU]Lk<qkVmOHPVfaXDhQAxkkTXbAO@HW\\dKC`lgPtdXQrxvQLR\\mNcHqe\\OgeQAisoxq=ixqHoPYSBdl_tmXpR@YJvYtIlsjmyVQMDeRniKr\\VlqN_iOYdn=\\OMIrlTlcUUGPYFhWU\\sw<l@QpAHPVyJr]v[xkZ=m`tmxarY<ltEp;eOxqPImQOhnJXpsUxdekLqlEisEXKvYrqmyLhYmxRRXmw=jx`unLPTDVoEN^dllAoOMJ<tSZiPODXP=VTpP<<TtlVj=VFxKwdyslSw<ynlmQuNMhpByv@@s`xJTuj`yNYxpg=uphSyuYylqiYtb]PBTrjDlZLWGHOG<TDdoNlj[=VaXPgDkWHRgUo@]Wt@kf]r\\eVSXwqLWftsQElBmr`hS`mxa=sQ\\s>vmj>]W`hLpfT_oKOc]YyDvp`@uTAxR?qOovpQv_nvpqa<G`y^t\\^iyaypxydNnA_[t?qa?gYW_MP^X?lDG[pawKai^Y^<@_L^lEQ]_`_\\@cKnjkNeAgoCgb<vuIHeV_kRgegPx<Y[_o`pnjk^[r?x;aaPh^UWpfHZnw^nv^sosXVbbInAxhMfwhHZ^NfBFo_Ne^VdyNhpomfhmEoi]H^Bhi@QxM^rdF]C_^J>a@OkkQr>OnWwwdaZBGtThdTqiPxmlogqHk;xwU>qhGj`WpYhn_Dioit?Rxsea]Wf?udAIvgieYRqqH^KhLCXQyw_kBpKtn?hGaInEGL[H?[S]IG>qevSdSyHkmhHIhTai>aYmECEQsZgSZKtgyBYIFCcW]GrhKVJiHw=guWCJIF=cUWCbhORyqW<CfUqI>ocv=Waqhr[ckcb^=YZ=dSGxciewyy_cU\\UuQIXccBc_DFeSS_YlYdSkxfIhrewo_GioiTyr`qvlkguoBN?HFOITUYNMGGkGV=i?qr@QGQwGaAeV_E^]V^=e;Ir;[GeCHLOupgs^av^kfcMF__rimHREioUsZgsR_I:;BB;RLbsYSaAiwEw<chLqHUYge]gGys]OvrWdWGfOorngW@oFAIwUkE\\=W\\MckiYm]sVKI<at;WRrCgnMfCwtWqb[qwqISlUi`Cs??uKGudqcYUV_UwGmwfwy=SgowY<iCQ=CvAe@UH:yXe_gh_WJEuL[Ux_hCWuB?wU[HCixC]C=MTfkxK]GFKhtOiFegParg=Urqg@MSGmiZMHnKgBSSkkeYuBgGEYSe\\mWpIRpKsq;sTSsFgx_EiW]XSKEGUhjUVEGy?YwVwinQCMYDm]cGsw]mVvaHi]ewebUwTiOVJGRZMtb]rrGEGOcUiwu=HFSd<miiCxV;ReWhisYhsGD_dLsrk=ESCE;iXWMWoOUeMhR]baYWNodZ[F\\CeWmc@EF_[HeqHQmvwKetedFmiBqvTUB__Huyc`EEUoXR?ueAdHAE>kUlccbkcMCG\\MRtKdmqrHEStqBgKfrcS^sTBcT=;DW_iFotuWxgqiwwwe[xBGRIsxVcuXWbvmUl=v:?fSaT^OTTwWyUu\\Qr?;GOODmKX\\]yduyW_Rc_FVcw?yDU[B;ORccscWT?kRAeeHCIbISEOYbIvxARqCSZgF?GdnOCxEC`_HSyHjsxPyYQqymosrgePyWxmcMWiJ=Xb[D@?c]ISdcdsmWYqu`oTmAEUSGxQruaxM?heuUu?tpyFB_Ft?EKQGHcfjCSSURFwxwCs:MYHcdUWV[ei:IudyU_KDXSfwAYgKDZCRnuDasW[IHJegkwgWCyIudsAYa[sfurI=tWOXVqiyMFUKVAYdJQyu?IBGH>GrRAtbSy`wx;[i]CE@sIoAep=s;MxocH_=Hr;WjsHaUXvAY@TW=\\of`kmHqsHR]HpG=LN=PFpJLmPcpTU`RKeklEYGhr?aMs`e@WobwpgWmcIwc_cMarj^[vpbWhnewdrpy]xi\\GvVY]nVs_Nby>^FNnYVx`>[c>eshhOFg:oqy?k;IxcnrawxmVhbA\\]YpuIatqqa>_Hf[q`aBVq_igWAcvahgyhAOxxIoontSxeyq_egxiY\\EibLokGgqd@gPGnXWdNWcontQ_adip:>\\rFgMVrBouEwbIfm`ax=wcmowvI]PndYArqQorhkBtiMVRKDcmrNUEEaey_xvStMWhrkSTGxKgyn[iw_UyGX=_U;EvuIX\\iwkgFooVWwtHqIIYTIwYTGhKGWHoEvuIeYWe_WhgyScflqBkOxKOt^=YjMdwSTA?DWGD:IsXaFlsiugfuuIUKu^OGMGsj[Hn[Rc_T\\[C]KeGAbTeS[_tWut;oDUqSSUffgG_=YwhWlHq:`TDMPnlVklqAIV^]u[tloDpFEsgYmGmpqLJ<tUiASy`VlDQKMs>`XNTyl`TVYSfloWHnRXM`xqrDuLHRwaxHYtiPNt]rZxZVfueNyph_jhg;Il]>fUQmdg`sAvuphGqnVodrpg\\?]NQejXxCgnSoeHH`Fp^]YvO^lL_]x^m_?iRInixsTiqDxtoGbhihINibIvXAnW_`U^pn?uWqhXymlFj?FbeXdjYxwVeUgfn^aVPfZ?nIvsUf^DprkiiL`d`yhKNbB^ZggwLWo>^\\lhhF^`@`pCinqA`eNhVvkVoqthxq?_YG^F>lgvg=ptTpoRijP?gSFcA>bMQwN^uO_vAge>F^Lio<vygxiqXwpphb`eEqa[h\\JFb^yrNNdsor@v^RV]T@wfYuivyripyV`>W_>f[`wfGnxfIsLnjSndQwZR_eV@f]WnDqv`G[Qiu@GoTNdpF\\<ibcpZ[?wmHqsHkDhdl_u?^of`onomZn[=O]_hgpP]XFncW\\=>[GO_]auoH`:pt>Ip\\nk\\opPolSweV_vDYoiVlCyfRpan_ltgnFau=xnS^]Y@nj>`B@wLiocgoKOuAY[qFoovdBhdJQ]aXgLPp@>eSwq<ik?yvB^rLfYcb>=tbGifmgu]TpOFditROYS=F^_Rc_f=qDAIH`gWk]xjYrvMx]siAIfsWTv?yDyTsGhniIdihGkxaYhZGFD_HUWuEaWisYWWVAwEamVdmc;oiC[v\\aHioeI;TcQDeWWXcdgADggB@gDmewtYenSeo[dL]wSOIFyRXoyw[Yykv<idaAgosHbYGFGxRIgIGX^Av==ELAwV[fuGsJqsbgtYwEweYwaxqyCjsIy_S_OvMegdKvrqWCqUlMrI_CHQHPyQ[ewvtvhlu`ArkPJAyMHIPmTm[@mm@sUmNGtO\\eX;YV_EsaLxoLSaLO=TtN<uH`rl]NpXVZUu@dtTiOhlurqL?`w>drvAWeXw;Uo]YxXIoaLY>A>UbpCRJMC@sBMCWKOTDoyxEc]AUVAi[GUUUdnSeJ[B:CB@GBHWFj_G=oR=ExwwwO=UTMWjMynMeqyiy=dMuftIDykF@iw[wbXkwa[XE]bxEeaOgN?vtObOitFCVr=d`Ut]Kcp=sBYuP_byaubQHVmhd_YCMV@asUeB`KTM=u;WRbYyC=FvKDcGSxCiGoG_OTUeSnWsF]uO=uqeDxiuCOtdgdh]u[SB[MXUoCouvuuRH_tXCtc?bR=DrEDMWHM_sHew[cvrsWoWSy_TfAD>_vmSRD=S__BuuxTawWYW]gXyCXvSrdQW=?HF;tTyFFSENUg_[YYyrmaI\\ednEewss]oTeOD?GVa;CisTbKHnwWHggeyTRmYsIIdwhi=fNYUIGhDmh?ArBEUgOFREvumGQwUxEe?WgQ=ItAu]aIkIuYqvKySvMevAr:urjUEAqIOuxHsXpsiHieGwwMaXEAihwCkMc;aykMs_OCQogXmrqQEF_c^AESshbod]kHPgIpst<MBiCIXiw]EVsKbfEr^cwR?upGbJKbMuFY?rp]BkYC_kgg_yGCwfAGxwfJEdC=EOIitEwA_YwYeyIbYIygwyPGtKGSlmsNSEekDIqygiEVSu`_hKcXPMt]?GBmf@GdVWgMUduAyQuylyY\\eXuYHfwdhGtYWu=arjISVSImqDAAwQsY]TLEdo;QpFmJAtRCaVPAuTQq;eoPqUf\\uwaQTUW@xJaHyjYTyIKbujyAxQtyUTPmEO@ynM]KqIQFDQHDY=avsYMU`UutuZeVKyNDdPk]oKPJV`p^Tlq<sO\\SleJM`XTMNGa]Qw_l@`vq^uqnXybhVuY@l<fyEiqhgqUAwKVjXr<cuQac^gSf;s`eHmUX<;dRkbZwiYavfIU;QtLoFBKDGOf[]bRoVFGW`SgLkeASWeMeEudv]Sm_RmGEjcIWgVr=IGmHeeXsuCp=xMuTbSYbIfAwxJ[BGob\\eXOKbZMeiqYqQFI]IKavZIrBsrkowoqro?dVUYfSr`wuS[VigY:WsGyH;mFSsCkotBeFLKfZ[HuSfKoXEmYp]c=aXLmfOuTq;RoOd`GcRiIH_hW?RWKWNUuE?foqSq?fO?SgORRoESYrNAU\\yGBWvrWHOKwWqRqwwvgEe;tXexWsEIQfoUiJeTbcH=OWGIgWuUVwvHidEAcZGrKwrXSFjiYTgxtcs`UDQYxb=y;kwlaIL=sYGGNQSqOHs;B^GV\\aVgKf:yvFyXxwsvidU_gVQiHywxyCyYFPWVMsrDWSQqU_yBi_yCkgkaIMSH?Kb:UtbwRrgsdScEwu`QusoFeSx[kf_;GIAWDiHUgx?ueter<yW@AyxwcJKbb[DFoSTaIwIs;kb`[BesXFMHSgeHEUyEXFgYuucLuDYYfSAcjYeDoRgCHKuvDkCicitiSXoY\\YtFocHEHt[hIGuCwrsYuauyYKHcGB^?HCKr>uYYydqCd@qwccS<=S@qJa]nyAPL=mRlrityvLWn\\WDivfdk@ml`UpFPYEpnY@L<dnLTxmYnaxQ>qVcqNhMySmxOTpFaxILTITNhdWgMXoqTWPXcLNQ=PbYMn@P^@ND`PkPkk\\SCpk[pTH@k\\DkgEUrpypttiuqHatBYoV`QtIpHxL^iq>aKt]rZR?oxDyRlOB^;EUSSBKr:Ab^cd<ssm;xwEceQEbeGjcSQStnIHGec_ECVsrZ;CnSxmIDhWU[eV_OrMsS^kr^UtN?upGbfeb>cy^GIPyyVKYl]fXKYrit?wwemhqgHGob;UhsCRwoecESKkwIWXsgi\\aCj;vFKxCxsjtYeqJhXu:EKG@TTdLE<P?qs^pM[xX<lsBMkTdM=`K_\\rCalOpsbHtPAyKimvMJOiRBLlUYuWej>`JnuVV\\N^UNDTNDHyVtKYtQGItwur:LQMEnXiWCerhDWspuwdqbDuhhMSQk:=n_`RRmLeUxq=YcIuiPx\\ytypjLQk]tSvdrcxkyTRyAwRDWIYVeeYWhjetLSmYoiJdYoEuQyqXoxPB<PF=OixOkauYuyoljcExCxQryOsPqrEjyxypymkmvGyw\\aV=mNqAW@xrg=tJUo>=YX]ScUO\\<xODu<hR`tVJtrTPUSMxsxurywCiVtIYoikY<x=xvypR`tWkxyBml[HXU`X@LvRyv?YPIQPkLXVXnApM_xor\\rNAyVtlQTkfeosaJxpnTmkBdYGHWDMOOiKPpThEPuxvBTv]XyrMwkxOjEyliRhlUt@jY\\T;dRYEXRxxylxCMk?HjHAqViMcdk?`L`dMgUuiDKgytqHtJ\\lEiJvtWL@NbPL>DsNDnpxX[XYTDn[=m^YKSmnauJrXTP\\Oi=qNYrLdv`=rgXQOmliAyF`SRaSFanRLMmXUoIj@Alc\\lDHXWAJIikKQKThXGPuP`WQpTSxUtpsCYnYTWCUMiykeurudjXDPbIvx`jJTQe@Rc`l^MV<avkyroTN]LkAtMN\\Uv@OrtXHLS_Tjj\\pj\\k:TtFDPFdk_Ej]AmBDVJAWbmoVEW\\QqkTTMeK@uRm\\KHlnk]MMTtNhUIyxXQQkXYbInAxp<pND`PGqn\\Ht:@QX\\vLiNMHysAm=yjq]NctxXDSA<NiuLrMXvYRvYvlyPr`wWxNZ<rPmLTQSvLJ<ALuPkZAmRhQ?iqFLu=]tVQMqlphXLALWAyVJQwD<ohLLZXJL`X]qsyixhTrkMVRmWCMlTMu_tOBDYvaxuIQo]wnTN=XNupTMyYPhloyUPLqmMKnUsrEpeMtIUwuqrLQJIiyoyUjYrihyGtpilmAMMLPs@qJdltfiYjaPkptVqQyqJQmUtElgXmQ=KUhsqhpWmjcDTk]r`QxvtuwYxyTRTmNQUoQIY]QxE`PThTDTJ?mWWmXcdW@honHv>mMMdjCqwRln:AP?MP@UPP`sGqQBIjwurS<MRdND`YhxsytrjanGhwBLnJLrZ\\VkEy\\tOx`yGmj@lNShum=mxQrNDUeAJEtpYmReERmpKGQq\\lk;otS?etPcc`ybVy`wkj?fYYjvoySxyHHj\\YpfwlPGc_X`FqwsNrAoajIalIqxptrptWFkIWiDWtiV]gi`svtOaddFgDivkOwoibh^eRWfn_pRQ]\\>twqyMfm]ymDWuNqgeninQxpFfNGnXw[b_t\\^p<HxSvj[IhU`ikF_Chn[H_`wrjYj`fx`gZYyxKGlZfmK?]poj`gnFqbcqZx?v\\AucqtphuuxxwYaGp]k>w[qq>wx^P^EQ\\nixS>aHPfv_ejxfI`fIq];sCmWVAHRuUq;HGEc_ECfSG<aHOkhW_I@=EdmtPQr^[E`[CBSrB;T^Uh`CgNGcN?VRkrhoDriidubqAt=uCy_U^SfhcBSagZOU?Suh;x`YejmyvOVyqY?GV^[gZqUIMHEMCh;h^gsXOrfscGcI?QyLQGecs?]Sf;cNMtk;HbEeJWD\\CDdAcKSYFwBtqSlGVg=XuUwpCbiIFNcEsATA_D>KCW[htwB;MRB[TZoXvECgEGLUGJcCWQThCS;MsHUxrYBIMHV=E;yx<[VtuvTKQclkpUl>duCaqB\\YIxlyHyftQrQsY=pngdFW_SXfyHqjvsexurQ]EvtiP^GFslinm_ggf_`Fu>vgMh_dgnJN`SQmoXeqFyAxyryyLG]FFxMg[@pjm_sFIaVhiCyfoGrI_fkPpgfjCO_[g\\=_\\phpwQ\\[FNkBrCXfIXNoxsyyxoxTCi<GSNCWvuTKcbTCW>aesSywmcWkYVGxkgI^Mt=]cNsSkQySyEKkbKCVZCxTGsweYIYfNmu:ixT;CZSecKx;wFyUL=>_Qx`BaflacGowaOg\\weQIxgQx?fqEW_`igS@maI_ppPgtOQFK]HCirEgFHmefmh@qCiqyUCF>khSofisHGqtTGrlQROOspMtKUERkhRGeEETbyHKMCdihrWHdkTuEBx=D\\iBKMdboG^kfg;GpIIb?u=ichAhkgYMGcKWRg?HuWy]iYyqSZwRFKQYUnU@Nrlk:aP?DmF\\KITK`tNMpo;YwiXKDiVCUn[=N>xk[]jBDL]=MDTtNAm`@NHhJ_QX>`lG\\YYynR]L^QX@Dwnhj]a^NVqAOnSolowuv?roAt=w[y@atxdFh_E?`pnflv`aWptPgjOv>o]QikrPiOGpkH\\mF`[vwsF_rX]<?cx^`sIhhhdhFdTau`>grAmHHZ`PctnZL?tH?bPO[DgvLVu`G[i>xJFn:gZDFn>wli@vhNdZY_NxoKoq@@luPpFNeYO]^NjB_rBF_s>`sxmk`srVgEXwbAjHoZ:oaYxrl`ohhgyxoH^^[xwmPheqZywyiyy>htUy`MHpWP`kfgaXxcOceV[f__Vqclf_^@rHgntfmAxpEph;QmHafR_eYx^o^m\\?gf@bk@l_veJ^\\tQgrhpVNdu^bkxcgpqGDPKT:GW`srlkW?sW?ETB]g\\MXSQFmWHAGeSGe;IXD=iG?dteRKkBT_WhsrGWGq;inevOmxgiI@AyRaDuuFYKr\\MdOitU=yX=BTMfnoFD[SlIi;Ktc_XauYgUs[atCyfhQI>wxAYwS[BCACmiv_UbfmXHgggOHXwxPUR>KD<udGuClwWlISVkx\\qTIIvoDRjUYIdnSYYZTlR<tUMX[@QLAqGerL]X?\\p>MSC`P^lj;lj[DPgTJudJTaU]QsWxwj<TV@N_avKPtrus^HNUtUvQvQtqruoqLnApMXQKqUW?ejJ<M@MPHaPWpLNLK<PVKMPr<OSHmk<mTPPS<MJ`vmQJAIjFmNsQS_@rl`L@HL]=MkLR>=RBpt;LS?\\j[=jiYynTmGqTbMSBxvs]PUhSTdk@dxtemteqHeoPUnPUo[QqhDTNDN>qSTQwuEv\\=t=uKiiV>IXleQcdl\\moYuKsUxGErYdyKml[IVMPUGUL>LmAlMjTQqYqYlScEj:EW?ATt=MWTrvevptPDuTCImsMnblw>XlKQU_yLK`V]pp;inGXKVAurpSJuK[hNQLT;UkN<yTLQWPjWLTZXrpmW;TQM]kTENcMnoLNolk\\MP@mlqysvdRVUkS=mY=vtikeaUt`XCXKQlOj<Pj<RhtleAl=XygQqrPYeqJYEy]yy?XuauU=AR[Em@LT=`LCqQTpj;hVS@mphjndsY=uApxM@lRIRnDV@QnyATDxrx\\Q?yry>`DgbV?qjvskYrY^vmxmty_r^ijI^X_icy]BPbGhfU^kFonbY]n@oPP^DWeGofqa]a_g^oj\\GnYVr>@dgWpPOq>gq`ItfX[dhnBpfWWdexdcy_FH`mfhBhqmvjbn\\@?xwfr_XcaAeXoeZHtnGgn^aDFy;nyMy_vI\\Ao[XPrnfoHahjfoNNcoxfOqwNNuqQ\\Lo^xFneyt=nerG^Z^[E`of`ds?v;`_Ap[_GpfppQInUNZUqck>dV`v<inqFoqv`RFmn?mVYm[peE@[vfk[O[\\A[pvtvo\\iGqNptofnGAkDqdFgqLFvof\\;?nCPeaIkeYqfxgVqfj@i:Pbh_ZMQc`VhWygiIyY_Zwpk;w[yP\\bqwV^^lQ^RF]K`[GFcH_mJ`bKhboPorPiOavPi_Mhj?FkPIZ@H\\ppqNnjKFno^bKO^kNxwguDgePimPhg<oaFpdUvdoOfQYvrnwvyaMHsJytQyrJAtJw^JvnAp]t?qyHtxpjF^[R^]r>vZWuXfr\\Odfaer@Zqngr_]wN]l?yjo\\=A\\WHZBvxhWi?W_ra_Cf[uwurY\\fOqe_lVi_hodiHlIw\\JQb]`jDoxghl_flf>yhavI^p=OsB``dNukY\\bql>@omnqnnfaOgKPcX>cBFjjNlSAyDWg`q^HRnAwa;YZ]w>CVRCD?ED[=E\\Yyxcc@tOv@x<lk]ApquwXypgtqsuNJimr\\USAUaQuetQ\\Qxmuu?qN@MmC=rVpLZHLbppADnoYXu=JMPtiaRy@n]LW<urZEuJ]wq@sqij^QypDQx\\WmiyaaWFTRLyUVdvrItAEoPQSviuqtq>AxN=sKxJm]vDpNTEWPmvU\\Y]YUymR[tP:yrx\\x?\\cTHtxY\\vpikY]n^udFhNVdgvjrhkRVul@gtYen^qL>^j_wnv]tOwm_\\lWjVGqpqZ_Px@nncGpyoxbVhuqk]WuHfuTfi[f[poxxquQ^qgYhrOf<Qf`or;NwNWokfk@A[QwoT_ohpjfiueWnNpbDq_I^j:Vtj@al?xKoiqYhyQmayewYhPYsa?gNW^V`l:qcEOwO@kohn:ht?vm`W`hwbN?beOqOOA[vDkBcag;MG_=FGActSsv_YpyWS[wUoFMoYaYRLswOKY>AfAWyXcu^?vhAXU;tRkRlCE[?TJ[sGIIFsCU[Ex[W]_TFotkcc@wSVsbRkRFGW@dsBDO=]nF]y@LS_TnRQu?yYNdRgXu\\qsqqwi<S`<XNLK?ljAxjShmWhnR]O\\dvIqMkqu=uKw\\qu@WUlNAtJGmKWLpCend]sIYOdePRxmQ]WgeJviuYirFuSa@pfTxxAwR\\Xg]r:MYBxKFeYN@PHDymYoYMVsHp:HWTDk>HRnXtIXl<qXaTsZXOGAqWHUJiPL`pG]JtDWCiUO<pJPNC\\sLEPkpTVpQvAOIaQvYmvDXjIS>=OkaYI@NB<XWulTeo@EqVmnVmOmHqsHsbAwbDufmXadRpqMX\\spYPi]uxHsOxMxumj`q?mNQXwrmKn@LgTTl@RK@L<dn?LSa\\nZDvQMmrhpbdxpES<pJ^`Wg@TMTveulxpynTR]pPH`lRln?arRqUxLy;yOJMohLLamsjLPKLlCIQnLoKTwEIMPtWYUvfIyQ<Qrtx:TypqM_ucM_fFhyf^oiOtb_`B`i=vpSF\\Ap\\eV_Eaogh_Lfb[nncO`v>a;YyXFybvZaqcJagPAlLAfZxi>Hr;HtHwbZwxeihY^mB>ZfA]gi]A?lDGblIyi?fSWrVXaQNh[Qb>quwPgQwf]hwQIlLOlEq\\sfhlIcpXwaI[hpe>qc_vkupp^Ypp`\\JGuDF`fFr[Yls^_uFfTQe_V^;h_uFmt?]AQmrNjj^drqeBipUwfrwu=WwFp[IIfBWxx@iIyqW_xBHbIvql>quaaEofQVkPaqdavefmpF]UV`KOscSFeSc_v[IY[;fJQI:Uw:?GlYdjoDoWibyCUEBqcwJWebKcBWvrWxmUYo]smaIFUt^UWeUc<Ef:Wvr[VlCeXAGMqEt=iIEtxcEmIYCasFGsjAXFivEIHOQg`UWEktQYVXgYPivkwrT[IlASHOVKAWg_IXyEaIh:=hq?iIwSGqYP?HDCyDihiShcigKCcbWtO=Wi?diAd<KI@MVouTDKXl_EHMR`Ki=gu^;C]CtXwrk]R^_DakxW_vEsSwqCYOY^IE@Wc][WieWMAWn;XWuDQiXkgWUStnCgOQWfuWiUTgoTu[rZqUWuBouTZGbUeGm_X[aGEwgy_SxcV]EsPEtAqSkwuOstJIF?cW\\=tT[s>]gouvpyeO?FngGDSi@QgL?EDWvRUDb=X=?e\\uiGcXY?FnEhgaDMUduAIt=ynSxOWg>Ix@CTZGhWCyyYhqqVkKdWuvWwviaemuwGgIluUdSglox\\eW^EhDWePKT^_FLodGEsNgVoUu@WuP[g@wVXMYJAecqeQGrFYb;oYT;fYKi;GWnWEb=s:gCFgujUsP?HdMuPgFSMHcCs\\?SDOVkEgwEsfOgVydB_c_qWaaes=iqqR@mDcCcnGsdOs\\iyKCrFOcoqrWusyaYYyxyAEXsGl?IyGr?WsycvoyhX]v:qiuEEWKu?IbcycmmxfiBPkgiCFfWcoOjH]RwPT:Es<MuO]QSmk;IjKmJdYNwhvCQKoxpEiPEOjlGej^`^FgqhahYqiPbuhu_ixQi[IvaVV`xnwoIqLG[pViw?r:giBHlKIbdW[XnlJhp_AkSYsWodQVbVwdlxgqGm]y[NAxDHsxNn^PrKo[@VcRnjri]=xuOahTOmGpjZHqtpkiypKQa@GsuXfBgiq_yD`mIf^ia\\cpsh>hLO[^`\\bffSF]cNnoO\\\\fs`PtpVt>`ciQfThbANpEneaXtSQ^BNrj^wGAloWqWotPqtRgeWgvTipe?iXxrnaxnwebQhu_mZWhloaf?__>]XndV`acI`qv\\MAgbOaW>gqHvOyd]oy^ycPAoQi\\ancNHhWisSOsUqf;IuEObC_econdWtvqwwxqI_\\AaiqovU`eWAq>xgvqeMn_fOmx^ftQtCPdK?l?O\\Lv[]NluNdZ^gdgbTHk>`nkv_HPhS@]SvvEyqnyakavwycmF`nFkonl[Hn[Nvrn^BNZZFmGhhV`frFpkHp;wnMqcPHypvmEfok>[_@exPhSXwaxe[hi]ojTGqVp`\\VcVahfFwZwmnNgZg_@_u^^[f>];NuD^poHwgyvE^jxyruWo:qneqagNhON\\NxZGixJPfc@rLQrVVseX`ngyHnk]AdgfkJf_t_hPNfVw_ZHpTFfgHnTw_l`ptVr?XsiX\\?IZ?voFiyAqa?Immvglgg`GlGpd=vbd>`_ncVViFXnqaaBXw^FdnG^NqnmqcTX_M@iqyuSytfXmG_Z@yrWo[WNxrVh@Ox?y_DouvWpBinEGZynyk?rawaeiqWabZx_]Nska^@A[Pp\\vooWokb_o^fc^qra`apowgNvPNt`Ah<Nk?PZOQdG@cA_o?YgNX_LPfSGdhPgDgfCnbJ^bea:qrmUcq?Yg_Yj[v<AFaUUlUxs[wgqD_=d?UDDcbYgU=;tySrYGc=OS_ObiYynUiW]YYyrqYdJ`OT=vsmMhXwLqWqHk\\@oa\\NXyw<epV`mVxxQ`wJdMSDTvqtieKjyMyYVBxwaUpEPjbLXsyWyioGqywqO]TNDXjATSq=UiUJ:TSSiojyqv\\yiEYvusaHyyuUyYNxHXxyOSuKQIOsdVvdv[dW\\eXS`PDUpw@S:hYAxSEMTd]JLDkkpJ]XVTmYQPqq<satkxMlitYdyY`atxyJbpld=U]ElLMvsmM]UV]]RK]RmHu^<K<LvrlSATVDDNhaOeQtOIue\\PihU?IPkdJAeNKXlnuVjlTZMLG]lVUJJDwZxu\\ho:Eti<LfDpK<O[<kmDjZ=vWLMiqxj]JrMPCeSdAWEXl`MY?El;unEIpKakkem\\TXExLseUxAj]tJYDvbIvA<YjavaHql@xq]mYhm?AupDRqDOflL<=NBMk;YphxqumnIvpyIuyQshieAHypyxxPsVayOomwovq>yFYlyHs;hiSW\\thsgQlgWngqb`o[j>abFaj?r_asSfsAyahGtTivUxuF@y`y`=nmso^@?kqo]Xq\\vP`hhmZWfcps?YpQGktFkMVthhi?okX`okFpe@bbYunfqRAp;Wm_G\\Z_k[^k=?jNAi>^eIG`jNu[ioSxq^?fZ_j]yZxGwPooDx[F`uO@_aqo\\WoU@krWmZ?sXWpswefGqCG_kgeQvsmA_`FcF@ggX\\EQpxXmJN^Wh_M^teih@vZA@]Wf]SQvgaia`eNVhlCp_svYIHMVUMydYg;ScEoCGobZWuOARFotksDh[gMcRKSipEYFwcuEgCErgmsOwsHiG^CgKKRBkBEWbVcEwksCGxM]TwOIece_KExQGx]u_Cgp;SxYTLEF^_R\\Cd\\cIAGu>IxBUE=]g]Mi;uD]]GOug@YRuuE[yUvKy_kYiYTyws[ieA=GsevXYylKhbCRJ[Bfog`Cg?UcEWWNMG=_SHmSkKIt[tmwWvgveiGEYxPOdb;xsUvy]y?Shiki:_c=]U_CT<[dJCsYEGLYy<CG>KHwmGuYgBmwausCEFJGwp=shYrUYFAKrTMVESbXOV\\?vJEX^kik_rTQV^[tquDRCuU=fLUXRAUIpqLTpv@u_UVwLrKhLHmmr]LQixb]PPAmSHq<ileTPriOAhk@]RZYWfhTfimxLsAmMtMKQIxjptLMOO=uodX:xJImQ;YLIhQEyRXLYLhMMTqMPn\\aO_pRvhytx`Wwol@c:?\\Ro\\P^`yNyKHftOq>YeiG_XSGCeWguZ_TlIIj=f>WwDahx?FGOiSUdxqSDaeOoB:;BB;RL@NdPlohtomYtQuE=yWesXXROlxVLOMEocLQgdSeHMMiWcmPTDPeUO[TsEpQEYkxdo`priAW<uuJlJCuKB\\o^HuTMrMeX@TWu@oPxjSaXkMuXTwnqVlAk;msWERyUPU`kYhwAmmGluYqyFmLtqsVHkDivllrRlPplPLpwAhQuqpxYKXqxv<ymMXx\\W^lr?<nN\\KGDOXdYNivDiL=ipeMJIYXBTR?@LhtPh]XrqrqlTcxt[yuvYmldr\\`ws<mWqXaP^>Ou;@qbalRiajxl;PvJVqAnxlAsNyrrIwvYsVOeuvsGpvooduV_COi^_tD_mQacTwfJPehalNGm<Xv\\AaHVv]Var_hYYvfy]w^rXHlw`wWfuIaxBqgN`dCAflfs;wwinofvlEakF`kjpqxpr\\Qv<fk@?caXlFajYqgl`hcVgFFheHkjYaNf]?`s@>scO]Jhfmf^BAeUYkZ>wnfoBWZdx__@cU?t<^fYgy;`p^H\\>`wmPl>yolP\\FViDPk]FkFhfBYlfHeE_uo@uhH^fW]TVokfsoAmHWe]A_ApbuGmEY`i?tcapbfld^umxw]^mxSCwdXMY??fuobNgB\\?G>iXLQfTqi<GVQIxRKEVSVj=VNSc;MCOYi@Ecu_vtchcMFZ?Ip]g:?DWkUuesjexdGVoetLiwTmilidpSYqqdrcXdORgovZ]cgICuUWgSv]Sis]v;wVREUSuv?wEwyYFkcr?C;cg@]uUyX=sujOhJcFIGEEOTCeU]Od<OVSMTcGGDiTAOVSEfG=sSYsi;TluFRKY^MEIix:WuYOSqyc_sD@CIqeGiaFPkuwYYMCXJgRG[YYyjelRH]J<MWhuNxml:DsCIssXPK<ScEyryrwlUseN`mV`LNDPq>HV=<T:Xr?XKglydyoPEQsMXJxnXPM@iXmHUAYuuEpIQN@Ds<AjNLk[PvjTj?HNHtkVTvXIpM\\UTeq:aWmmj?ptvTSgHY`UMm\\rk]k>MVGhrbUklPk=TNA@MdlKM=l?mXH\\SmIpwykkXXbuL_tp>LVm=PSHk<<uVhJopPk]jcxtA<MSDm:yxi<pppLKqWUMvrqxX@LmTsP]j:yUYURqxPj]SF@X^LT^psG]nhqXcek;mNJ\\KCAjyTL=TUMEkptWlTSgLR^dqJ\\WLAltLSW\\k^@j[uSKeSyXLZ`o^DneEKtPmjHoSuUD@OPeLgikRhkoAKe]NKWs\\QxOn_XGiMX^ApclF`pxluw[yns_YsQ?auowoNj:yZe@uofhJhyuok[`mxqjl?lOrCeG;GieqgGEerwGQgDuqxs_EsKFsGX=Qhr?WBSRbeh>sGw_Dmytyeu^MXLifXuXtQEIGC>?HNScOkCgyiYke<oWrsSUai?uhW?ipCWgEWqOVpktM?g;OX?Sb=qGOOi\\GiTStgAw>Iebcw@eucUbLOcUSEQ?XsmewYiXcVYqwuUt_euXWGysD@CIssIA_SV[CF[CZ]cciHqSC=ACgWvnsCKoUXwVHmSHieGuyoOyZIRIwrXShVuiX;tb]hbuhQCH`?bJcF\\Au[igq_YxAxIsgmKIdQhyuYKOYWIrEeWFSdIQiwwDxqy;MI:EscCXv]wxmCI_EAQVCcX:ifOWxV=UwsR^WFNCS[IgkoDA=IV?ukMdWSBu?X^ORCcbLms`WiKkHcQgFsI]mhsCYFYxD[dDURnMI=[HTCsFgwgyIYkVk?B;QyOWC>SsmAI`kSTsgoQyO[FyYwqUFlGWkEhLcYPefS]T:=bnOBOotS;SL?W<_dceG<gDRUWBOttedlODFoDV[enoE[kSeqDDKSJ]d<?YOUhteH:AiJsXGcco?EyWVCgXFUfo?sSWhiSXZuwKMs_QEaswwaBXWU\\YyyKyUkgYAi>;rAuExtMu]vQ@XNXtMTo<=sn=vVhwYxXYhjpmNF\\nN\\kGHQvmymiLxpyoEjiyVAYj^Lk^tYwytglkWTOj\\QfAPtLqS]kf\\j>QUGEqVevXXjqIxkxkvMmyxYcQLWAtAAWApx@]rGHm:pTmlVluT;hyAMsfQuYMnx<wjPpJLtRekklr\\QYCQYgeWb=pD@ogYpj`P=ijEyojxVtAUt]sfusoymETjV`mxlWx@t`El=PS_PRVtrnTmGMqWqKk]MKljkDT^=k]YQ[QRRXlMXxXAS`mTyEyQhUPuTE]qsqVOpSAYnWqm?AmW=KK]VweQ`yWyqXWhn_XxvqyiySlaxMYrFuSadJCQS_uvCDXUuV_UYclQcuO=dWnMVYMO>lonEqiMxNtxGmmtijYXVLulTpyHpwiqJ]=NB\\QplP`DxwQL[=OBXVUYW@EYU=pCXOM@TjpXcaMxQrVLOHDxDeRJQqa\\KlhVnPVMqnNeV\\=RR]L<dWtQTC@pR`pPARU<km@S;Myq<tC]t:iljDTn=osPlhpP>mNc\\THhO>mNC`MjpVjyOA\\sdTJK\\XUQMghNxurZIsR@OHTlbmjKaKH\\klAwAmY?xkv<yNDTN\\NUqtg\\xt`LYaQrauHXjKyx<mL_xMV\\lvQyixtrquq_sFa^=py^nr]QxTYggoy=yirpcNfbvqsiawBgZwwmov_<F^?fnDGjKHx<VkEPj_IqJXgQOanx`nfnLPfdwcKhyAOsFnkt@wRr=cFpqEP?VgKIHMi_wXUQeHUslSY_WcDgG@QwFUdhUUlEVJWdmYCBmS<qGOOS?Gv[IVvui=QxlQF;=D[Yy@?HVQeMUymWWUKXlMXhaFFGSLMDXSYFiV_efDyexIwhmgXeWKiwhWVFABJEReueQqUE;yquyhmbSGe:wuwiuCmCX[G]gHcuXOYuwYGpOfp?iGAuncT`ieA=wlwW@UTDwYVgxLgh@suAgb?GFfgu==Et]RKoi]MTfSC_OD?QbA=gNkeJ;UsGUaChSixrSX^KB][RicdBAUEodCei;_hPcd@]D>Cg_khWaSuKwdUci]Gh_bKQb=Ade?CngFpkhaEXTSUEuHp[cOcEN]BeUxTgB[=cEMB]YU>?dnWIkKCEOThMIeaeOUS^CDfurc_xDceiuXTUugqrk=Vf]CpewLaUsOFSUUM=ScAfo_RcOFausp;yiwyoQIxwEkygxitXqeC?R@ghP?FfQhjUf=TpxdkODSN<M`tXs]My=pHqkcQJDEKTiSGhpJIW_lTmpPgyVK@OJEjQ=LF]SODp[HrQyTKqN@iXDTupUu^qo>EQstw:ism@PUHyCPl@UnGixeYOftOi=tgQWdep[mRAuRR`mVdsWEklMXpHJUpK?EskPUc@K@uROdr\\XrlQp\\huhEL?mJ]MK:XjkLjPUslPpLDVFpViqu<Tj=pwUaMHqWaDm=DTiauMhvUXxmhUbMYEaYMXTGYY;AMRXmE@y@yPp<K=QNGprtTlMhJH`MS`woenyhvKeln\\LZ\\n^EynYsfhmxIPkQydlU[@lF<xmtt[`tSoxiG_mbbCyq?DUeECOh<ytfiHS?yKKJgLS\\DL]lm=AY;En^@NlllBQp_qvCErBENKDOxxWRAg>O\\n`jjnkR>oI@xjIoIOxsxexi]@pj@AlcH\\@qvGogEw`[xxMpyY`oN@nTgjeyt[Quo`rg@_HX^>@tbg]KAgrA]]Hax_q@AsBXue>bPNZFH`nPuGnetgvA^eYhe[N[[?f>ivbIsTVfMp]DI\\>HbLf\\bwpFfw`OvR_tXAcdy[vqk`^[fFdb?ZC_g\\NegidDpubVjoHcVw`cymnhupHdh^[lOhxo[UwcxP\\AIxRoehGhsQxlVcEg[tfmJPEkVf]WRgeusrtmc_cyheRUawV?dMWx[?fymRUiX?cxt_VlMT\\]SK?FBMeXgXuoG@adJKrZ_d<yxGcgP]RVsRbcVR;EjUtNcbusGOWfY]FvQrUyI[sw;AEEasF=sYgySQE[=I:UfkGdtKrFOTb[xQkrXQroMVmSVBCSuqrfccqoYD]ip_beQIb[WdkBRaD?Ce_CGiaGFkhDKbgwy@;CGgfOSU@_I?AS;ETNObJaFKKbBQU\\SdvoBZ]iZATLMDE;yKGriqFc_R`Kcs;YIICxCxCwskIgAye_Au[yBKMtSQFBkW`qSRyshuG<SW?SV]MbHurl?iBScEODYySfwb;UD@GDgqX>upjdQW]nPUXLUN;`VWPYhej@UV=HiE`ZKWjWVt_nhhi_\\_k_XuKapTPm`QeFQw\\?sLamIQs\\_rTQd>WhgnnMQtriu>QqNAg;_]AaHGSmGuZ=YZuG_QtJkcD]EDohMqhDib;mkqAjJLjohp:hj?@lOitGltPGeYwkcvlEa]t^`?Xv^giH>^QnZsrWwSP]sbAI<Gv[EsrAiAEhR=FD_ITgSAgcGODZGGN;fNMd>Ed_QuooCgodIeihCGO_F?Ob>EGSyxSWecQGwycWicRUWsoYw[viky\\GrtQYCoWQkXiqGk]xbEe[IvLuUKyvggywIcuUTLACfGYpiH<GiS[DZ_fF]B;[xC?b^wE;mtEAVE]TZcyf_gqEbBeB>?SYyWfgfOCEvCGRSiC]D>qtLCEE=etoEOgd^]gZ?cGMFRKR=CRf=HUCHOshDYHyoyu]ImawQ?IvHsgHtaMyhyYBXN?dy^uQYQUjaQ;eqHdmH\\Ur@lrTLceoCMs@iKgpTFImmdMvtS\\QqJeot\\TdDS^lnLmMZ]WruLgqWUtQT]nv<v]AQLf[GeXStREcSeUF?UUMtnUuCWbNUiWStcEEpKEkkYQAf]_f`ArTEcoObsibE_CNmXmKHrWedeVbcXAOi]Ki^kieKX[=dMxLjHUB`mVqtQiPEYs@hr?qJEUSU\\OitXSLMdXXlavx\\QIIRcXQimxjtNatvaUpSdQBmVYtnaXKFpkPHK<PPQpO_LVy@TJalDmlDeRLMOs\\oixrFqshHnNHVb=s]`UHQK;uYPyXfmQkuPBpj^ElMpqHdoPhv_xl<lsWXpflOt@QH@VdMsluwwXJqhns\\UPpQ?<vPXsnlSy`RaQxs]nHHXN`u\\LJ^DSnARniyUMRd<L>uWSYpBEr`uSA`vu`p;@tTmNDpKD]NcYRkhSdUK\\UK[Mu]AnRPk<TV[<PPFp>?bZh[Ufuhv^HgiVx^y@xUawyNhiOduPua^[louSF^pVqLx[HN[np`f^_>aogHinPeCGvpO^H^_K_fsGv?hhHamcW`lNvl?yjgZQil>Ip`?gj_lkHtC>lWooXAycFnIfwnNdjPpRNpx`]]^g?XnAqxm>a`HoGNeVwckpqLF\\A?^O@^cfwK^rKhnSQe_`vG@`oniRHl[HogXumW]Ng^airAIasvw<pmMHj:vseNdgpkZ`tbFfrpkiyoK^ZkwowhiHocHqx>Os^vfx_iV?xcxcs`cIW_Hp]O_ysymen\\Qf]VwpGxv?>iXpnVoxBP^QxdYggMag@`]yne_AsKHfdht<NdxXqSgugqevNmsHpOO_DXvAYsvYry^gZggKhj?vjEx\\W?^@Ocaqp@gcgptRA`:GmRF^MHZxNb^po>o\\>OfMOoBQkIHr^hb@Im:?dPQnGO\\w?\\P^]CnZ;?o;A_Rf\\DV[cgc;hufh_jFswQm]F]ng\\D?[TIh\\QdNN]=_gM@i>_v=AxhhuNPgo`rdntT_jLwaiyf_aq=v[v>nbn\\[`dLaiuYu?ooWWkkiyRF^nOw^nvlOyn?rQoqlvjopjificwZDg^AIo`HcJv_]YyWO[?PZWqc>WfoNnkp\\[goZOfDAhZab:xdhFjnGrDOjhh^HhcL?vYv^cxbGipRVf@>auGvOo[iiqBqqcYdCwvcig>o_FNHwX;uij;H@=D@oG;=HB=EHOfouD]mHwgsmMXlmhYCUDEdNGs:EhTeb=yb_SR=mEuwXEkUrERjSH]CxwuDAIxkeuRsrCMEWcgiwrVMinGRNcRFocDKWosdLEgBWwt?UeEgPUgbwXR;wguVK=BUeERadl;b_]YvObJcFHaek[excEk]vBWbMgXciiGCuNKgRMflcHGEWr]drEx@Kso=r^kWGmha;DpSeUGUU?c=CexkFMqF`=SE_SAKxgeWjiXl;wq_FiYcuiR;MGFKRMgHuSSxwf]gC[MGDKR]ECLAw<EgT=VqIv=aTAsBMaxagwywWVQWLSD;;Il]RkYYywB_Od_irQScVWIa=UXmB[KURSV:OBQkGbmititO[gOaIkar:SIqmTb_deaCIscLegOCxuKeoah]chl]FMSiD[ExCU:cthiHxYdDMHr[wKkbCgXsGtPsgZCGP_D?QHf_s?;U[YVgoSP;t`mE`wXxgW[mGFKXlmu]CVbEOdMugIJ<@V<TWQAlLiRBpUUamV`mVhWBuyoQUD=oN]JuxXaTJwiuuhJmUXhTkEhJ`qvVMmGqK_PT>EoN`ne\\pUILEYs;lt<=L^lKAMT`dK?QOOPKLMs>qvJaNwQJVtr[@Tb<ThtlclLExwcxX:im<mpxPK?DrhhUhloeDqaqMIhYuQkNMOktYuyp[TYqQWdhTOptW]u\\HPKmT]IVGLRs\\lapxJmMW@notP=XOEEwZeSnQyS<MLqU@dqHyrUHw]PTB\\MU`RKLJ]EW>Mm?@N@<rCuJvIUtATNpnIdx\\hJPqNcpR@ALR`npANDUtBPJ=lqp\\RPQTW\\omXyBITdXj=EstMq?TobqW\\TLoQR^LjxarCdRRLrjAp?IXD]qlQk^hu@DNt@qhMts@yDilRxvXXU]HunIYnYv=aSFeKKuofaRApMEUxgLUG<XN`V\\Mq:Ij]eV@xNVMnblNDhRdEUd=TDAnoprbaRNtVoDO_QoE=QLTpTqYMXMEuWjxWQYr^ePAHuxEmoITciy:XQB`UR\\fsCk]WcqXGcc@WsTQUOCGAGUWeXsOX_edwSY@=EUSghEcj[v^avfuGlOY=SWMoR`Uf]Oc[IVCotPgtOudEudVkVaeU>?cLqbMEB_OT>EifGbBsuI?C<_XJAVFScEWcRUWKQU]gh`kc]]EAIroeU@sBACeR?eZ]Yv]IokGRqIaccfETegTCIcMcRDgrPSypIr]wcDmTP]FIiIa=yByRTauyuYSOS?IkaqLuXLC<ofIQBeVIIRvYPiPnjHSUTvnIWEqTK=V?hr;=f;H\\<@cU^i]GwbWr@_gRo[\\O]KHNCBlCw]=dOaDfES[Ks>Obk_Xo?RCSbpGeB=h>oTJ[r@[EQgIAucmCiiuI?QX?gwbuWsuFJyGHKS_;YrIV?EifEXWEcNoCioiDkiiCXVse\\ET][b[QyoesqqiQaFH_CI[IReFjyfjewXmTQwU;SFSCelAuswt]=YFIFD[CW?HcgTBWRE]DTMvBAV;CgLSuNevD[EQ=vccbaIEhwGx?s:EYLGc[WbNWs==UMsx\\kC^GDe;fQOdjuffuxV=E^avvWSlGrxotZYyPoVMEhpoT>iXA?UXmDVmiVAVj=hLWC=_MqEJSERlhpCmOw`l<dn>TlMPjCHKAxRXDO]]k_eV_<nWqx;@K]]Y<Ap?ptKDXVTVghNHXVTiwpDVRLL?Es]IVRLL@HNgqXUDN>tjHdM\\YLY@y>dtdeXEutoYQW`WSTS_Ds[Yr?Lwo=xvTSc`VCXVryjy=ksYvylWkyoyipEIl]lSieY`twwAjQhKjPPCuudpwy\\sZiqI<tsevuAmOhJ^Xw`TplQjXeo;HR^dKIQTk@jL@KAIV[hvmTtC@mmYVtPuJ]TCeq:<ps<yqplRaNKPjGur[TSZXlthjbdSUfo_^cUFn?a^ihoQqZs_xmweZ?f^_[[VpNXouviUyuC`ghYd<Pb;?hdalEAyrHfdOclynyOe_ayswlrnuZ@dbAdb^rNO_DF_[axei]TX];V\\MXnfq]yojefv?_nqpsNq]QPu:Xbmga`N[FFnY@uEQyWWcbY]\\@`Cg^Mok:Y_DNc_Fcs@_S^pDvdC^yZQ]EfuYNhw@hNhuuvcLvrxnc_pjdnlJNs;g\\DXmGOLOF?uhmAyIib;mkqoyTPfgH^B>nSa`f`oB_]a?ksHaGitePm=vZFoxH`xioi<xsCIuhaxaGy^hqm@hV`^YailOp>hp?awSqekAgPp`^hp`HufOtb_`bqhu`Z;?bRnjnWqWo`pn`RXmUXvTipe_er@h;XlavchWs<`fcV\\E>s]yrwnvai_Yqyppfgg_chrtQyQi[Yhyf_s;XZ@Pfkq`^XcSfkf^\\b`]vnr:IoIPppauYHnDhZ>opW@cth]QVtOoqZYghHyTpnK`lEq[axdt`eigZRV[]fZ?AiKogDHZENqQpa^wpNI]>NaCp]:O^:NZW`qa>`Cwe=@eAAqXlJINXdyoxOLEoQypOhn_imHmXBdSGESx@y?Er]xkDmmymUlimiASh^vLvrg_lDFhVfcoPw_V\\xguKnbAxm`y`YhqQpfjQ^hGiGplyVrVQtsOqW@jhWcj`qRinSau:WwBvtM?uHpnZ_]pWi_ohPXkFFcEaxtpn:@bR?bvpr\\yyryab_\\dAgcF]rFxjfnWyZkq^qG`lAx]Aa_Q`<Icuii^gtvypsfojv\\@FA@kk<L@@vuqjHuJ>@Om`qf=mSHkbmPuYkJxpQirwtNatvgaxIHtqdQsYYIQtYPykqS=LYeeOhXwLeoPEWpTmf]Wf=vuqQXxv[`l\\XtcAVFHNDPngEwdmlB@n^dvdAykulyXyu@koixB@QpEttlVoeLxavIMMNXsPxSyMqpYXgdUYyTtEq_LL>@nrXy:TJI`Q;qrmyY?`k]\\nL=US`KXaj:hrZlvFUP^QVu\\Vc<t>pr\\dVE@RU\\STIOq<t@pW^Ml\\UVU`stYwnHjSql\\YvN]P^]RP\\okdqQInNDVa\\VnMWDXTY`yndx[ILLUY^`QFayI]Ve]TD=nN\\LE@peul\\Ima]NIlQb@YeiO?YMi=Oh]ubAnN=jLELZXYuQXoPQ;qsWxm;YO@`JKQMAlXf@n]AM[eUh]sWuVoHP=POpDMStO[xWbMkauvSdqxUj[hv`loN<qP=Nm@lNlLMlXjhwHLJbuqjytf=QXlpNeVxYMyMkqXXYTnYdy^TjAySK=MXTSamMFllUylP=mE:nk[nkGFd^Gj<fk@@fpop:WpcAZ`WePN\\`av^ayvOpTYjFxpIXvXIqcHneQqbflO>vTOrj^cAf_Dvrk?`@axficqXlr>wY^jcf^r_ykQ`axcuamwVoCP^qfkTdiyYygshgU@GtKErwyxQAtTqxfMFy;t_YsPKDjMgoMGAmwa=ymsyFoxYyIAgxu;G[;ck_G@CHi[gnEegaRnKf>]DRUCpktboIUIUG[B\\CXgKtk[rTADUafAqW`qRNSu>IcbwYekrpCXiOH:gdL?IB;ETCE[ar]wckAticYPCgV_ttlur`wwAv`oeDGjeQrbAoZ?iR?`xn_rxvXvj_hn\\fs`xm`PZ@@_ONvtFZHX]]A_AvscFdjOgNhuC_po^rk_k^?k[IjW@][YvP>bIHgJYoBPvO^tGXxNydhh^o^_\\xv;_l>gnfhrRWkhqpChs@Fh]glhQxVfwEvgKIqlokOX^qY`j_y;nZIhm^`axFkBWnIPfeac>i_[v\\@FAF^fFkmAnGWyT>qnWqHvvIY[HymQ`ewP]mn``QdhVsvptZv^aq_`qf[@xmAlLOdfn\\chtd_huheTgoPFhVVfFHceA\\vigSpbN@[TVkk>hlafKXfAQfhhem`eypgLqgJQk?hZEypxhp;Awb@flOp:AsBXmpvntAjywgyGha@lrWvM_kvVxU?u_Iatxoy`jM^hBFdVog@_y^GqE_ffNcB^l>FlpQnBaeE`ZZ_a;xqMGje>tWWbnp[kqj`nkMwZ\\VmNV^YacpAm?^^PffnvxVyhVxjX`iDhuAwk=OqWypQqlYq]fo\\_Vl@op>Vf]o[]WfDfowN]GP^GqfB?\\>_bK?cVVybvnEQvlIaTfo:Vn?Fpp>mbnnfq\\c^\\e@aoQ\\;w`^XuD>[o?jy>e`H^D^rt^fZH`AXuUYfpfZ\\hp<VZCaf:NjRA]\\@eMn`PHgwafKpv?ypRgimid@x]sOjWycyVcc_gLfvsGeway`ykshZ^QrZv^aia\\Qq<PgO?vsGsConVohkpp:auVDymulmxf]Rc_ftab;iGDceaav^auk]V=sUeeGDEGdcdDSf]WffgggGD@GFk]EMaWpEeWgU<UWUoth[WYovaEu:WsT=gOaDYcybWs?YcTWGQ]H?QfEuf];BIwhXQWmihiggmWYqWraqIqkR_Ofj]EkIrEWbxgbNgrLcv=urS;YlYCbifs]rfIIngbOSWJqCN[f>Mc^ocFAUUovBwWhSecKCtwBW[tJWbhEE<YW[CtOUcX]cMqytwWawIL;f:srbmXfqe`IrIeI?IfAkEdii`qXFaCy=UbyX?cuF;sC[EA=HlKvkKHLHxIQWH]oOaOyAvAamuTy]mLPtTkDj[PuG<YZMxjdxuqQDhoITvtPJi@JWpp@Uw:pnj=uJhJ^`TbTVLQvpavETPaYoXUtFTWKmLJMK[`LLQUvqT=pvEusmpXpiX>`lFxQvIKdUtuAxddtXXYKioTYQNyMvIrY\\y;iOtqoV`mgUSpmsHmVs`JOQo^ixQYV`mVfTLMdLpmwfLXZAjEen\\Ek\\<uqxs[]V>mniIs?HRHmSHMjNPLQiXKPTltQytsDQS=hj?pLEUS;tKy\\YYlmaayVQm?XQO`OuMX^]Rl@qb=Y]iK==LN<xwAj^tYuLVxmq?Ysitoj=yjEmWXQE`LEPpaAynUSBuS\\ijwxJ[hu<uOHItjTOf\\mbDvV\\xRTQTMVrAVKtoh@xQiPKut\\MNE`TCQPDdKp`NkTjLdwDLj\\`neQRNAtBAxWxqLqnetrOLj;DWS`xZIuyUyyMxZyoxEl;IocaNT=lh`qgapwxpmntZGeGy_^fug^nN_Z;wjiwqji`xXy=xgjpica[Ax_YgftQtSobanhj>iII`dYqpQdpge@njAGl?P^fvuZpamojWhss`nB`ae_dqWtqqg_FcSWrT_n]AnVw[MfZFqayi_Pp_Y?njNaHArXYZcqikWwLaslGfJXlmY[Kfqvyufol[PdK`iyYyxv\\iN]powf@hjAnAIoMo[UV]PHysWsxhi<HlK>xvho?^bsIiyv^aYrCqtmAjZ`ddFtfogjVau`soXgG_ldPx>Y\\qygMGfJ`mUfkK>qh@nWqtVwqhHaqoc[_k?AmRF^n>\\]Yy[v_w`pDAuRxr>ab;PeGguLFhJYcOI\\Z^n<g[IH`YwglGfvQ\\tI\\QheqydR@aXoffAiCHkMff`vcO?]t>e:A]jY]T@q]O<]tK;c[_VSWr:UvAmBYMbUQHBcio=Fb=BAIXRKDTGS_Guwch=wfxyhyYc]uSwSRg]WlCwUEdpDpwmpoqx`xYLxwgyk_Hw]mrJUoGTPn<PCaRAUPwexttKtdPDLJ^ayFLPbQRw]jhEn<ausxPsEyimq;tOyukwYom\\ktHSGIkBUWFluXDKLdYpDqCYNCeK<<unXOl`XVLUmyPb]OFIj]QPtuskYUTYwZtS_LsCIYI@OO`nMDOO`LndKF<r;YjjAy]AxoxoCmsWXlvHx@pVr=ul]wR`rmQPiMwUiq^IQsDQqXlGQv\\EltdLG=noiLTdks]nFMxJvovhmEHyXHwIYvp_];iqqQqvQwiP[`yv[asSPZeWg[FdNN^>xbNfZV_qRNxYoyEi[vwulIqIiklf`O?^HhclV_yIZ@?eMPbJWk:?pXOgl`quhbv^Z]Yv_Nv:AtgWg>NjLAk=GiRif^weSHjWibhpyrWjsytt>ymG\\kai>xhf@joGr>qlRWe\\QlZNoCO[eqZUv^?IsL?[dQ\\@?[R@]YVfQIxM^wy_wCoKGyOMG]SvrkeQwDUsu`mhtWc_;uncta?Ub?hQiEZKH_kT==GPgEV[C\\Gi<awIsiEitEutSUgGOhjmxG[xVaGuau:GhTWRfeFwyRkYuLYs>;V?KFgGTFQfDKr<_FsGILMvLShkmOhxYyYuFxMyDsZqu=<kn@owYjXyVlEVJX\\WWfugmOfaI?`wfoRyqYIbcfcNFg:I^B^ZEXk<xvYxw\\Aa<hmuf\\=Yr^hbrwphHqIocHosWXcp>kpnf:@`VnrqYcnWqtx_yIiuOeXvfaipCH[?YfIH[PodnvesQk\\XugNno_jkF^J?ZZyrynwL?_fV^_`vSyfA?]UVhMyuY@[ax[ha]S`oUqhv@cJ_e@wbkfs?fstQi:_\\T^eIOdfVcDhfAPujG[S_lBQq^pqUYfwai:Qvsvm<GeK^n?vt@WZH`^hFjUaprotJ?dJwdjFee@pmOgAVtIB_MykwfRIXdIDdUvuKYeSGQcBqmDS?G:=Cvit_MIiwy>svDiR@;dBEVkef^EfUSXtQtOmsvGYOociyVK]G:;BB;RL^dd@jypq@yr@P[fi]ePdlg\\TQuXIduHirVuXXaKoxyXm?VjJ^xfXh?hZIYxBPjHV_ixq<Imi_ysvrx@yu`dAwrKooqIjEXjV?]^aV?bfAymkFsGC;cb<_vJIFQGuSesoWWTgv_Ae?gb<cs`?VoetliuiqX;;Y\\Ic<cdD?fLEuXWH;GIsCIiyGwqW^WEUKcpUY>?HVSFDOUwsEoiwBui;;dNObcGGCyvysCioiTSD?mGQqgO?WqWvncgBQVgGv?wDTarkQBOOc^IgaoBS;EjUtnYsGISRwCDcffCTqkVxQSQGuECDxuH\\_TO_TemC_Qg\\_UOAuJiRUesRqw\\StAWS>cSGIwaYef=WG=iVSVn;E]EhTAv>obl?bKQdEaRg?shGv;mXVYXNGcAmEaMw]ye\\=w:IDNWw\\eccifIcvVIRRquJiE[cFesWvOr<YCYafmexVctLEb<?bp]fscuFCYmGEloD>=GuGrNef>Yb]eHp]TV]ho;uUwgkIgb;rhMUQoVtYfQiVUouQux?=Dfkcl=WWAe_igioyCcvWStVYx^YHNoBAwIjqYQCij;sCpOsHQqDXlMt[MYTIVpmL`yvgtWxHKmYx@tuq\\RK@v<ijRxQyYx@tSydU_ItAUOw`P;`yt=lMXx[qNU\\yi]WbmTQUgqx^RN]l@gWVZXVusOZ[Fk>`^HhgunHwGyEuL=G:YxIyDSGek_hTEHCuR:?E]]Fi_iLKxiyywaGeYwWmewmXVgEuKcBEGuQfACuaqiyWw>MCQWwQURx=yWgDPoVEaDekd\\EUJegu[CFSIFkCu_hqKFVsRlWVQEdcge_MWA_EVQi\\yFIyHReUFGc\\SRVkRBgchSIPgGAQwomxFwckCXrAEMweviD`oevmd\\AtjKRd_Rniv\\?vHgFO_BZ;RAEFEsuwmcbQssKg<QToaUfocsEXoWrsgcJ?tRMw?sd<ODvmVlOrNET[[g?UdRIt`mc>UePefUUyS[VccW@oI[?Ry]R[CYJMSCOd<sikxPxpya]wvDyJMNFLtN`rILWyLs?HRHwhGwikAn_Of<IftOu??kJhlOVr?YkjPp\\G[=WbRNc`wfGvimy`gnr@a\\qiuQ_nR_drfiA_E]ElMXx[unUi@gv_uc?ir[MS_?cqsuvGrcWTu=gNMdnUegQYD?s`;TVsBX[YJYrTAc[GFEyHyGU\\ihQQd@CdJQRcccLMc_gFEyExIvvScEGByGxUSdVcITuy:qsIOB?ghjCHrACAsf`=Y_=xDsDYayCKTG;f]CSaUF\\eY_kVo=F\\=YFYfx;wj;I\\=wn]H@ScJATU;Xkkf?=DbmXH]w[ytxevm[weUE@wXY;VZqe]adqew?igNEXeWBCydTUcJwHu]t^auK]fdeIRuU_QwqsyLgxYkYAOfYqfPmGKIc\\kYvovmefMcF@IBDkREKcAyRe[uUuxJKR^kxpGwAAE:MwRcVgkRB]hBMTCWH[;VtQf?krlgRZ[pA\\oGMY;@QPlLHuq<asEyQ\\@TYLnplQsIj@eKluT\\`mVxxBmXKYTD=tcAUx]y]AjOiTCPT?lLP\\KeUWkLUAaRK]R]HLllQh@usXt[`UP]TdLpaekpUsfLylMXlmwRLpNLJcDvoxt\\lYrYrJXpaeO@AqFmSdmKYlM``UH]YOypeIQ\\UtqlQkEXext?TYpAS@yr_doP`VsEULtr<trk`lD=TdDKvtSKljThxoqOK]Lm<PZaxPYrIqyXxxppYptUhETLYnPEM]`UVLVcEWXhpohNtlYQ@QHHtkhNF\\K;xoCPRGephATfDO<@rLiw^dRDYWEEJMUvqIxEySxEkalQoiJ`pkXPVrAsCLOuxx]iKGPvreJ>MugQMcDLU]ugQXhAOLIRphP@pxVaOQtyryy;iUtpROEKTPulmnS<X[hM_Hl:<uWmXsAwjEkuyJD`LN`SDpj?@NWQsB]O=tNYLntuwC\\TsPSr`qB]ueIlJpX;mNGpM^hSkako@WLqwBqPK\\KTQj@=LUERaht<AYXTruqK`lPq`YjUlEHqj<sCo]bygJPnN@rqIv<ijBpfMGtdGifxoUOaWVjkF`TWg<@^@IhfFfRFdc`^wy[vvc\\`tPWw<amV`mIvZwQrZitQWZx?y=q_Qp_SOnb@cNfbvNybA\\=YrhO_Dnpiw[Npy`PdXx^Rf]O`cF?[dg`jpd[hpDWaKQeDifR>]J@cCfuh_bJ^b:HbDWj]A[VvbxXnBOqsaucwgd>tRQyvodjImFyrTV]\\?xc^\\WnrAonkQ[?N__IZN`hknrZgk;Q]C_]C_q<`bsNjb^`rieEwnOFtgWrKYZIHxny^yiZunnIFvG^kZatd?cq@tmppHQ[FXx`ifqo`SW\\t@qUqnsoxGn\\xpyAat?hng__QOuKvluF\\KHpCXtNX^sxhZ@s=Vj_Nwh`c\\XZB^fYqppGjTYrYfnnxyJn`FFwXGqB?gfw_O@_MfZ`x^:NlAQ\\[>psy`Hgr;_gfFp?pb]HbgwtXojqwwAY_QHw_>bwxsuqdXPcNXLYFjkFk_GWkEP]uuugEQyt?v_ydGCVR_xh;c]EbkKD[[UxMxMoGQwGq;TDATeGrkYvo[IIevHcRsCIYKXDgr^=VfDRehT^irQdLmTPPhQu]KOPkmIRQAMx=v^gaU^tiQu?vmyaq\\wthFrIniZ@ycycOvtiXa>GdQfnvO[?vZ[^_mYxTxlXOe]HufAhnAgWHkCP\\OQoAXwd`xma^DGoq_yHacV^gTWrpio=W[@Q]PQmQ@gsYhfhpHYnGwlMwkVvfbwb>ayGhb`wf`IeSGeIOqMQaD@_DH[<XoVAql`cw_b\\fn\\gi_>rbwj;IrKnbAo^tw]hgo:?kfXkkowIgqw?clQi\\hxoNaQxsL?wf?\\NNkVgw>_spW\\K?dPGcGAr[PoAIlTGj[eB_c?iD<SeH=EdUe^GEEEGjSWe[RDEDigg^gEOWtbABCqITYD>CWtAt`?VRQGTKhAie<Ed?YEQAipQyIEusMxKKg=YFRSVJOxWwc=wYDCij;[WOtiQqKHigwtdOlMx^E^of@eXaiMQvuA\\@P\\cV`AOfC_]EOmGGrqpqopjiyZ>Gl_At[P[]WfX>lrPe^gsOOhlOhhqgty^Ix[V>hSV]M?__?_PVc:AaaqsSokXfjlcweYGkhqCSIob>=FFcCckexMUkIcI=SHueP_IyaiEYSicDREUSAfJ=CjaiRssEMe_gUyoEJcREawRIFSOedCHr;U>QUbkDE_Tdcvn?SsUHD=dCgbUWE>ixfIVgof]yGmQxsygjHy]LRP@XWErOhx;\\QAYVfuyXmKXTQ?ASsIN@MoAHONLWnPuGmyfYWyyPitqkiT\\eM[AQhttiPy>hMIps[iSEHUkUtquvfUJtYQFHVCttP@wVXYWLjhtL]EsoArJTUEerK`R@QpiPvlIx[QLuLShlLjUtgemNiJ^dP@Lm^vceyjywkknljf]ZY_[>kio]jyx\\^ZCOyJO^NNy]N[pWpRGeB^cVVpxWvTfksYw:YjUg_HquAOh[?LFwy@pQPc<XrAhe`wfGVr=QmZ>lnWq\\FwbG_^>^jpdLnjLx\\Y_uZWf]XshheXflDPfv_u=AmGap<x[d^_RXlMXhaGlWNvuyxu_wRIvj>`Z?uuxpBIl]n_axcA^mrF\\mXH_XGiiU?sLEHGGSfseiyiYMXjAf=ygvQc=xUp=Qqmo?]LsAqh=kLENDerRUObqXgTOelQWqWLQPDIXVputHP@aNcxQPQTehtJMS[QqhdxtemdepthvuYmgIMXmQyyjfpjYInlLVbPT`\\xGDRJqNPiW<@q;Qs@YUVATYIVfpyBtRqayTDVj\\jHhJtlP>dU=uTAaofljRASLdJ^hR?IQUQMcDtK]jyUV@prUxoj`oD`O?LM?\\L_Ml`\\pi`wlAybEm[tT[DsTdk_eUqLLk=lJ`w^QUB]pFMn>LtRapJDQcxQJqXmdUbxTE=VgLufmnIdxLQk:dWfLM=`XWMUeYontTPPl?qTY\\ssIvhQQeav^au<MpS=oDeRldP_=qiqQ==M`dKHann=TDISgyJOLRb\\oo=UWetvuyuYwFxku]uyuYW<uTupJXW<`mVXqWhstHJQiLrlKNXsj=v:@vEyU@xynymZIqaaYDhRAxkv]n<ptCupoiwxDVJyuWDQsIOUhm]Ys_ul[IV?YrItLBXVGUoO<tb]XJMO<QuHlmQ@k>@NB@k\\`rRIReekPQM]]Kk]MMtrkltTMnbLJZ=Wb=kApMt=k;Ir;]MaDQQtX=iNPQjQHoNIVwEuJaUqItkhroArc<U@PW=<SA=tHlWJqUvmkBem]mvfxr<UvFd\\;XvdntPXfn__jpb]hhFh`UapkabHwk^xg:Hr@HZ;Wq?QgfGh>Ot;AuMOjCQn=Yb=g^@ha?Pwun[mpSGSgWR?[WPKHUUcDuyTEBP=teWFJGwUgcCar:MGP;hceW;gS]?Cwlr\\\\MAhlsXMf\\Ux`SbYyrer\\DsQwigXcmGfJ\\SQaJxchngMWd<xkw_cJag<ayvodVwv\\hh>>_fhd:XbehnsfitXrNat@Viqq`Sypi@srAiLPdNyuoahux[<NhlOhxo]Cac\\XwDnxhihSYpAWfF_cwp[xxwjyhyw\\Mo_A^cIWcp_wbfxvfyqXysGnyGxuys[hj<@fv_eln`P@ywyhuhZTiwL>nCPn:>k:`rJI^DP^TiwpFfRN\\>FZ;?\\Jnj[NbBpuwqhuhsTQuTfnLGkAdXKroeu^srU?eRuXSWIQ;HuEhEuf_GxDOFcMWPUdbqgIEhfCH>=FU]W>ug]oB[=WDyrtoCWoh`[CZ[C]\\TA@oOqJj]mYxwV`lmhQBaOAUQkpNj<vCEj@lRvdr;QkAqk\\Xp_xMsmNDLt^hpN]MJYk`<SLDTJ@qOdNuqqnpLc<ShmXmLtJHk<@Qg\\PPqt`Lv:AuxPj^Uk;=LtqQ;up=hP`qvY@xxHlETjVvyBOyiNhunhBomvOt_ghOQ`qvfsVh@InMI`:Xjop[C_t:InUikr`is>vUwuTWfggsjinifclnahixl?hmAs;ocHUMyeHUvrKb]urD[umuc`aus?eYoyNKEGCssWXPOS?yv>ICrQrQKSUqiBCyW?s\\sBw_HiUSIIccOUO[TeGujafDmF^_go?E]=wnMI>IXFwwuaXtcEtceHkiiYD>CBWoSAgdOgDPuTQEImmvFsrHgE]_UhSF?_roMWN_ew[y^yBi;HyeG:MCCEidCGO]DoGBAgx;?cTAb=Eg\\ATgWiNKchSiH;bn]Ck]gcmgAaXTEHK=EmWYtqEpqSYkrk]uXacgqXQkWYkV>;DS=wdUc<[dN[CrKbwcVAgU_shQIb<=dRUd<CWKEXl;tIQTBOh@qVCuC^EdBGbniH\\wS^;cXYyLwsRaXYKh>qFwyXpAUtAipoDN_RbCeqmIHIssWTCqGfmge;ER;dV[IbGIsMtLaW<UigCb<CVbMtNOFQ;cCOFGauVov?yDq\\P^QpxpMm]vBE]p?iFn[tHkmGjXQeJ`mYwglOhhq^pVtCpnahepawkGy;y[nvarIZFis?aj[hvvIiGYhIihsOvC@l;HZqfaQ^gyAo;is^waaV`SNwY@^CqmQNbpIaVFcdixtOyTWkiYyf_gf?pppp@?\\>>aHXtEw_T?eR?^BNZFH`bfnbVi]awV^ynfw@Ykno`t>ee?gi?jN?dd@_@vjvnZAg[=Vr@FmHhq<A^kXcogaCxwUntQWqFntAAi^IrIWhrqmMHwLogHi]aagI_k?@sRO^=fb_>\\LnxP_aHndVOwh`bU?hLYglwc^^f\\>^G`ZJYkL>jlP^cqgf>b^LsqSqir`upjeWgusT`PlHSDETiqVBuWCERluYQ=xqYmV=M^avvYNbyXbLsVMk^`LfIu]HYZIJEawf\\oiXKFHx:dSqXM[eoE<W^`pnLMKTWemQ[=qDitepQYXyVAPIdQNunVmTr^v=inF_oiQpiIqUqZ>Fasv]`Op=IiQq_Qhau_\\K_t_QuoVcaXfkpdk@qb>yHyht`yKy]g>xivy_q[dihOphMnquys=vwpada^jZ`ddFnNPnMIwJqgqHtTwx`?xwvsEg]\\Q\\KFdlqbrxhYyaaypxWxlvewQwY?hxauO^o;Pb[@jHh_Kx_bapffmPOxxirs@ZQYl>fe=@\\ZQqZ`f;x_wqxyqsanapIe@ybqOfgHcGp^lopuNd:X_MPi:HfIIf\\@vJGdC@_JPfmfjbxmxap\\pyyWlH^yYIwo@pSf`byk>?e>NuTabN>m^yglw]\\o`?PjxAjEQelqZaGasvy>OyiNfXx^bht>flDhrmAnOQ\\>Fj?yxugfDGw?`bZ^j\\NkZHtJasHQynXukVn]p[?Pj^PdC_`uwidGdh^[lOhhq]ldjSwZoqGTrsXX?LQW`NAhQCelKaUt`t[Av;ujCHKIPXSex_`uVim^uvtpyUyOxuk:IXVLmGqNgpdWpcApgqXcuhwm_yrI`dgpdNdD`xvO_R`]u>s^Aw;oBGCDcRA?HB;C]?chwu\\UfOQfwGDJSW=eYj?RN[FGesTSwxCXZIxkwBy?sMwcyYX@qRqMfNWbNKHIUFtWCjOUMairqDEuItqG>EFuWGXSf?sb<_S\\gTSeW:mDgYulGiimWnwRpehIuFICBeeRYue<oIaIfxuB\\SCKghC]v\\ccX[VqYR=kYfGC_WrHYvqYXYYvYorkeuxgRBYcIWXlmwBKyIgR]=SuSEasCtkc;yxMSWw?Ip_XtKeZ;tRSfMqRrKepUuJiwdmdQWDacckGHQwBX;tVkIfEGQWDK?dnKw;WUhuVtUXvsIasFaiY[SIVOh;=xxgYhsSycU\\yFyCckaI?_dCGV;=DBmGX]tvyvyaY=?FJaYdYlRTMmAk]UjLuMHIrbuyimst=MBEOctlEakHpkLQWg=L?E^WALQtRSd^wXnSuQIURUYGgtPIUNWVc[CoEiqIr;mxYYxrcsO=WfOWhwsWmFFOi>QuagEFYHuEWWGvKQFHWfbeH\\MfJ=vtMbTeX:ssgkfGicy[YUAvh]rTUboKE?gV:iTFCYdCcX[fcMVw_B\\oiGii_whKuumeyKOBKoiuCYjUHF?tYCGrUul?taKCFgFFqWPKbRUD?ExUQivuiY_v<AFaXy>`lSaKZ\\wVIoLur\\TRs`WCTRAHysQJeUWPtuqdq;pqNPPgaUb=qleRmyuyYyLTSEmQWqWWXVAQWFxkQDs`=Ohqr<\\rV`mIrroESCTv[xJwr;Yb[sWxGmqllLIrTeRVTOxXxWpJ?Pj?MS=YlImkl<QbAVF<SsuxOaMvyyfiqS=l^utsuvqYQaaugtxTQqP]XoqqZeWJTQ:=jZQND`nnLMgTPTDUHDOvDLHDUKlKuLr[uQsLrI\\YkYs>arv\\kY\\wBtjAqmRDs]lk@qM?]sJ@`\\fZ:`^BNjRQmGpbiYeOghoggSGqaouoa]y^uFQsfpr<Ob<WnuHuqytKhmegfXaehIqayixxwuyiY`jKqw@Qccn^av^c_`T^ohpoMAgnAgpf`k_gbhpiFpTWyKVsUw_Mq[iVfF_kgwvbfva?mX@qIhjwWhBAg;pcmI\\N@sMguXavGxpyXs_YgyWjjN[UItnXeTpge>vVijM_htf_@Q_MA[^ynhg\\SHhU@\\<f^OnogWdLIbTwf:wiKocJyhoPZ[_rjo`y>kbYpuVvyYjMohMyw[pf@hvbv]mYlS^bVNf=FnCgb;_fLAk;hdhVvOVcYFusYyMA^MnZSF]YPZ]X_:PdD^eQnnah^IvaFFfb?lLAhkQnGivEAhgQeT?mVpcni`LOgfVcLnjThkGVrcXdW?^[htDHat_`IauVok<Gr<Ih@Fw?w]VnhxFy;HgRWqj>gAvy[xgb?rAGe]hkNNf_Oo_V^]Ylk>\\@nl_>mUXdvWvUnjGh[=gqh@k\\Vmj^pJNr<^]xXxWP_JV`pnfmaymY\\rnsZwqyxpann=FhZ_k;ihWO_OH_NP_Kgo@`pUQjpwn@qfriiPOwyI\\Yw_KxsQHxuH[;_v]ybU^gppc[AoLVl_yZr>ifY_F_\\pIpnGqBIoMifTfpJHpC@]_`[gql`XtFHohhmahtcOl^F[PhlOq\\VioRHl=pmkNmZ^xC`j;I_PFx<qdyOpYpxmnucfxW>k>VhmYhG`uiobhx[hOusygqyufQayArYinh^bKpjJWbB@nU^bVy`mvrFqqwAuhXqmaeYpxxymCVjF`kIGl;hwbptJxsEn[X^dRqp[Of\\FvNI_?GpbFoQi_<@bLnj@>[JN^<QpLwvEF_[Qt_@lGhkXftdxcwpe^IwaxrRXme>vtXn<Abv_wv^yQx[mnxexnAOmnanc?qwa`?pyFirRVjjVZk?`TNdO@mKAidAvKvxjab_V^]EFkXmGxkErycyaoEUWeCsycyIcksXgXBSRU_tGas;[EXqYuwrYwysQE]YvpsFH]duiEMYHGmeLoYBciXwRmgT\\WtCID?KbEwtYmRFwYQSgjGrNWHEicOoHWoh@QTLsro=GNKSNMxqIhkgYTggpYwFwdHKhvms]yfieiEEYv?bJ?vqQDTicBoWAUdqMxRMs;=sF]DvQgJcBxsFi[i?id_YtNKS_mxf]gL?EtiH;kBMycL;WLuR[We<kBuSDtyCO[B^grFYbPAsq\\KFpt[<mKDjZ<twEXJLM=]jZXveMxOhQNmn`=rR\\XL@NiERq]xf@yrTN]qLkLM?=ON\\NumxBMOODSNdn=UkiYKNPSWaklEQ=mOAloe<saYt\\YVEQL>Hn`huH<K=atGASDEjguKDhu@uUeYLFaKpePE=MRUNBHvCpYxhVL@n]AKtqkBMRD=Llux]uQ>]LfAkD`kF`kYMM[<RcDsfaOfhoSllP@rqiJk]MMpl`LM<@Rm`qV<xtYwGlwuxs]usXtJIYlbeQFPMVYoupuZdtlQyoAmEtL<llQMJdetTdvchWVPxDdpgQQytY]Xr?xxT]XUHK[xoCPNG]LSpYadvRdmBLk]EL?HxPlWhlNY]p:DRahVbhT=\\jpAylYkyAmapMyQPsaUK<MPLSa]u_=MmXpYaynioiYxayutyusqyexOKtxpHY>EQrpl>ErHIpP]khlrGlkMhyePm;aVXaKiTmnQXLpqNyJDhk]IrspwqYObYuMpKDdk=arJ<WB\\p[xlRLqkprBTr]tOv@sCxLy@s>awVMMIAwQtqyMm^EL=`kFN`]hku_k;PfK?lIY_`xn[`eHw[hivl^\\DNjoihCWo_FhWGj_grbflZQqPnoEfqXOrTQeVyabgncvb[?mjf`_Ivso\\photql`xmj?dRFm>Ym^FbAGZt^[kFh>@lDVl>_rxwkrXu;wZxndx@kDivk`qV^[lOi?@bbV[OXs]^l<nbMOkhotCFu;W`]Vv]@]pFyDwxMhyui\\YgydpnSa\\vPydhsoYwsOrjnZ\\OvRnpqXfTgoJxisy_iX\\?ssyve[SF=IwISHAvsswwgYh=H`aXuOeTeGAeWumbggwOKEOIEVgtDsTQ`mxun;hWS=qs@lvEPgMWPmMIHOIhjrEYCxlQ\\S@MmlAq\\Ax=HYPpOsaOYMxcuP=MRYAPyTPIyTX]ywLS?Ip[ajkqMvaoiqYtITqEW:@kmuTyqLyDQEquA]PMYK?lTHYWNiNGPlLDw^hSDqJYQpNLJKyqx<oU<PtdL;LYaxo;uQTAti]sQpUXlu`hkcYqMDmWup_dYeLTgmjWqkAlL_HVNDvPLKFiMr<sXhjw@Jq`s`tPMlJSDMq@l[UTX<pf<mWhLveweMl]urNtvIYQvPh;IsMPkZ>pJP`>?k:F^L^lLAqh`wuP\\;gpdHamon?go`Y`uVwjV`MXnVohByvW^]AIbcfpMpanY[Q?p@VluWfBPeo_yoid<hxONvtg[evl]Fwp?wgxoJiesPcJguZviYIZlYxE@imVxZ^^C_\\[__EVovnccAtk_wkH[Nhw^xgL_xmGoJiykxx`weq`kF`kUH\\]NfTIh>vkynoBVbJOsjQyeq_EWc?NqWafagjmNkFvaxIhAHmSh_nptvfynGmSH]Qfn@pmwyxdajo^[ofxt`fwgq>woqfjCVsNft]AsjWldqveavmq[dhnbw`NfotpnSwcbvkA`lAagDYfpV\\u_]libU`eXQ^Y?d>Hb<wpWF`sn`IYpIgiOXnAp];qpWXipYxwid[f_IIl:OjM?wl_y>hccwsrV\\]q]UirhV\\GAjVg]fggBhnRFcYN`BIllWf[f\\rn\\bgkCXfnptunl^pfjFyYFcEO]Vy`dn[LA_<H]kP`oVrMfy`Yg;_rxxjH?pj?yBfJkXEuxkaSR[V^]u\\[rbQDtCwvGIYwHNKC<OVKEhauc:qh?ShmOdGgC?uf]?c]EK<]nF@pfduqeM;@OLapTMMAISJPP@LN<At[PTCej;hVc\\pHUy]<O_@pNPRSmtHETX<tYEuJAmPeMWuoLdWi=Lh]oL\\og@LhmoKtPeAUhxjHdY<Qu`ly`QQKUpH@ohXlftU<yMYPrBDRLtrRdV[PS]=yEuljmn`=pDeLvHws]ucHWNmoJpvwlw^EMgqpaUs>PR@mrADMb=WgHV`mRkaymATb<MDeN?YOi`vs@YKUthUmxuM=`pcptexop=k\\@mhuP^YKY=MaMYTYwUimHdutmjIyYi]wqEyv`J^TUUmKDeM^UqT<xvatE`LlmLeUWoltPqtBXrBpUaDSeuJTMlpUt\\huB=KtMmDaj?hW=]M_pMNHkPaTDYYr]w[xojikipy[lk]iwT]jCAqUOgvHZRVm=xZHPdXxqBHhPA\\@Gtx?u]HuN^vXQ[kppGnogNy_>s=auyIjk@llgeNIn]>k:ybYwe?w`dAg[VyK?jN?\\^XlxIfdGtZB^SbeiYK=dRkXqMIpSBe[tnyuCwGvEe?WrAAdwib:EYEOwVMH[=dKXPZ]Pw@KZ`UP\\lDMlSHM;YPIAOh\\UJ`of@OplPfmtQYYfuWE\\lDDL\\lRBdkL=VUQj^DjHuN\\UWe\\NDPY>Dj>IXNll_Dk]aJcdNhXw\\IYXlo]an=lSYITBAWGHK=MlexVBtswamhYQiHLWAq@MtRquCeNLMRZdl>=S?XnNlkN@wGhL<hte`xnpRqYukxNLMVftJliNfHsS\\wSYyR`YtiR@yMwMm<ayx\\ngAPnxVRdoc=sBAsrAQ@lpAYTMMkIyYX=ThTWVtr`<KDaUr@nBML;`lW]a>QpZatc@ltgiWhxoq`yHxUVtfYuQo^QXcIfwqvcVwaHalZqwX`vDnZhikAykQ>qyqyRxqvYs:@_T?v_xlXYvsxvP>ygxuxYFsEvCrY]YeyUmMyFYUNUWe=y;udjkB]WXnOE<?Hn[DAaWfSS`gRAiUGmGi;YlYsyGsQketYVH[wu=Bg]xHUTm_cugBmIFgEYFuyu_Tr[GLqg_AD??dSIyLKR;qxmmC;QUWciO;HU?C\\cdXKsN?waWD[=D@[Tk?crybyWcOqwZwiuQDtiegKDUIuCOBFkTwyBogB]OBZCt=ax[GVQUVmWTi=fK;E]Gd@UHsSIEYvYEyTSXuyCXQxtodF=E^]n?akDLj[EjZMwn=Tb<KNPPrlkGQv\\PnWqpSAuJ]WhMu>HV>ptKLT@AKKDN_]Rhtnk]MG@LCDXf=xw=K<`xsQl^dL:LTD]lL=S[<SnpReemPLR_DKt\\KCxPq@txMRL]m<IOoEsuqQpLJ_DJcTt\\mNs<OplSuhPT^w>@cMQZeFb\\>bAhaFgx@FfaHrpwoGwv\\IglYyHVlY_aFGfYI^VIxc^w\\G]RiacFsHNoSF]YfsZwxjaa;YbIFaFas^Pb[YaYI`vxyx@nMIpkaqHnoU@dhVaBFZavc@^htvtsoysq]InarnrNadXfnhiqwacc`tuoqOQtnPeCnpw?lqvuWWv:YZa?mS?gmY]yhy<vqwYeyI]Qn_V_nTguZpttpsSYcyNfwgp?qxtxstAm<Ih>nk]>xw?gq`iTiutFbNqwyPriVwrqlkwvKyxUfwMpeLa]T?y<ftti\\pNqG^pcX`P_]=qlpfmAWbTfuRHkEpZ_?rBGjPnZs>xXAZFqhGVxLypMa\\yhoGOf[VtCgqpVa?grCwylOnqWk;HbkIhnN^@NbGFlHgsNgl:FgFfjlgjy?xYyyI`_VNa<PpgXeXP_RH[=`KYHZqvw=uR_x@Ss<OTcccX[CbgtNctdWRmGEKiw@]b[]SiwvM[Bw[EaCrpWVfUU]UucafYUw>cgoCcPaFCMRLsrcIYL?fM_FOsBwYu]AG\\kxu?EgAf`sxLmH<SGC?xtSu^hWF`TRDNJlR]mJKpJcPtt`j;xmmANiITeuPQXk:=J:<L:`N\\@NdLv>ULqQQ>esTdoohLTtwwhjwuu;LkAySjlyRYpNxKVTNy@pITOQxRTqsA\\WXQP;@lKHx;mJEH[nYbCiiqIryNyAOj=yjWnewg\\xxxwFbJ>_NPxk`oBVuPA[;fxt^mtft\\XtCFuyxaAawfomLGs?IhVHl?GkIvuaqiOOdIpZcAek_mtYr>IvfvnXyqFQvuwu]IlvI]tGvrfZiolsX^Onky^h>`moifpXgyxbiX]kYjQwyLhs`YqfoooG_Nfe<w]TgkJphehkiyxLy\\Riaq`srXvSNm=Pg]H``FcantBh]AwmLGp<ay^YlrYmEapTv_mvqJ@vAG\\kQnZWneQ^B@qiaiFhfC_l>fZBqq[?bV^j>xwWPZ>FC_R<mxasywQv[Ibb;Ec[FHgXyWhkuytAf=IX^WtNSF;;UDEvqaYVaU;gyI]IGxYgYMNprAyXDlkmDVJHlkYOBAoMyvbmpGEnZ@XVDsNal?]Mu`NCpNCMkcaRYujbeMK`N[<L=LQW@xaDKTAM<@NZXtcAL?EL\\lkKQS[Lv^dU;AlLDnNLUS]JpXki]NWQtnDr^=kFXRliq`LrB\\kCUr^XnWhKFHPu`j;AnUXk_<RRqL<EONAN^LqkPSwhtZHXhiQlyjHXTxlY<HuamU^`qyAsBYmPIW[PX@mR@yjLpwdTr?\\jwYy[MV<QV[ERjxXi`vLiNEpVMqwI=U=\\WuDRBTRmHMkeyt]K>\\j[ulwTYVMXstL[\\JPhV[qknlRT\\tZDO_@xvtwp\\qEySYdnZ`T<HsCErTQm=Il=IY\\@vxlsxxU\\tQopR_]WGpUlek<XQ?XVOAOOXYVyqqaJ[UXPxtxMyyItgaN^\\rZ]OteM=UqSDtcuJ>HVB\\YLpMkDMqxm[eQ;]m>\\UYQyCdwZejZ\\xkDpExVGUpjTxJdn<qMPlVIHLTxvRmWhTtkyO]EuHluR`nx@WkEqO@tSmSrLL:hjZlLcuQ=DKZ\\K`HuDuk]QRZhrBXoJANd=nGDP=TOLURb=Nl\\wBLjRunKYJ:DOLETJlJ;DyLEk?xrXHvcxYlyrF]si<NOPSA]jU]OTYP[=lKn`jNmX_hmnk]FhVVZBieIH`@A\\AIhya\\K`^cQsAA^l>n;px`QakQtG^jYYr<?^qas[Ok_Nn:y^DP^\\@_<qhV^fRN\\rI\\K?wMipwN\\cFdwQZcHtxY[=P`;`pyVsJ?\\BnZ=PfTVdONpiGwP@gnxu_>gqF[Qqo]ytd`hqvtKopGO\\?`v`pfjX[_^_QifnvwmqgWgmFAsrhlFpwPnrBNs_Gr]wkCnkVFlV?qZ@qxgu`GgCqf]WnE^Z^QhKFyvHrl``Wqg:qv`w[ghZHXlD@hUqpq_j;HwQy]cgoKOcK__PFpgWmvoaIXwt@o;Otxvh;qycnZ@V[ZGeTHxCq_EVkgopppxjipiXcdXeAAuvpx?nsxhi?xnX_aC?\\?arKQ_optonpTy^snvX_nOga>qfwa];?t;IsCNjXObupocqpGNrr>uPXykYuJHH]CHwG[]u`UgxqIaogxIEgAw\\kiYIriUiJksm]XkYSfYUrCrrEYYSt]uCJICx?rdQsSmvhYxBYYJqGekH`eFUSCjCYOAHc]BD_HgyBLYv_GDLSF@SyNAtC=GSIG\\kS?ERN?eWCRJoRLKt?ah;GbY_d<cf[kSL[WAiV[Iha?YvyEyyvvKxeyis[uAsI=gYkSD@CESshSWeWcIA]S>oXWyG>?rpgWfUu<AeWYDe]StOriegWUfsMwo]RuGcnQXNsvxIFdEV;?rqYTk=DraFTUtoYRfoRE_foGcWYW\\ar[kDc]C\\qVwOHjkVM_wnsWFuBkSHvWtZ=D@AF??rpeU>WvZ_h[;giEtf]WMSywKEestRGY`YcFgEvKSkmVx=WeMe?mClKHxKdKIy:MeX]FRSEM]IsdrMxSt`tdmOeXosLoOAjXuOZhtdUN_xShtlZUuCDTNTL>DWdEvZEXZ=pZ@PR=WBMl><jVmOAIr=xJS]UV]nLEoVqrqeyCAMFtmTUjJlQXmYGHxcYWbDXFxLY]jetlWlqmytA=Y]ila<uu=wa@Qh`nVmOZ\\nEuoQiVgHylDnwQP_IydDnJ=K[DKtMm`UN>aNhTPumKjTpadxHxqOmSjDMYpN`ut_qRuQKimUryUSEoxAmDAUH`UKQnaytsPY_EkquSwAk]yrxtrKhjiPprdyvTTsynrUwnyy=Ay>uKEILNTXDpw>hrDYRHtvdINIxP_Tv@=LDpYg<rZpwHax?HrBXLKqS[DxHMwJuqb@qyMJ;`L@dN:UNtqS?Mmbxt_ExsxOkasYdyCtrx`xohUKYrIQjfXxkmR@iW\\qv@LrqTK>huqhn`AW]hSo]jJTQGlsLpWApruywjhymxTc]qsYRFqvo]TepkgAuRml?XTS@RSqPBDRiht\\pqpPsTijm<mexvRtUyPs>xu\\@W\\]pbyqHTjHukwAk:qs@eKqhv]xuRMMM=L^hMNhXL@LAlQwPypdoGiXnMlZqkGMNOPSu?uoImVuDaV@mrgmVZ;DtiF:=YX?wa?Es_wWYeaAt[OHEWc_kfaWCFgc_AgNMc^YxsMxsaIPgVgAeK;rjKWJkb[cwpUeOitOmdQwdCyvmasGiswQrt_bucCg=B[UvAkboicBwHXAhrEvmiRPuTOsFYiXSMi@kdomEAiuZ[C=]yXMb:KsOscSgbVCi<gcJKdhUUMuuDGikOiGqy?yBrQuQmy:wbX[YTCG_iUqIeVYwRKFpSEaGYaQrYGdi;urkc?gVe[WEqRCubggh>?UQEIoMyGkuvUxomth]WjCTx[cQEg\\EYkMWQkER[YyCvwAF<uhnSD;[SBeRv;cdgCpyF@gUJWTk=tiyV:uyvwiiQE>qSNWsZ;RC]hkPj:@uRlwumv?mUryoyyJpiQkaMDQpqEK=xs\\yXQhRFLPlFfv_dqfsI^nXfxMQiLDbqWfOhtQsE]txmxdCr?yxk=tbsGA=GFKtiQvHgS[Kx_KdrCfxoi@icmwwkOYliG`Wwq;GdqDHms<=IDCV@WWgSbEQbnsXL=B\\wES?EfeerArcchjUdwus`UupGrlGwokhcuWhGX]atu[BgoDXqesmfHsE=qsQkXD_emWBgmR@yrm;D?CWTIrZQi:QhLYXAIB[[DTUU^CcEot?=FGuWR[f\\kRK]RJ[BnKEG[YYyFFSRteiXceHuBIYxb]HT[B;=RVsrrkSd[uiay@GW=uhqCF>SxmWVvSy^QFyyVx;vWYd@gdeqbGiGCeWmEbQyiyYy>Ity?VpuWWOT?qFCgI@qf\\Kx_cbgASv_i^CSnchdwcjKcaueviXHkwywEEEUq_tukI]YtacSAghJMf<WG`IxDSgroe>AWJmd`_I;SXueI<AF[_HP?hsOi>YgykiHar>qEhYUcAx>yDD]SHAIroU<mIaCh`[GXAUkIcT=xsATJEtW]hlGddwIsuEK]wcWgJMUgwV:ctiiG\\]VTura=dRCVtqbZCB@MUFmEswe=wUyiIPketmeCYbAEhwsWQqYqIUgYbS?HBAKqPtYeRRQQsYPplurejTYuiHLgxo\\avl=q<=VcDkSQU]HxmyPchJJupl]tvAletVHUtXEqDqmjhr<XnSyTn=p^\\R]dsDxRktPWxY\\hsmDoJ=pVuLQMS\\qU:uWoQMQyUuqQXEpBEV`mm;]j\\TN]TvQTx[Eo@YJk@PREUNPPwdYNINxlk]MXs`MGpR=pWqXk_EUBEOKQUMIwn=WnLMNUoOmv`qvhQJK=P>=knHUNENiIXrAvNtSxDtZQwOUrGFgmVpj>skWfsYhvxypYxnQaiP`sVd]N[[`ah@hwfjYYcMOofVcJ?sQ@i`IpYqvmycygmcIo?XqdYhrxdkfyvxyWVwFVlHonwVgTha?yvrHpwywRXen>ePXjLFaN@dFgshOpopZhxfKnZxv`POwfvonFoqh_`vf_nkQ?bSQZUIl^aEKSDos<YVrSHqYvh_eakilmc^Wt<cgKSBuwWg=d^WCdMSB=H@cEa;C]=DTARV?f]Ae>AbnUXF]wyKSsAu=]SymwSkDXOY;OtfQRdeEXyYYueoywhSD@CESPMpuSGiXRLLuiQdunYqVmixQHkPpO[eRxlS[@j_d^Ka`Uh[pVexvtpVafWfKAkLnpPpo\\qhdaarFl]osEYdk_e<foC`hdAkjN``p[YGqYF_rib\\AfRFaby`:HwyVlLO[EAj]w^>ftootYqyCflwxZjq^qAdVPm;Q]rNnFnfrF]SF]y`\\Yn\\[_y?orsnl_GddflBOl>@`FvhLWkNPcu>oQYwGnpqXgwGfjw`fQl=ivEVnGNbRN_]OmAw]iHxqxiMXnWQsiaqAa^hVpvGwq>ddWmrNi=F^t`\\Eq`HXlTac@ni<hfCnv`ynsimYayiFal?yKNxs`aJhbovw^oZ\\@frWbtymk>lqq^Ry`wQZayuvqaMYhgOk?gj_Nx>nr[vefPv`aZk_ZsPj?avFGj_qhAPuP?r_X`GNs]QjwVxHNbC__?nhHqnvAs]_cwvxA>qQosZouxI^;ivm`rUY]JYwZOj:FoLAw:@cL>c\\?bZ^l<?g=@lZwvE@eXGj>Qhb^]tns^yvXHftIpaGofyaFPhwheAIrUIxUXs>Hb@SqCHLEdV[HdaHQoGKaIyMEyEwLkGZQiXKC=OHT?uRkG?ObEgeHstPms]yxMgEa[ERyIK]vxIsvStXgRiCtyuFemWmKXtAI>[feGG<[WQYriqXbmUvSrOwEvuBywt_AwQqYAOx<quI=ydIESCEYcrAiDekC`;sPgVKEgN=c\\?c`UhC=E@_FC]SVsF>GVLyw=;XaYHduET?wR?FdUDacSvaVO_yXwTCcsiUdbiy^owmIgyOUqWxJctoygJEgnGxAyu_evduCqsFJmdZWuH?c]Cr>arrsBpyE?YXwKh@iBqmH=CTZgSLOusUwbcwL]Gg[dnGsaQcfyUv]bCYTi;vqoU_?UcIv`YBvuiE_TLORCETior>Eb@EGJKR\\_d[exT=rNaWQOxrOS?;iN;SFkh_EvGquAwhyAHHYTiKDvwypcimswZyUrcSjOi>kc=`NritG<Wp<LpXRhmXiMuUARd\\q?YrNtkyLjf\\lSHYtYKrXLM=SEqMtulYQvHqry@kF=M^]VViKfAK<<PTAVL@mpQxOlWvPxLlyLiRfAOZtvs=qP`r<LwKMrt=ljeoQTpPYkciJ[Dkp<uL=piPTZIjDxrnxV[QonXS]@NWEmrApCmyb]pZurkDkUhYYlQVHVSPXYQvN=K>HPJtRNyOYXJitrNIpADpEdJlelk]sBxkempttlKHXeEpgUmkIxkMjZ<VeUWE@NB<woQNVtrJdRqUtxylhdWnLUe\\mypyLTOUuo\\Yw_lxx\\UaMyxhRTikk]kh@JDTVN<t[UYeaJAukFEPWEYShkdymkpp^@sQdL;xMMIWS\\ulMjktXA@QDASyxyX=T_UpxqQOqtsLr:APP=uIaw^YjFxlQDO^YSvex?xQ_yJiaOKUutdrvqQYtNiHXTQKAiS?DRL@MFptNTSL@PJ`pdQmeyT=mVPLNDYvHLT;Xvd\\WAQuklvJhjlDyAyUZtxBYtbAP:aj[<S?HS<MUapu^XYoQJdPP;arayYWDVU=jBeUuauV<SC`wQqoVISwhYlDVJHlkuT[<rbMlZ<nsEwFTsYqyq=Yk=SXIpc<eHP\\B?f]hmjYx@xsGpeFWaKAihOusatOPj]ifIxjDo_p`uOhksIrQIjWXiAw]]xbhxif_rZ_^gFgJwg:p`ROc[ivla`qvtCxsXPf]auc_qCiargvkH\\qYnuHgLOlKHhqA^>@u_Qc^AaHVv]YvFasFAdgpgKAg>?ePp^Dpgmqjxi]rvpniEydyYFGquLcrLgSc]Um]wmuYEUgp=dtqxCKXssbXuG<[G\\ASkqyuUTNQEAAumuu[kf`ydcuhVMiWccYiHNcEtiU`Uhk?wHeVRoI^;WpmTs?itQDQstxYB@mHbqhncwtWSssXBWREwsj]XYYCFmShKxjIfYyV][DnMuiQv_QXNSS@oUaCrkaFpWGCMD;wwa[hUiGnds@\\PdmO]Ut@@Uq=qyAwQ<Qv=x[]WAIrRdmP=sCDkj]QNXPbiXKpOjelY@Y;Pv=uSZ\\l?hPpDtY]wTIxrqSQLr:Dti<WIUJwupyyxPHK=`kFXqFtqphr@YmiHTuDy@lXJiNiUOvdVK<W=qTR@pOlNVew>`P\\`J[<NaPtB=rVxnr\\Tj=UjaLh`LuTTxIrTdrH=SXUw;HNrMQjEKk\\wt]sATNBTRItvKax\\TpeQyGAMFLSCMnpUlEuovuK]`ODYxuEXmiJNhVIlPbdQyXJ@LsF`kYeNhmXtDONLKFysi<xxYyQ=WpdPhXoCMluHVyXP]tl<mTqtSmPXwEmZ\\wLLys]yXhrVQvUawuLY>PYo]kXuXKtuqIP@QrRTkteu@yKpQtduyPTTmxOK]oVunQIKcaP_dUq\\yZmutmrW<StYQWmUuDs_Ywy\\nOlU\\tUnETXMjYtRf]UUAVoewlTOeywLxv[lVpaM<Ew]aX\\YMrTPUAQsDjQxlRmPrmo?QrvQJItMxaMUipddtgiK<@Y=hoUDKqyQr=jatMvQQuuxvElwUXI`xWIopuN[QkUpTvioLAMNPOF\\o@yJRTV:]K?@rWPNB>s>Hb@SaSXMeD[GtT?fPeVmigYCtssyXCIWSvBcB<MTIOFPeyRgvh]rp]dZYwnGXDWG_kcN[EFYuV?gr[StKCUMRfwBxMs]gUGGRRqHDQS=YetCtwqCEQY>=CF[YSgsjqHMoIAAfsWkBPRyyKpeXjmwyplLMlJywkUvayW\\qSGUpiIuiLTShmatTh@Pb=upXoAPR@mbIg\\KygiooNhb[@`@_]IOtdG_lIiG_]axksib?`sqXm[?flnnXwu`gytwkXw`[hdmIhVWkCIm`V\\mx_m@hZOkHWfV@^BYtmYfFHhJQa^XuSVfoGwSnsX`cRYibyg:Xs^F\\rphCfnf`__HxHfrj>mVW[\\Aa`QyTI]pPgQF_HOurncHvrKakIojnVwgnoihm]h]VWnmhxmn\\`pm`vdjHsIo\\KGqdFy\\XbhvgjgeEVsCF_O_aX@irIilqurfpTq\\qn`h@jdWhjws=`_Foa?AekwaHhmiys]Yy<?fjY]sAsWhv`GZ[nwbF^jW`S@`BEhQFL?HZKgiUDhsU;mtq?GtoCxGbtwEkmiO;hS[FnUdnehXYdLcc[MrP]uYmXs[Tj=UFYUusBLUSHsFsQRqigOaGEsVIqEvgyACtwoE[eg@uXwecZgu@ACkKFDkRHyB\\EVnauF_I@WeDcduyCLKS[cS<]ucQtvoi>QtUyI_uu]ysJWGQmX\\wDSIRsSF]qtKow`EWdETRKCdixCMiWLrJML?uXAmYwAVdlNJ]N[hrpqV>eX]XS[@wZAY<Pu`hRx`xxTY`yqAupstkYYyDTMUHJK]L\\]k=\\N>En?Iwqxq@uoM@Ppdt]mY[Xs[XJITlEiLmpj`uX^Tr\\uP=HNKIL[]v=@trHQEDNoLQKaLeLkCiQsLvJEN:@ShDxWyTHAlmxLrLy:aPTIPVtQK=roeJsPR<@TWMwgiKdhke\\QxAwQHOQtNuYK]mJUIpKMpYUNjIT?iyqdy@mwPyuFmNFLPlFr^X\\cWtif_JAyUXgnwdh@rpQa<yw:XfKWx]odwAmd?mJicnnZ;`\\<Vc:Am]@eFIuv>dlGu]Q_liYAIsGgB?UBSbK;VukHhatXKXIsI<ogQITEYSrixT[HU?W_oX_ODG[R;owagCcMyK]BmUhR;Hugb=AvweCDUdoMRiohGQysYHFeEr[eXYXQoCbGESsX]Cgj;tfwgQljm=WW@noMXuxPeYLZ<JQhYuuwa@UrUl_pxPDTb@pfDRoUN[@UH=ONpU_MXXAtRQYD@PfDTexnGquLItd<RaLkexLxIJmhQCIkAtPrExsyUAESCMlRpYmDqf]StXxj<M]HXfuk]TyXHRPloJYpyMRs`mahe]`j\\OfD?\\?G[ohsRXbAwnbxgdnoW_qHY]yfe`htU`vZIn=@_;np]ynw`[<q]YiyUyiEYnIniGPhkO\\Qis_xo^_`@VhI_hWIs>Hb@SAUtqUG:=VL_bPihE_hi[e@Qwn;coMRQAuf?yCSSW?Cg=rMEWM]dBUM<=Xf@wl]q^ApRxpKPNgMV`<JE]wXevA<RB\\MUQrSPm<eMy=LsHp@DjIPqnEPGUOTDYfATN\\wxtMGPMbmQ^qXpUK@<PbDoBPqWLWE?vqVwuVuLHlKHxSG^JQelWv@PnQYe^Wf]WjOhlH>ZDgxG@[FimrXe`HxIWtYV^Yhakye:Ol]in\\yprIwey^cqxL^aIinOwpBNi[NcWpnrFyi>aZayq>sef\\dhd;_\\ahiINt<OdEpgmibhfmE?i]ixSowyNgjhwn@ZSWgMygTvlkWiBwkxNqY?xenh\\>ucXvWas>Ybfo`H?pohiLHmSgkjn_CxeZFkTavEgavqo<yw?AqX`nNGxbap\\ooW?wkQwInckAr]gZ>@tRol>Qp_FfR@l`I_ChmQquWwajYowYaBaj;kH]VatTkdXv<PTULuiQttlIIts@YTdL?`XK\\WsOqwwqkWqYP]NV]bNeLH[AGpRxpRHhg^oxAZaGknvtk_p^ps:^xEHlo_\\KfofbQmiIoWoCCQytBWIg=wuoFv]T^?FGeEl;WZCEs_immIbwIjkfY=ev;GHmDBUs\\[woEutOYSot`qB[ugAgvt;ScOyYcRPIXnSF]qTM_FjohPShwgI;UiW;XcQDnUi;CyvWsWWIKKET[DbeeJwx@IYfIfi=dmmxj?HwYVhkUscrTiceaHUeWtceXkrVUFCmywkThkVpqii=VssRcoWHMvASU:wcL=f^AIUUE@wEvuIZ]glUbAyEi?Hqsd]sdmoXoaSBuUpqSwaUxeXK;CnGSjCSd=d[cf?GHTOV[]eDmwrKHrKR]oYLOS_MDYax:ebrkg\\sTn[HeEHXmU\\ivfKYWSbYYtVgISUVtERK]G_gx^KRBKrjKSgWSAmihYYcYiHab;mZjVZqPZg_`Cxu]xhwQ_whnE_v\\AkXHjGva\\>wqy^j`rZOth?mn_\\uQxpVhXhc?ql>iy;nsTFoM>]GWx;FmH?v=AlbGiCVpkpcV`^>FdFO\\@@[cFlFV[HXtCwyBG\\lweZ^^uNbZ?iuA^TAnkVryX`=Yh[`_\\vuaXiwGktQyGNaoigDXvM@cIgf\\@^]rF?tTKWo_bGiSESV@Iipesjoh`YhyuiE?D`YVUofWqC@SdnAIC;wnqHSQWVGrIWgBEC]Yh[ssvEVysBHgDcogq=uVAwkGhxgRmgT?EupccTySbiSNAGNmiDmijaCqkgIEteqhjgwXkcM?d^Ke_gf>wixYwTcgP]r]ucOGuywiBEifaYZKWjUhR=iS_WvQyuQdxmicIH]CfKIiDeiwEeHugDkr_]ij=eCGh?]Ia?snarkkDdyU\\QuDiRDcbJCW=gwd]EAEvrKe;ySRAdZ=cK;Spkga[Wf_RrsBg[d_;TDkrAqFkaEICiMcFrwhxWrF=E^]VViBRcgkCSFggM[cPaW>CHOARMicMIrHid<_rR[Uc;eleDAUchsbEoCOSIW;u@srlCrGEWwSbxMVwQc^eC^CXFMd^[F@AdbUbjCW]MHg]CLCdt;Ek[cX[CV?cpeeqir:MVZCV^?Ss]vkYbTeB^_RAEF;utahtE]Uuuw^tJH]QHermQp\\\\vF`kUmStxkSqpZ@UN]XtLmXuoBQxlPvWyXwmxhiO[EUqmR]iNZuVcTjx]vkHuSUv<QtqAqlpyQajfPNN]S[tm]]WfuKAtMrLrMtSY@Ndew[Uvt]SgUq=Xv`IySYuYqvwYSYiNQMqHavN]kguQ@qt@mK[<rkMJVuP;ihPqtLneugo;xwA?yx_r;Yj?Oc_v\\UqlbftIPnxQ\\Ex\\SAapyhAaxWV_npcb_hPGqjgyUaoPyi>WnoPb^yvRVhY@vRqyiN`mfhRPdkOm]XkY_fcixq?gOyu\\`ahF_Nfgtg]G`p>nke>rB^__WvtNjj^[cqh\\ndQPqFosRAepH^QXxRyyZYtNO_M>_OpbgxwoxwGgimYmYay`iwXAkF`kFhufUAAB<=DoSwnqTQ?gygx]KEQmGlgD`[h\\UR^GSEsf>?rLObCsRk=FiAXZ?wjsemGh^uiuSVy[RdKyXIs=shnCtIYfVcUF[H@Ad^CSyMXimRpGSFshGguo]BuCD;LnZutg]x?LJ`dLVdy<<w>Aj@=L>EPWqWQPvfQJ_Hmslnpqw]tuquNL\\KU<r^]V^]Yt]knLMAEO;qtPMrSYp;TmUPkZ<T>ET>ytypmAIX^im]qs]mJyIK\\@uaQrLYovuxoyySpXjeK_EWNhoKAynXQU\\oQqSLaKXQNYMol=XYqUXlQpQNExxwLrtqROXpaqYH]sclVpqm^PPkmklEoFPLM=OOxrk]K?Qn`]WFMlEIOthuRPWoXRuhu?Qp\\]nNYQ\\ESeeqmDjviVshwYHvWMRTPXTpnDqJKUkMuLyyUxmYgyyZ\\PEAqsDSQyokqsCytrTYkyrn]yU\\vleRdDyw=U`mjoQyIIxDhQVtK\\AUJ\\xLLqWAKM`vRtOV<nJXm_huhXthapB]S:Au^\\LEEYDIq]\\YkIoyQkSiQuyXtMwVYWYyTPDPBAsrXTSDL@ly@iKdywwhSmQyldwpUmh@XJQRJXTcavTEKbTuLhrvMw:]TjFjaycta\\=xn^fkL^[fVcAvrRg_:o[\\vZB>dDF`f?dJp`^VwIO^^Fw>weB>\\wicV>k=`f>_\\FN^?VrUishA[=wao@sJpb]Nl>WfL`Z]XlKP]EVrwp\\@isBAyfF]fqv:npWpnFfcGGiNXs?osWXwkYnYfproxSQ[_QhtferX\\`AcTAg^@dVwqkolMyfyOrTixtV\\MWfbA[Vaq@YsCqqifiXF\\W>fcghMho`yq`_qlig<qvKoesIsIFgqWwNN_s_phG^gyq?WaiVh\\IsyNfdPxI?woo[j`qvHkkF\\DGgVw`gVpd_`<o_X_u`hup@oN__fVcZ`l\\`ehvwn_lPQe]fn^vlEIlEivhwxAghQY^>`^COfdixGoilqxy?nvV^jaqLnl_@oFh\\r>hJQvlIuHvnHyyGvvhfqCXnI@x:Iri?vrwkKIowpbVGu<isUavEO\\aWu<?o:xZXniRxrHxyh>]Ux]xpxgOfgYpqAf;XbAvkjVaxaZ_QrX_gAiqa^]BpaF`cR^FPJF]LLtpU\\xteQtETFHXV\\lBULu]nj\\vNMODlLmmP_UU\\pRuTml\\L<LnY=Yv<wamn?uqmIpK<WKpnGDKKpSxYyhDo=AO=HSMMl^LJcMtyXLqdQyAnxAN[=mD]PB`Q^TN<INkTN\\HjNQOO=O?upMqnxhpC]L@DW^TRDYYp=XHAsraOKLrZUucXxHIn=MkMtNVMj:MxgyWq@Ql]RMEoVqwg\\M\\]k;AK=UnSaVsEWWXWQXU>dmvlpe=sO\\J?Pl?En^@xlQJKtpJaJ>HSBxTB<XaLmflQrhS:@NChOL`JvqW<upmhrvayptOvTMMEO`IqnEWFpR]LnQYw[`T>mOQDVUIPk]MMIwRLl>\\nFeLOqtPqtHqX?IXFHP@dnNLSc\\pPaSHmSlTPmTRk@UVIYViqpPKwyx;MS?hWu=ul]Kitt:IXMuV\\TVClrahWdTmpDXN@tciWkeYmpsuuQyPRhtnR=QPUv[xNd\\Ofim^XwOEsOLLLdu`eXgaQuqvP=YpIxYInLEMaDSLLXsUk\\EpFmuW@RBpY]Uq;]TwqM]TL@D]hQZ>HtZX\\vAa;ykoNsGWt=`kHW[DX_P`fyou`orm@p@ork`h\\w_po_INaDVmxYf^H\\cgm;nZ[Oycpb=`xWpi>?fJAyWwxAFc[_sjqqx@kBwmu_n@@fapuZ?mp^p]n[bY[?>uspgJ>[EQnMagJgewpcJYw_Xufnjs_qF`qQ`kF`kIwj;q__Ge<xjYnxb`dvov`aZIxahFoQigxiwyhdvQuihrFocdnr@a_np]`P^XqpgowIwtvvnBh^d^tpf`t>w\\Gu<vtM^vDNl<Gu\\```@wHxg[Ai<@`L?is@msYZgokwNvLnZXVgeF^GQeFWocHl\\@rKYrAGi^Inco^@i_piweVtfOgThsvFcLV^>?kkFZZYvrF`<_^>GdB?\\>^rwQqf@aHWi]^bK_bVvn\\N^BNZDhr\\vZH^]ZAykYvS@arijRhmtPjK_eavs^GyRFhv`klPfVvr@yw<oeCon`geTftRF^\\_mv?rSYdaHrr^`wWkCHovVtMAfSQ\\QY\\Rol^qrti\\hfesfraymcYjagl:>ZZ>ZC_b;_dviaPvwuNuynqv?xuAqQfb;^f<A^]be;HBoyccEhcGBeuO[BFAiPSXsSc\\gFS[VtouVoRn;UKyyjyvXkI@muneUBCtyevnKSZGEBCb;ei<uUJ]wN=FFScLWdWMf:geBGR\\Wy<CRI_tS;C;?hfMEUiHNite_hdiX\\?H>qXVwSoYXFAsBAuGAfpAspGvCyFmawUyt@QhZ=HL[UwOWkieiaXRGek[IsaVXCIjoGpshI]EFkDFkxFeGj]yjYdV_ysYEfcgV=RBCbLMBUId^QCPcfkSc`AY>EYFQfQihKKrJEelEGIGiFquQCtfgrfgg>]bxov;WvI=xBYRIIhaMWXSsL_sGIiFis;otX;BCMfkiyJ?FjIb>_FC=xwuehuhE]EAab[=Siwt];C<KbZ;rqiyWCdj_hn_RqWu_]Yv]e<EfJyYIsx`afmYvjSFc[f=Cvn;iGqhVmCf[I?IiGwXjKYW_UX=Fj?c<ES_]I<yw_;E]CgFWiFusO?uXAxcogA]Uxpr>GrRaftYujaaUPgJinPwu\\Nk<_gEIcYWbFn\\YPpbfh`^[lZ@V\\eIr;AeC>p^@rPPlSvs\\oum@sWalpWpeNdj>aY^]Fphdy\\@Fg<OZ[NtvQn[OiJAdN>kK`b^HtnI^kI^qHrBOcKqk:?v`XlSihhh[Zf^wpgQprpglZxt]Fk]__UqsH>nSF]q@ln@Zsfk<n\\EPk]xbWnsVH\\vavaF[Wqo\\XuO_y?yen@uyxem_vBXr^anWy]ApgYqiSpcRf`MX\\m^ayawq>hVWmyivyWyY@gnvpKIgjglj>kcw`MNuGfbaObMYwT^_EOpwH\\J`r@vtM?uh`rRFs^AyfvinyZyi]Ap[VvbcHbyPZKptNGsNAq;OcChgeNc_`uA`gEH^DP^Tfk@foPW[YyxCNj:pgqXceht\\GgcGkXwoAQytQaAn[V>uoypSVZ@_b;nj>wjBF^KPb;@\\rnkAY\\I`iWhsYnm\\NwwAZ=Wj<Gq:WqX@fSOjvoEIf@SVROek?WPaF;wgsOXxGcMWcsMwEUDcywPMC>KD[]GLiVhkX>qWpiY^_V<AF]SNDAVR`L^XLbAt^HqrQoiAPN=p^TTpPV@ipRT`nAZIAcdwsBIybVnqhw>wZtirAIsBga;qc>Fv`XuZwhWIrZIaAwma_dZ^w^`[Wa_J>cixr@A\\U>koHrROZcGoWXjkob@orgxrR`pIHjL?hrAp?IymI[aysA@upxjPI\\gqpGyewidQHocFsY`yCa\\`xmp?iUvprwfv?oNx^rowcxuZOnvxlQpqqi_Hgmsgkoise_xtf[FF[KOvKIwr`hun_DG[@ynf__E?thg^Bg^r_xKyskitawyUoaqAsaIxv`yhHhaYlvxbUqpS@mR@rphgpxpqH[=A\\EQpjhgU`ehvjPQ]u_f[X^Uvux^]gX\\vApHirOxwKxx`HumniVPhxo\\:vrkHuqVx?ooPylca`Yqf`GbMYw@A_U?vrO\\_`Zk_g:O]lGiUVf\\OiWVboga[>wRpyiqd\\`_Joltxv]VZYfb`^;nZ@f`;>[N@ZAonWika`]CoUKSDGVk?H=_DZoyYocFgY=qbDiy=WtZsXYGtNKf;]f;awDIRTiFDkRlQd>AsYswBcbxiWuCW?]c>=CRkfRcr]Cd=?sR[cJ;C_Ot\\WVKgCUIESse?KRfaHqsvcyfwksXgxs_XCUD>SBEAS?IumoIisiVIvSyVE[IrAVX_Fk;SCyBTkYWQU@WBI]e>[tTydbmXQGb>Gss=ygyuw]dicY_ITPmde]UxOP@UOPqpHYpvPXKPuPeM[\\KsPj\\]WLqNbiN>dq>PVKIVdMXIloUXukhRxYqHMu_`lNTk?]pPaxteQTiwpDSL`xyTrIPS`aqqHM^yx=@nMYolPUwUkEtPxQkPxYSTl^ALKaL_uxZtJpqQCIj?xNr<qyAQCQxQDqKIomhUudSc@QH=weMYW`JEqS?IRepMMqwnDk<<PbLwOEslivhTYItvChS=hjsYys=vrYVrpo=HPtuNodO]dNMlJSb:Cb:MCC_dcui<sTDKSP_V<ITRQTJSEJ]C?=riKIfguvuirGwpgeaIEFGu=Gcy[C?ObSKC:CF>qGKGHvmtnsyc=Um=RY=DFOc<kbKSB>;SoUyeWEmKHhIG@GD:gyuiGPsDg[UQAtb]fH?HTUSTeGCYwiWyvYgyehHyexIwnScEGIVuT\\ghsaS>IrZMVg`jtUw@tTPuU[UnsqK[pqKpP`PxVMksujkhjcMsMiVHpMy=JImQBqVoHr`qtGluytx`tvitqHQwoPM@uLCXN=UnP<RjhrTqvolKfyYbdL@Lv=YkHuYSqsIQScLK?PJ]UV]]WiuWMdRKDVRDJ<`N[]NqmQULvhmnTAq<Iy_xwlPuvelVERKTWRqoXMv\\eyNtTPxYHYJqym^MnjALXhp:aVhYxNUQO=Op@XwDkQXTrlWFhwDMx?tluykwDRahwMeohMvqUuf`UC=mY]pSYQuMjwXLypr=tjXHRDeRT`xThRjmRCaj;KEAsDTlH=NH@LC]kGHnfUODll>Ql\\=wp\\XMIjeYr@IqUXSFljq]xIqQ^ETeqvtIjI]qwYJyuWLEXJTgNIn;_Z;?\\`Nmhw_ZogyIdHnalA__Isc^l_GlsH\\__fVQi@W]WhvlOkwYyOVypi^vHy`H^QXpbahNNeenoWWxsqtqppkaqRxavYrsn[X^sKXscxsF_]:H^DXbh^ewgkqpswyunOnE@i?VjeI[fwZVwt\\vmi>`KOm`ohpA[MgrCnxWFaHOvynj]WiV_qlOlTghGPbKi^Ch^GPe:?ucPh]ggSfoM>`wI_Ky^vW_=HxcwnJotpH]Yv]aPdc@tb_`jiyJVffNnb?^hO`K?Z]hr@Qj^FcRWuv`r_ivq@hebeqDkeUGwuoIgh]Wj_Y`EcpMX@sTYSVh]wSMX?SeXOe;IGh=VSiBleBEsHQSvrKb\\EUlAwKwDj]gkmhpotSqgiWTSSsk?HXEVt]w[mvaseZMhl=hyiE^Et<WeCab;mR@iU:?dDcVSAUPgbe_D_SSLwTLGRP_vGYxsIRT=tAqIaybviug?FG;I^GfnItbARLygg;S>?FD]Hx=DKDQ?ay[XnNLsO\\lN@WgXTKMlomQHAsrhv^pT^Pjuywq@YhIQrTYpD^eWvuq\\TWeRVfkpp`?yawyfG[AIlvqyiysj?yjGZEQwUx\\jWg>_ybO]H?\\nGySIsQ@eXAq>hw_>m^@jH`Z`vojF[babMYwXwfmphGHqSy]jvawQ^gQu]^eUgiIPwpQ]PXnbapLNV=wpODfOf<QTXyflge=OR^EF>keaIhr?iBQytqBWoSF]EUKbZYTsEeYES\\?G^Uipgr`qvPSXsuJNDVuPlDAq=uWt@SupOcaXt\\mYMy;togeq;ErWXVyIlltJgAkwXkHDQilrEirRmK>EXQPRKqv?xnyUkcHxw`jK=kLPL_ESfdvZ\\jtin]<RqQNSItpTN]qK?=k[EJhXTXTnr@Y:Pr>Oxsa]sg^jxhtvZyiujv]sgviyrAnmdxmD`fR^xs>`>qrJFwx_x:W]\\g[KpcgGe?qonNnfv_qrragJOHOsBuuxT]YcYSpsUxQh@=C;gVSAC[UVFgBRAbGyIyyvQAyqsy`qBQwGqAdLKvrqtiuUL_FNYeokuwuvnSGQUYVAiPChnEg?ixegEPyTt[Tq[YTSuKciH_fQism_i^AtHoSLeHyyD[Evu]cIurroe?]ebMIgAEywBsuWVgyEGgUCtbAeuyx?=C;EfJERBGHTiWEOYw[rqYhkaw]?xv_EMcd?KCHaEUUwg[hK?V:Eu@Os^?VxueE]EDmVayFkKFZasSyxsEyuyWjYrQOUnQwDSUs;ihOroaDB;IuExGMwGgGfUu_?diCvseBfUGAMG@[xgqYuwXnKwUwuvqvqsWqqR^]V^]YNCw^Cu^CCbabHibqAteytcCULsTD[G[;d:_D<CG@gRAYN=mQn@yr=Xw]v>HVA=Wv=vNypNdPwyr^hsEqjaISydTb=ui@v=mStxOB\\Kc@Oj<LoYNBlYNTtoYR`yKYdViIp]asY\\Q<EpllpmPyPhRFLPllWgTJwlmPLNELK?<mXpLVUq@dtd`nQYtbemZ\\R<Mw]yWrpXGynMIkS]UnAmSHXJQYjaUqpV_lTB`P_avgxXx]sLip_LMotmXuRJAo?`PeIPwpW<=MbMnJUL?HKxuSaHQaiL?mqZ@P@=dSNl>QkTqhA`qqnsMvkxGmixyTy]\\IqXwqBfxiy^Hnjcgbc@td_`^vthhgmGwLq\\GqfFY`Ia]=IhNwaoQwpWqufuH^[@AgFHtcowdH]pa_JqrJagOIamoya`sgi_JG]EIvsf^>phChcIvqe?hmOlr^`>fe=wo]?gPY\\dVt<vxyyfiiq<h^uNtuvqYofXvdhqtoqowx`:Nu:fajXZmVZfAh@X^HvjFhvL`[h_j^@tM`x^fagYpnApkx_D@lnPkRy\\KOe?Q_^FlFNhO^vjGsSi]HhvFArG^i=fuGpx`QiQoyr`sNYrsfdqpg=^pMAZtHjmYwbXeoWsVPaoOwpomvyvqiyyxoLhmwPqWfcuHoSOqMavrIva@mUhaBPlDpiVfauqi>G\\k>yU?_Hqp?fZqY_=W_aqgopbsofXvoLgbdFaBgssAqCXiyyxyhggOgZnZhQqiY^IYwiwcv_kR?wai^UYqXXanhoWxoKVjdfb`v`Yv^sG]Pa`qAcBfnJok=@]^Y_QVZqGb;ynCwui?ddF[HT^sGx?WRyhIQHlKv[IY;ktt=bIghXshiUUxayIyhriyYyU^YrISi^GgGYSYOuI_G<]ylUyngerAUdcTrMvKydbsB]aHUcIpktt_WgwffgG`_usoDkUv=qEqogpAUxgEkoiLShl_DMYWUKblOVdmta]WLYfkgt]wtC=uuWyRsvHaIIehlKrpQRDiiSSXtqI<SVd;WwcSegT[EXkGRL_CioTyET];C\\sW^kFmWWKgeUkF@qXm=VQYvrQvJcepMceYRJMDbst\\IyLOXOEVnGfVETNyrw[fN_xtkbIssq?UYEc@Cgaoc]?c\\?e^kSjoVaIHPKb;?Ib;yrMCIGR;EjJXqA`OcQqrhlTDr^aKKAyNlpspjPQM]AQ=hltaoIHRpMRphymXq:`uO`QZYV]LJwYkWLu@ApBApUyoWlmoyYVqPpxuaTya=wAMMtQR@qKTxm_prLTM=HLLtoVmVtusxlxXTQCEoTUJkuXTET;ER;yn;uYodpLElvtyv`VcES]YyDXSQPJPmTLMl^dswdJctTiPWxavImPSDMK]yhywHApquW:=LBiMx@juuL;=prmoAYLaqU^EVcqLixqsYNPpThMteqpBTqCduH@nWQTnXmDpT]dnxlvL\\l^lke<KDQL_@nxlvjLTWdVIascmqvavqDQsMvViQTyp[hqVLMmTQWDRehPH=MHAl`XmRTVhIobMYj<uxArTAWtdqOMvnHK<QnMURZqkLMK@AOAdPpasy\\sSXvyprtuvI@pb]lYDnv`LQiTNPOPpUAUVFHRdTjl]OZDUrpMmXYyMRJ<QBeNKLt\\dnDaq>tMcQwM]mImyhLkNMn<PjuIlvMRv<oSAN^LJbiuvPkXeU<hso\\nH=XWuOIeMdyXYluHDlx]vV]QNYUZ=yLhRT\\wA]j:HMlAPRmpMaktYOxiyNPNguju`MIdPmTNe`QNpvKDjNavcXR`TxQ\\r@QLSTRNPWJPKy`U_IxYEy`tkw@yoLSOQOLEo;msiETO@oZ@vMYVJmoR=K`xnOTPmlLQipnUq<pTEEtdEuvdnB<RJiwTmOV=WkTP]ATiXOddL?XwDiMUQwiuwYdrHHmn@nVEOmXWQqU@uR@AttdnUYW[]WpPUVpnP@On\\R[HNGeOC]Wj]mf]XFTq@pSa\\VpMv[mqsQtyerMukyUjcHkshwNhru=Mg<waPLwxyxukqlu:XuqhK]XnctOv@pAPS?yRcxOHupWUQRETL\\puXWVuUtIJqpty]stUwwlWgtq?UnsHjJLK_`QDinKlVapKkUxHYMNmrUAY_`LE\\NkhNC`O[uSMQWRLuGTRVTMnHpnUuTPSOMPllvZYySMWSXsFtkxLxolvauKHLQUTrQTvruyl`L<AnZ@vxur`EnaUWGDxDQJCqrlDw<iX>ML[AyxAn=EX`<L>muO@UfAURDMHuJDqp_uQpepyujB<pwYWUXk;TQJDJ@HnuAuSItrdNitRTyyWaWahK_lNmAM>qtLTNBhp_\\k]]yDAKMYYpIXdIqQ<QnmvK]ThLKtaL=HY;EraxSPPK=TTMMlSHMEepd=wn]LQpOsAM]=JG`lPtuQ=YXPvgxpp@UXmWmlP`Duyxqv<MIppqxxEyyylP`DVsUvWmPuuWmxVYaOIemuEkAmSvDRwpqEpSalReaJQYlBEvlHpPiNGePx=nJLRLiw^`Wg]RFekWlvkYpYaVxmxJ<VAdKhpQCDVjqwuHNi`qLPX_Qk:YxVmkVDtFisG@vsmswdYIYyU`OH]OJ`YjwmmqxoyyGXuUxi;W`t@r<QsU^qpqvqIqswvWO\\Miffpa=at>qeDqwXbbaI@mgMMGs=EeECuodjwD[Ygc]E`GWgerfogi;tdmxJoS<eWvCftkVBSu;sipityErCWFIEThctbYcL;y\\_EiyUHOFO?gZhyHmQ`HKcDxauXKMum=jbiqTLQDDSoHRD`w>\\NBYmHhf^vZif\\UiuCXyU`siAuKP`>yrBhjxHorqon>^m^]K?wA_]jXZ;AtYqvjYxtId@fgiQiHppNOw]`wy?wKnrawvj_eqWyFQe>W[DN[xV\\tIuBPd<hp<HyswlaqmM@yxOkJn[YyyxA[UWeLfnt>iX?kiYeDivLvtiXexAyIxlshiuhrQwqtVrvaiOfnpotsyusqaYfyyiggH]Rvnfoapi`tVcVwetI_QvgyyiBvnC_nQG_sif`pr`Hmw>aHyoYNm\\Y_i^yXFgnx\\Qgk]?crPhoiaxymywyyFpvWi=Vf:Ih?fmP^mYWi=x^Hwu\\wwvIcVwtyabHxeyYn@I`fggSn\\P^eFH]]y\\y@jMwnfftdy^lqpqi]pxi<Vp<@_HFayGyA`hLqZoHtCOjLxbCyp>gmXvpige`gimyyZYjIvqIgtsVr]wkvg[KqiR`jhnoqPmu_[^nkeFcV@kMynx`ri_iwyq]isqoiD_\\@`lep[mXiVofqgds_iyI\\HfwxGjdGiFHrS?prvkviqc^j;[HomP_^NXbsww[^xPQagytyOjhihBOtRFoNN`Ig`Da_xhyUgybNrHqr_ObD_j>^o??]=nrZG\\UId<py>hyhYcyIp[yrAXtDpZIxgE^jIpaaWqQHbYY\\`^j^Ofhw\\apmwomciauwZuq[?o`bGb;yfCAxVOsmaZmXpLxfXHhS`m>XjAVZx_x]>qxge[goMXk=VjoploihEYiiixJPh?X\\aNafIuMgff__:YxNviQyydacv^vKvcC>]EO]pAqpgw_our@xA^g?xwKGot@aXHr`f]PghM@_hVdY@m^OgpWjDXu\\>\\aH`KqitgmBFfWOaggkyHm\\Aq<ptPpbAiaLabyO_Pyegh_COnCXf;QytGmiqiqnveyeIGmTP`rnkvayqVaUNaBQeeotQq`B`dB?dK?dL>qX@fvOu_HpSV\\oQef^oX_nwHiEX[QnsMw]g@`sxtlVj^_h<I^bF]DifIhooq^Gpx\\fldxrqpqkymM`nSwm<vq^F_Ohe<vhFPhjnkNxe^@oFiq]@\\@fZ?RFmVQ;D=gxtufLerYGu?EwJIC<qSE?wtiR^Ei>_Tx;V@SbjODZcWXoT^UXk?da_FsSFo]v^aFFqw<oV=SY]QGtWu?qRkkFQ;C`=YOuYZIIZYFIGe[?G;AF\\;rJws:qWUckv`RcHsyTlCUV>LlkHwSlXWLQFIrAxSKumVPuxau?dJ?tx?dyseliYS`yvgTLMllSHMAhQuMJxmxmDsOYoDdoOlqYDvuQM_`KWqo_Qx_qOcMMMYw?asIyJFhksalDmMPQUVtr;IXVHnvyWUhOe=UEpWqDkqlTCUQgLt@qNwhlu\\Pity:DqjqKMmS<=T<ttM=S_EplXRUywJpML=wKiP@qXYUnvdXGpWn=kq>q<_\\qFtRNiWfkJ@th_^rN`:VoxFtCVfyWt]XnDPc??vtP\\AIojGx\\GkqvuFHmYxxRXmEnaaQrZ?lvPk?^]Aif^`pIhj@idTgkPniZ@hwFco_raOh@AtRAcBPrNFvhHxty_hX`TWmaOgKIvbwcjAwmVnrpm^>_u>^Lo\\QxolGv=ydriwiwiOf^uyu_qhdQupxaiYhu?hyF`DFfJ?djwaMy]NQxS@qj_aVIpcN_AysZxdQFww?xPNsmAdxVbeV`SI[PG[E@pSwk=>Z[__<Q]bxtKxjIHrMvs;iwU@td?l`F_`Xu=Wc?H\\=Qv:qwBP]fAk^>ugqq?FmZ>p=FtZ_g`>\\Fo_H^hXF_Jq^I^_EFjHWd^XwmVpaw_uokW@fqIl]?aXx`rau?AjX?djwyj>mjGe;xwEn]t?clfag>ap_cjQyeQk?ibIhogp[@axBNJyxoKT<qv`MroWWU]XuOdSGEIGcCOD@AEvuua_TdCvrKC]MyCOcLCe@aRqsGMQYaiHLWUQGSPoWKkutOScWt^IF;CURCF@Ky]ac_cGC]tGeRUoHtIfgKgamDcMyysv\\ihO]TcWbGgBK=WKQUMIW_[sIqS\\Yy_]fraVdkhISYekCX[xSoepAgNMTpuwh?D>kGisivGskWVCSTMEUCisxMuKyv]=sUIUdoTBoYn=u\\IYXsFHci:QuUwDSAUuudDeh>_dXCbQEVfMrL_rcktbkV`UWVAgdmdQwWm_hFCStkrXYBOKsoEb]AbY;Yf]GiMxxirY=DAIF_?fLwiaGfYoH^KcnIfy]H??Hb;Gr=DbyH]ED<sV^oSgax]AuPqDCige;cPqDkugEkgAKS<ghbSWkGYMYhfCTb=VwORnWujOi<OimUDpkTkKuF[c=iYI=bpkXA?BJiY]GhsWsB_YQwW:uvaKWWwW]csGyrtsuhCYTUd>[IQifvcH?IhicICqi]yFAcSFQyOKRDKCDkwi[RhyV<oicCUkQvEOdayeqEC=AbQqUmEIymu[UV]wB>?IH]baIW>?h>Ih_GtBCSLoB:me<CeagITSbPQEVsBkghH]x[Yi>uWviH_WCiWTHUVvss=EIhSrCSdwqGdqrD[XMAdxaxw]Rd;cXuXcqiVMVvYS;sux]VNwwH=IVEiJifmodosIeqXMkersxLSXmSyKOT[]c;EGousIgTyAIW;IZQHmSvjKIdEImmr[YGYEXrYry[XrPn[IlAMT@uRWInbHr=pQhix?EjGyla`vZPWpuyaYrAym_ay_xMk@YwQJUdtXlmUUn\\qk\\YYwLS_ESRYjXuO_PQ\\@KuHJwpk[eVk\\vgxUf@XhYs]@UR<YPMvRaVOePJTjBYTkmwrivc\\j;ER;YJ:mt:lNU<x^=T`<uu=mnAuLDvOyRCpQrULwun;MoV<sQ=rf@JSXMJXpNPnfEKA=JnUqRil_]w_YKRqSA`PFDtcpR]Lpn@N]lp?Lrj@OR\\SxiwZMnYySULwEdj;MMKHsYxVtyoEYt>\\j:dWjDWDeVn]kSYJAHQlmxklvHlM@=SsIp`ar<Pj<XyI`sN`mWqXVDRoPOrMxCQLaustaPUHKUVbThsJ@^Ja^CwZ[NibflJpncFhVV\\pQiS_hLQeLA_\\Fk]NlNWl^F[C`o[x]to[qwtCokVGiGHkoXerHgBhlLF`NGdGOufNqc^_Bw`:G]j_o_fqRYnmg^^OiPYvcYj<@[?Yuc_bmXljFapVsmwcyyfFacgQyBgt^xcDF^fnmQhnZgmvF[K_d[yoyQa`wyxalQpelGsoFtaqjf@h?H^oF`RWjJN\\cf]>NllGqFIqMyq@w_XavlisyAjaIq>Hf=fvB^]IG\\N`_gpj[`eM?qUPkrnjXwtjgw<?s[Xvcotmxb`gnoNl^NseXfOvvGXiCyvbyck@nZY[:AdFIuUHu?AsMv_LAuVwnq@iEVfFFoJAecF`P^loHE?S:_wy_C;owpEShau;mggOVGgr^CuCQUEgW;=VsWgaCrZMvYyD=SucGRTqxEYdTMTMwU@OSUoxA_Wc[BHOd>GV<=udIXraxQ?IsasmawuCyBSVMYtSwB<=s;Ew:Qb<ObuycuwFLYre[h_OdZ_UP[cF?S`ofVKvr_cNoDgWwRUe:CU^=fQiwJCEbaGYIfUaW\\wR@=tLMDoUinQrJ?toEwrkCUKt]EWk]eKehBEI?_TfuheOwagHD_iZQb@_uf_CP=UFMVCwTLmcAqCCOdR?TkOIsssQmisyUlwXqIt[OW>ueNOHj?E=kgeCIkMr]ayses<QR>ihemEgodZyFyCcbwtgsBH;CHkEFkBecwIkwDwxpavvkcU_MayScmxh@tgqXjDSSPUjxk]uJXXVfppQXjuqM`EYoYsVaUrts\\iwU]SGaTcptW]lFasBqoeDS\\dSixt_DSGlrr\\WfPSPpWa\\sgIxKmS<enTMVxpY>PTjIs_`jwETcLyR\\LN\\QJ<kWtTSerHDkd`tjHTQLt>TueAV]AWjQkxuu<TWAhy;LJ]]KtdSKiqhDWNTnmaT\\HV]EX`yKrXSN\\wrppuTmQHufxQ;AXyQjxqPFLJUXkH`PC=LhxSsMVDxRX]yTtNXXyDTPAtKMMoNEM^qjDEy:tmVTKDlqr\\YVUVlEN>LTD\\QIMTdDO<@r[`TlAOQXJDen:PXc`Rs`U<yS]MnqpYHpqjqLOtu]]vBISvAra`UdDvuqMcMLmPYuqL]xph<PMlPB<PsMY^uQA`mv@YK@MNDPTquC<pD=ldUsrMORDS?dn>=PwDpQxVxHxIImXXuAPTHml\\EOiiy^PXZeKm<nN\\XtLm?iRGirEpLYyOkqtUMmUupt`nc]rNaLVHQMmM^XLw<t]um?pTaEmItWwukEUSy=rPuxWmpttlSMUwPrGYuQ=ub]OL@m@lknAOsYVZeUh\\YrqJ<=UDeVAto^Dr<=uOaXTPjteXilmMENDXN\\@P@MQCTvMmKxXQDqoCYXVXYryPSYqeAuZywjIjxlXqIL?@Pb>x:G^@fZ@inaYvNyrKgpK_d_PctWxDNieg_iXdd>p<o[FYrpxa;w^QvZLOf^PbEGaNipRq[GovAPd;@uPfZcAbJ^x?GZuniIoZO@k@PiV>[JNd[hk`xtdGdWpm[wwSxbsVyGygm_xcxfkYjLqpR>_Fwr?fZI^]UY\\mhm<GfaHopvmFY]GHwoGutgvA`gvwxIHkYIiS@^cIdWyhRfdgHZ<pc]WkGXwQ?wwhymokhhe]_mNvbDiwL^ssqbqXtliZwqckIu<Yi`IbB`o_>xOf`[F]OQjKG\\JO]WH^Rpm=I[DAsVYejIsFHaUieUijj`ohPeXAi=A\\Ai^hpeGGwnO^<A``NkLo[YnlFhksXjHfsINtJ>aVpyc_k[qslYivavGyi=wsx?jY>jeYc<A_^GhcGlEwlYQnMveaWgmWZAotRFoGGhgQyA`pTYmrGjZPdm?dh@nUqcCSkmx^ytSyiaIVdgdtkgeYd`kbWYiqQXjutM]etKygkEtKx\\KRplO=xJYYnkuYJ=K=PZI>[\\?iLaaR^ZgNrk?d;G]cyZBF^KYgE?fFqxd?eXownxu]@frxm:wad>`JvZuNqRvwF`\\^Xa>IrHAw;wiuXU_hf;riUxMgXVcbZ_D]SipQXrYsYEvfyhxIGmyrIMTScEU;C<oya]Gb;Gr=hcygXqwRShfgrTURLIWmOytySs_yuyy]CvOyCjUdJChtuBk_YUow^qWPkwVIvWwEvyFx[yhyel=WkQBaQwxkgDQT?obQqxiQwSAewgBwIhaSiWOUbSS;EsK=SCcgGgChwitYD^asXKGmUijQGOIrpoBukYIuc;mhQextOFGEvvIy>gr?AboiXG]Ea_XtCHqmwn=ilef;YHIakXuXATqjANHhjCMLkeypYQvPxpyMJuMI<x=tLQYlrpo=`LhToELmRuokqy?ytrVjY?tbogkxiIIhh_uvpbNfxb`tNftKvjhWeMiw>amxFyLv_wvyu`qjiviWpiwwKOcha`ap[yWmMyrxWjWY`I@ZUyrcIbvneqY_?xrZ@nZIZ]xeiHqYi]Ngt@GlX?jjge>XvLp_YIrfgo;?uEysFGy^fayfkpYyL^xeWcaGw@WrKhjWPn[qgk?tQfZ=pi@^wfH]gF^y`f`yfKxdSN_QyrRxawok]ysw@s=y_xWfa@^ra`I>f;Gb;ynEoeTp^TQu^GyGQdhxi:>ZZ>ZC_b;_dOymjIryQxYYvnppji]APleAvZGqnQyEaynipqIedwj>ho`VqOpvkXrM>g[njtNqIfgl?wtYvfxnwqybGlHQ^YpkN`lwwldOu]YjyWyyVdTPm[>ipymZAyY`caYvxnr^WrVgo`Fumxbkoyvprk_^DG_LadKIwbnivYv`vaxIh=PgOG@AYSud`yBjmX`IYxSFOIE@Mb=]WhwU:Yxe?S_AfVUrBAi_MYXYBeITeGyVaitOrsyXxacwSyaGWqOi>cE=Aw>]Sw]u_oTqAixeXMwdyExQ[cOqxmatswWkAwcyVs]v^YDrocAWvr?B=eIjKChiF?]rZ?fZIR`sSeKRB[VJmRPOgrSVM?uXUEw_XE[XLgfWCIhyRlEWuyFNIbyAfyCuyAsgUi=yfJySIKExCHauts=dysgEigooFGMVnGhF_ws;rXyGwSrcwUyiGpeIvmByoHlWFG;vM?UkWGb;GracSKs_KtCMsTYuiGXcyuxYWFieeadWCSZ_Dg_rjIReKvOgcJgbgonWqOu]YCYtMhVH\\TwxkgQjhuwt`xiYP=ux_UkPLjNQRCESVDla`QDDSeht^xnoluRaN]XqqItqHPIdKDuxNDN:iX;MS;yxyxm\\]kE]L_ET=DNnDWdHqpeo;en\\<mUXxbxtW\\pxxqmqvm`L\\TQrpJ=@L<TngDVRYv=YoiPvALLYystaLN`qdLmXDTIQvrPj^lpfeoa\\pTdQ\\AO_DkGlt:XwCmR@eMTUUcTWehM`qnHXXrArS\\Qq<Rcdj]Pp`@Y=Il<XyoAMw<oNLrZ@nZIJ_=Y:]L<=NvtMSMO[PwMDmSDQHPPk<VF\\nCLny`Xo<UcxLYDUoUMF]ysAwCuXR=JR=sMajlEPZ\\JptSO<PTAVfHrZ<OIesllY^aJuxswdsxxNYhVYYVIMTW`mHQx<upOArH@w;Eb<xsAFeZO`Uvhtvhh?pvYviQppYjyfnhYqN_e?QifHyZh\\kqimNf]F`^Nujdr]IxCT`IvKABi=h:CdaWRlWhLIupAY_uhu[hIcRlSyw?Udoc>iT<_rRMVGCTfGUUMU?]deacX;I<wTggwBSIv]XbKy_mr`_WF_XWERc_FSuUQagf?STgSBUTGghcKRRkTQUIf]W>?ih?VxmIZ]V>IiieCCYu\\=VrcVfSIxqc]AvdODiiYjQGkGW[AI<ssoIdLMVB?c=awuOSMUSRibPqTLgH;UHJ_rP?GlSb`?WGiCGqyWycl]yjIifKSZeG<=sIofcgDVYTX;rZeT;ER;qCtYddUVJgfDkuXWbBwGyQCHauXMYiwyR?y=wUJ_Uy_dwstiSFNOsDMbTUC@AVfgsUcCoigwmXAisxwR[wsZscqwEs;sw]B<UEfMeLoRKKUd[VcOsvIua;uyQvqCevKYLOuFaIHwEnyXtYtukI?cB?setSrMwrrgtZeygyTcmisYHd?EdoiEUHHdnWDXchLmhlb]lJ\\ksqKIhk?\\mgXyNiU?=gfPZchwIObmPpAQuRIn?^[UygFvabfpVy\\Kn`Yvr>hpZOx\\Y[D^t^xcRae]ghci[Pw\\IWdWhi;Vg<`qBNZSYklI^i?`pixe>^wYZSqmjV[`qvNvqqYihvhhA]Pyt_Fd^I\\@p_SadFivOxdTAeeGdDOxUxqsfsrAqMxcxWpINxSws=xpGprP`dA`jkWjrFg;n[OPt^noMOrqQsFysXnv:aym`EaQPiTItRs<y;`RZ<KDQlbLPBEK_Qm:eoD]nFqKLun_HShxRnUu@HtCE[r?c[pZ<>bDycLa_X?ta@\\@f:\\MKxoPyV<DNU<QOavflq]QN=PLHashLnqyY;MqnUMwHq@Hk=]WTPV?mVFml<=VlitQDOtyN>qySupyMjGqYqpr\\]WPuuB=U=htS]j:UMGlkAxUYTnpdPEEYxuOOhYAHmt=wFTTalSKmMY`rgtTxLlE\\UF<x?dJYXVfhJ[DWVAq<QuEyQZ\\qrqKoQS?TnGtvUHLQMQCDkoHqB<pV@os]mbHYFXYD`r<xlqdQNAUJmKhen<XUgHtUAuZLwoAP@aK@yNGuQ\\=PnEsA]M]ERe<kDQjjPnBtKt@O]@KamWmPlvukcaXNLts]Qa]MAeTJ@qR]O<QRpYNUeJsAUiTrYYNwAoilK<@JXTYFIvSyV]lppPP[=LAqQ@arBDv[eWDYoipXcmPiATgPQveyeYvFpkt<O_<llxuO=ymHMqtj?EjpDKUhoeaOh]qHqVuQKbQLupNY@V\\pYBPXjljailrMvfyprXpvIJGixqATdXrBAoEXwD]MQ=l?LpmXXDXwC\\p`=N>QrXHVkqV>qrdpV\\]YHtsgdLXMjIEm\\dlb@nZYX:ANnPSP\\XQpmI`MSdrShuEXPotjFLO:hRqXmRAQHQyW\\Kdtj:AnFLwZwfuvuPqfi?jGYa]vfcVbsw`]WfmAtwhrcxkKouoxkSxrXpfqYhYWvJyovWkCYfIVdTvm>GqhwiehbR>qZ@vEFjW>[=htQDLQY_YyrSgqGXDeDXeubAXwWD]=BasEdmcPaIxGHMeVp_v^Ed;;R;KRD[bPadaofRcylyTboymwy<chl?RieYW_HHWhXCGSYi_evPwbiKDBcGkAg^ex[ub?yv=khXgGMsejAdAUSRGeN?tyGSQmiFQWrYBFoxkEe>MDZgSB?D@CFVKhwGuXEiqkRaYD_qyrkxICEEaBakSB]UQ=hxoGSmUP_rkmhaQRR;BpsHosIyIY=pKO@mYxxc`TNqkLyoYhuRImwmvoioe\\qyUxIDQyUyqIubqqCioOxPrux=xq`EYoqJhXvlDQpXkcIww`xtDKqlWX]VgUvPdtdeKg]KptkpaxtplGitNpV]LnWqW^mUrDOmPsOESIhoGqKIuQxYovTx>yPRXmWyjGYQbtVAAnrtXvMlNDL=Pj<xsUdynDNfLRD]traL;ImaDXquwa`XpIM\\YwQ@kQloMpogTlhmo\\xpp<pTUVMaLWtRRTnmpUAdy`uVpxuMArZ]l=loALS[N_rYnM>aMVtrXlm`dqy]_PqiA\\_IuW_l`nnkYo]>c_a[FIt?fZ?veJnZs^aLf]A_hhnq=huRG^Np]Qp`u`_nQdVaiSfum_^uYsXvsIglSVhONc^WltglaImEO`k?^GOkbgg\\n\\iXnuhwFys>qhn?nY?^[xexGuRV[KhnuV_SWyl?jx_n>fhA`dAa^WWcLV]\\AsJapPprTqZ]YdGotsyqKovu?cD?cc?xvvmWWtaH]e`]]PvX^rQWp:qhDWcyYnT_sH`yqyqS`wkPgOOxOyoTsGes_YsDoSaObkKeFMu^ebUktPaGyQxYmu\\ihQqHsigYQe`Igaor@CirQTxMuWKdqgGZIST?xpirySvtQwICXdkdleV>?rq[ucuXrsYcyBVAimqGakcwudCQsM_Ew[yJSUgwU_ixqQVPkWg;HscU=EIP_HOaB_sbMsFHWxoyvyOs<QvGkGWmYUgtogBNOXRYheADIuIkiCHiewEbwWYH_vECS?MEKyf?EFFKCDkII]C@csv[ChcFl_U?mTd=IMYijqCX?rSiX:sxHiH\\ibU_feUS^WwEAopDWuhRTau:urklTdHjj<TP\\po\\nTUNDeT^AsbLnVeRPQwrULm<ymTqClvqQTUyXRPxvqWVtQ:=ov=WSLWxUTF<w?dJY]KfdyNYR=UyHiSFQrGLnHUkOeKEdqRdN:EK;etK`wgTqVHMG<mE\\MFmm@AOCqn\\PlfMpIPlRpWQpu?xxCtlQ@wg\\u;`PGQtZDp=HpdUqeUq_dLJdSCMUIAyBXPO\\qcILFMKgioOLlJ=L?pNe`j]eJPUWthNJPWKTWPHPT=VFhRaPlHMX?HocHQdmyKMs`IP`PoIMx;irq<oNUsFqSiqV^pP;HtTDOW`u>dWhQPltWA=SqxtB]JmXpjawmPjOhL;ySxMT\\ioq`OwpUpQReUNFHpVaqc=yexqdEnN\\rkMscXTOmRAUJfhuhQvjYSGXo=UvmyuBmqYiYLaP`EY_qPeYUe`SQhLL=O<@RlLQ[HWpLQfhWVav=XOU]RGYxfimwtRVdRrPo>QvD]jeqJrmq:=SEMl^<QHMrhiuuHYnaxm`ohhqBUnsHj]`U`lraEQl=wKlrAyVjaUyylyam?tyZLK[=TJWhCwag>oYom=af`XvDg[yAvk_uWWYoUQSe@AfoCxliW\\ifU]RqmWZWrhKrkQxlcfpSS[KH@ce>AI]Yt>SxuExaqx\\qcI=F^WbniyfWcbwEZSxNGFe]SKEWb?fZYcDmI;yhtcfmex<CtdQFGqWBqRd;tPKSdSiXyTpEIwKEj=f\\iv<=r\\kbT[doYxvibN?wrkFXmU<uGVIFOCeKgTCEHbYDJyxS[xUwH`cT;uvCABuAY:wI[QfFgfQcf>eI=ugECXRgTyGCDMdlesS[RqchKafCGFHgGk=gSQut_rWgfEACwqGnuu]AyxgFXqIyYVvsh<as^IB`srqETiwtSGevkrBeWVsRs]WQuWByCAmYvkbAWRQib]wR?siwYuDWrAgDyqwYiBV]ibGuVah>Ih:EgRsuQ]HTKeQuUgABccgP=sSYh]_SHmdjiYogwiSE\\yWX?RiUYNKyqkyhGspguhMYm;SgcdLMVLAbjggbahLKb:iroEfPuXS_ehShH]SaWt`eY]EcIsGXufTEE==s>oUAkHPMVDiHCWwcKvbkFPWwfwWWavCyrxGs=uFXsrRSbZSwkAF_mWtkyAMexWCxIxNKrZvs]fiqXePOl=piCaa>@bri^Nx\\ZV_]FiOQdSHyKnn`Ixpw]<a^kNbcHrCas\\>p@AfnpbOwbjqr`>hAq^Jgvdop>w^:?cohiX^pUYyZNyuQdJ?djir<QjOI_CQrGOmUX]fxx\\Ob_Ydo_^chpNieCIxTxsxQpu>kF>_shqtfgghrFvhGol<V_NNbd^no@_]WxNXnF?[nYc`V]=FoEFshwZwycd^ddq[PwnnWqU``UI[Wq[nppL_ok`tdq[]VfHfxkv]J`hTG\\[wtJvBqGk[ur_fCSYkcsgWwnWEQ?IsmvOKSoqCGiCrIweMDAeTsKX^ADIgIviWXkIxaDoOw^CW\\=HT[EQETlYgbcvl;E=GuXkeeeHCIgMMdMsF:[DyEyQgFXAY=Mhn_fJOhGWv^[TdKcj[tvWxH=SmGELiw@_IpAu^SXmeDDeFqSgbYxqgYGsXAeBfgsD=s<mEs=VUqIk[cbyIQGFyIe?yxD]cQqCleyHaFUSgQEgPUB>?drkg^]X<IrRSR]eE`uv@IimeVGWIqotCKSHcfLwrTQS>eIk=C<_gcaeocUhkYrqFYeY`WSgOIH?X>miYmFySxBORN[Y@[D<AfZV_=po<Qfj>sInd:`oGYcmif=nqun`?X`pfZAnkwYZYY^IP_^I\\<F^_wu[_iIyaHGb;Gr=hj:?vtPkpH\\>pZNXZlvc]NaWw[RYepGhlQhAqspYk@fnJH]px^Gflafl^WuKppYOrnV`dVgCFg^GtMN[mOsapqIYbpg_wpp[^w;WhMQpv@]LYgbonqGyFhcs`kH?ibfnBPicFc\\?k]a_T?l>qjOijRXsiypbog`@e=niZFeT?glQrSI]>I^r`yxWkEywiPxExphApvHhXfwwq^]W^A>eW_cb_g>asiqolAtKyolneYykNnuAokIo^^_[XxnrimYIdfIu]>yHyh^vatIl\\Gf;IrmQerncF?\\BOs_AjbNpvAvAf[pppLnsWX]aAsKHd@obviw=vxqQyLOpdihPAgfO]]OtnVe>I]LnZpvuVPx=^jLWjugkPAc_AhvAxm^_ixe`ayoYwnnr\\_nD>osqa_Pp^`eGGk]F[PnfqalCO\\CWqKP\\oWfVvc<Hjb`gJN\\La`\\QbmiaTgwGo^@yfk_lEo\\SGl?`]ra[c^j;Gb;y\\CpySox]QtvowHV]y_ggoqvyrJg^]HbN?nJVZ?fZ?Fi\\fqoplbhtZQxIvy]fs@WZ_QabFZHX^s?o`Yh^PwKGh^An<FdygaWQlqybCyimnl;wmOflioelhiK_fxPZCofRolP^l]>xeP[i>d>ho>pgAWpsHmj@i]^f[ikHVv]p[mvfe_cgQxKOZ\\A`[^w_`pUH[UW]cfw@OcmW@oYcwRTSUDidxEWa=WhMWPsWoAESSXb_TWkCXSE[MXPiVtmuaGVx]sTQsIGWo_Hw?UMQUk=VfyFFuraAEmqe\\]ilACLEgvOBI?RDsBOWyk_IYkerMRj]xbOveyUqEy]wIlIileRL_Fw[UqKRDaBAIbTeGZUXMQxXYYU_WhmhRWemAeSGg\\cfZ_UhXxvhMclRLmv?AOnM[gWtxHi?puli]\\hjU`jqn_MnuxpklQ`KQti_\\a__RfvjnxbYtrVvM_Zux[jNhnIfN?\\Z_o[wxhXZvNhfYof_`hGhoQtqAatOfXVog>c=`lSW`qhso`jLgbLoobbeGD<[X\\EwnOT\\?T\\KxXYe;wVtIBF_e\\OVWyVGEFFKCDDTrAqNqmgAqwAtMdwp@OrAkr<sMUlfATmhm\\prnER;ErJDY<=KpdSbaoiHVoMk]dJXPLF=qDXJOtllXlG]p?Du>yUfAYwmOBlj]hmsXyZ=UB=svenUMKJltHLsiTOCLPiXjdeKnQq@hxUILetwpEkitRFyyHekCIyfejulwSLnBUtRQSRuUC=tchNGhOeUskltTMSOEkLEupejN<Qh@nWaSbmW^\\ohdrbaL`ln=LsOtjbLKCTYcLuT]jl\\pullUYkQDWpxTcTYiITkux[`l<AMExvclRdXXFxTHETmqS\\`nAAsB`nPUlNYwLHtKujOiTGitepOqxWqEWoPRvtO@EoNTVndqXhVmUP@IX<]ogIvr<vuqQhmwmQP`TmguJ_PLH`l^TUeaPilqEMy;YMRYSiUVpttjDTBhwp@pLmvAeqi\\KflRBmPPtWZ]yLLXfMKyus;]yshqFhQpaPohYA@Qv=vKMuWiKPtYjEj_hj@TLMeN<Pp=lLVtPuqP]@tZ]k@MS=hpLdv^umwdS^DWTTN>`ViauXLs_POd=oLYT;yVEENFLKD^wF`^N^\\NBy_GP;h@Sd`;GlgDlITQEhyOvLUX^AFq]iiKCpmfFcvP[VKyc^[v\\?BJkHU]eJkTZ[R`[DlwtIcIasiMUWEMeRMug_doYEKcgeID]eTAgIaWGNqFV[BJ_rPoXMUht?EMAuB=TD=d>IuX[cFWIS]h\\weh_vB[yL_VeeI_GhKOhkOD]AiLoT]CFHgY\\ATLsxV[hHQfiOS;]D?ah^QDW?XOgTmmEe=FGeC<MCdihcmV@yGjCTs]dDWY:sRPGdD[eLWrSYXM;CmKsgYu_mWWaXSeUeCtgqb>ITBwvA=yxMbaIWFGScuh=]gGEwUoegghbegkKU]AihKBE=uRQfoUvpKVeWrRQwdchGiFvEGl_T[SdOGSoGY^Gr<kReMd_We^or\\@qFuv<YujLQCUwTiR@uSylsrIoAIQt=xkmSVUyTtwWeyM\\nBHMSds>Ejk<v?LL]HRBtJAIjb\\kCUt>hWCxJMXvMwxbydbpdeYjbFbKf_rawc^J=\\SHn;?qRnkEN[DR@?B^OrGKSrKS\\QEROxOSx;WHr=iykvFss?Sy?attqCWEHnGix?bR;c<SuyieWss=_GL=fMSSVKETSEcSUqWVFUtjSyfecCiyxkgiCCuKeXuTmghX?ht?DMYwd]fDQImqt@Uhd?I@Au;udXEg>kii?US=cbahoKRDKsOEC<QDpaHwoSpEHPQvsMdtAcAEi\\IfNgRaOerkCCWF=MdRaGDEtbMtfqUaEgtQC]kwc[EsKb]QUDefLSvOYfN]u=_sgIeauuxIHnMT`UVmkfkgDMsFwKvr[B\\[UqcRDeSiWu_kSLKtncReeSL_F>IS<]D@_R[=SVof^kYW_XqIS\\AI@yikqGoorLAvrwxI_XyKWZgDbss?ihJOW=MDqACiuU[EyTiRpkusecHYcq?EuMw?kSWKYPWGqou^ghseE]MFDiTQCGmsICwDBkv`mx:arBcsPqDeUEE=GcCdLMHlKH;YFasEaibisYEOTcOea=fgag`aTjIuJ=C=Ob<Ob<buURysiWMGVQwBSfAqE\\WivubT]t[MrqETsuf\\IVYErAaW\\uR@UvHwrhqYWmUUahi;DJ;VogRqaCtChnQYTord]SieF;YSfSFmoGx=fl?W;]VcuHMmtPOVTesNgx_AedAc=arFWS_ofBSi@SV>KIo_R[GfQISciXl_YsIdKaWtaTeWIFwSs_xtOe@qV<=uo[B_Es>ad\\MXdoSZqSKawfGtcqgL_xNCTNgfdCU^kcN]fkWRN_WkUimyd^Gg@UW=_DDOSs]blEiDIbCwu`mixQF_uWHGcc?ecGEQCG@EDr;dQOdpktJQWnCSFgFhaXbaWhWtm;dBcRNiWMkxt_xtgITicgkHL;iskiAOt`QHMcs_]TXCF:]vAOhY=cBKhHerP[DP[UACvt?ITQtwgYGWgyyvyorwIuqAesyVygs[YbIMxEwhPCwoqHR?eP=IhgrTEbaYEXcImaGaocxQEk]fsuvwwe[Iy;tr_ArxXvVPYbIODER_@kP\\ua]L<AnZ@nZjZquKxLl<lHXrbIj]]WwpxQaTMpKOtR`eN@uwCYYviKqIQ<lPoLyGAlbIPYpTAUtcIMdpo\\uxXuksXt_=lPNl_ArqX]ThkO@m_YuKnoa>uy_n>IxmfdNX_rAxWq[UV_Co`cyuB?goNtv`rcXk]Q[DgfCarFxjeI[Ppg@``qPd@obWn^a_a`pvv_]AW\\@Y]>IdI`^<peif^fQgVwdlN``Q`lNw[IyD@aCHpcg\\WN]L@uLd[GhLCvrEFWoryYsOAvyCbgCbJaBx=rvatSmfAmE[]FrKcioX]ccZoItkRaqsGKEy[yHSwyKyEKguwxMuYliFRyYF_VlMcbWu[[eTofuEwLcfUwDbwgVArAQdHCyukbGyu`sxh]CtMSR=dPQFk?YxwcOQeXitE_YjyixYGPqSG?tfeHJqc?MsBOT?EvrkCWoSIgvOYw>uBT_etCyOkCW;ICOTHmVJmXv[Iy;iQsYCcBqAe<=EN[DN[<[Y\\;C;ki:sU`mY<SVGKGICCRaIQayhiX\\Uyq[RE;VboG<AX_aH;mtBCr<KTZUDEgiX?dxiRU?Xq?FBCf^[FMgD?wHd?rD]X\\=c<URaggceHncuPoV\\mt]OUq=EUOxbsTNcupofsgdLIWdMdRAHwsvm]yneDQydroe:ix?kt:QxW?e@qRDwUL_SiQxSguW[V@qvbkfUYwKQW`[WgWWtgWGWvBKwMKdtAiIehV;VG?fOawK_RUiuRgcCQXoYSOcbKcWtGWISd`mu>StN[ggmu^OTtIC]ih=_SG_e_MfxmCpsTS]yHyXSAy;yC[exPCtDiGVgfU?sauiCoInAHGqW>itqsU]QvesI]YSWWuFGtGQsrCuuocy?ENkdDQTp?hBMhHStlsGOSwB;tLMv`OEyGt_MxWAeTWdjOTm_WbabT]Wk]IEMDckWXQiDihSwxsSXliF@qRaSxdESUiuZwhyqSD?W;iy<EFFKCDKCDBhiILEDF]sJmgPEXtWERSWj[VOuWfmuy?rHKGHcVViTYcWAEbngE?QtfAtdmxZQdwaT:wuk_ri_bNmD^SheQEWqB_IULob@=E?GSgCX^=c<eSVcVw=UdYVHcvTOsd_EC_giEB:uh]GD<=hqAXCWXIitCMdVatVaSSEUB?uVecciXFStmqIMYxxSF]oSXiISUtd]Rfwg>aHq_HDEC`sVvkra_IDiTCgh@?HDaBDuhWgUECGbcdOSF]oC_Qc=GhP_HCabCMDaUyfgXUgSqEegotgKEWYgfwbQ?DisGJIycYURWUE[dwEcMIWlGY[iWhuhMkHauu_GDemWwwxPStGgR`UwDOSSIrZsI`wS>qsTetqUYq[VXOh_cb:ITD?RbKwUGGueDnMTEQIcKIo?YxGFGeBwottSgeWsbee\\IYxktTWivcF??Frwub[b;ER;ER;rwWFiYX\\cEAGd]sFcmSIQFpsDKQuZgd>EtiMeXgdRcHPqvwOCxKG>KhbIR`=c?qv<MrhuI@uyskXuIIh_BQCRvOgcwg_;IcgfWKU\\eVbqUEGcIOmsaRudSlhk>dVCAyNxRc`oBMVEhrJlXmatX@uJeos\\shqxSipy`RqXlSllQyT\\mtPPVpttL\\UIMPxdwllPcQnV<KumlXurjHpdxJ_=Taxv=lXY<Kb`tlPs?euHuk@UO[Xtn\\pTDOPlJWAmAMwhLTBMqWaljxVCPYS@O:QjY\\lj]l:UmBhopiRppoW=ryqUMPs\\hn\\IQrpo\\dRjEpOIvGyTYUV_DYGTkZ<k=mqk=VVHuLXkNPLm\\VhqMBEjvAnx]Y?QwxxLZUQg@SBTkLPlWIk_UogEWBUR]dprqm;AWG@LL@QDuJHTXSxlqpO>DrwYSK=jv@nZ@nZRjusJcy`ybLETWyXBsWpuH@YCBWtNcS`KCnghUytnyYIQIcWexiWlCTZMXk=tIqDTqcn[vIgv<ERaitFoBkyBQ;tS]b<UEEMul[xx[cRaubAtcar^CXpCtPMSZIyL?f^CTLEd`CYyUbJADpeHR=GQaDoGTA?GDQT<OuGad`qV<QuL]sWWW[keiCeTWxbotNCWhmTh]ga[Wf_rnMeS]hZMVTisvCCx_rbUSNihnoHGSsECDGigNstM[cIEiFoS^mE@_RUKvBUD?GUoafjwdSseAuF^SDmoG]SV_[iXECsieJOsAOclMwLMx_KrRmqFDycqR>QT^=kMaLYds]XX]]Mgxljan:uvwmKp]R\\MyAauhUKlhmIIsHHYY]QBDN@duahY[<uWTSpaP?DWUAthMWTesNTmt=qHEM_Pkcqv=PRkiSO\\LN\\LNBh\\o?EYxTNaxm>ImUYSNdRb]Jchs`Dxtxu_ut`mL;Hr?AMFMlZMvRTVlQqtax?drpYxghJ=hsiTupTJgeO[pPnULE]VfDok@UCDSf=urUqE=qVpV_Xy_@rk]MddTITW_dwPMSLPM>`jb\\tbaQT@vtMjKHT?Au^XkH=RaHUS\\tHUPmyN>El[pTQ]lDQK[DNGhOwpkHQNDTskdo@MkYMTfqQJ<vrDUC\\tb\\PfeW^\\oh>gqf`;Gclvpa>ftosa>[>ntTNnjfnWQcSAeCaZ@_]SNsoFk]`^_PhSvcuariyhcpeF?_e>]oi^<ArOpgFykPQqbWgk_jZOajGi\\OnFyoHallvi:AbnGpWIwr?wxpyk_]VvfhQ\\JvhOXlL^fw>\\dIoZwgI?`Yi\\b?nOQwlxfQI`XNaki^VwrAavwQ\\DnwiO[[?dJCNBVYI@WE`KC;eyfYdNwcYGRAcD\\?I[ChpsDAkHQ;CpUUb;EE?gNEXpqwAewy;ChWI^kEtQF[scp;XQ?UjGeB;cFgfQwUaot\\gSpauNUUtSScsHyQh;uxHMbLEGXefAeVfwRsoE\\eG^GXDMDA]RKgRe=xwaghqYiWVcmWc]bn=SM=c\\SSNKUnMWkYSLGeWmIX=FBUXiQRaggSQuF=UtgDKoFjkI_QTYssxSSLCe;EYNifUEDeYskchKubkGGQOT_SePgrKgfsGdjohRStguV<IVdmsaMV@yFb?G\\eEMsGn=CHyRNagZowbKV]EiVqcsuVeKRJGYEwf=crMSv_keY_gJeTLsR^uxaeC_WhBtNqdLqir:mLCHpUQvetkhaK\\XPpUyohYyxJ:LLDqTjTuM<qCHvrItMaY_IyYuvnYNIuV`Uv\\dkbIjZ@xR\\LN\\LNJVYTtYoBAUExQwtR_arSLnEtWKdUtuJ_aTKlPexjcUxdxPLqV_IX^ptBPybLxFYVBHsS\\xqmy>TpxpmsYLrXUF]VqxJc@S^Mj]lPP@SaMnZxYCMXKA\\FVgiphBVuTHyaxxk_vBI_`yrgfswnjWY`IVDqtbIxXceHQF<=CvQh:YG;=E`[gf[Xr;XfORVCELAuZ]c?IX[OTM]T@]E^?dbaFMcCwoc`guJaXTEG]SVHcvdOrmiBWoh[[CGcsGadOgrBgt?AcZ_fROemIgH?IBCGlqWFIGeWckciHormiF]WDhShu]YdcD?MfgCvD]BQWYNyW__tEMCgeGQYICsTtCCWcWlog@qBH_TwkEcWyfQGs[r`SHSux]cGPMSvOuBcvAue:uWhGtxoXOoutQI`swoCHJcBfuflEWpWfqSBiwrZYSQ;S]EgA=xnqeAAYnYwyGr]uUtEckItc_iEgX[;CX[BDCVJ@nZjZquLXk<\\o?=QXdv]xkJlQviNptOwXSfhPBEkolLe<RCAtu`S=<J:lKMaN\\@NdpY=Ypfds@`Y<TODiLFXvF\\qBLMKHk<TVqMK>`QW=SULp`tUsiNGYNMDSxAq;\\n]DWilj^DSCXnI`m`awKyW\\ej<urjTPkAP[pq;ikoyy:]Lyukj`t[pQdYPkdVkpRLpj_MQgdSVln^Ho?MO;xLbLl>LvJAl`<jBQN<DTiTqbdNb`tNdvdPs\\LLCmvU=Whenfmo`\\XTPmShUxTTmpMx=NCPiwpo[WgwFf]g`;>nTwhRfmnA]U@hKIk_XmRNl_`jZQiFgpGNn\\>qWqksPuCHg^Nm:ofMxysQl=IoKvmwf^Af^:IwU^q?>g=NbCOsoQaox^YHbYWqF_pxpBeU?UGo;cD[xe?SSoyiyX_wYGsRIKyYIiagGuaucmer=wskVaqC\\;DSUxsoyYiR;iYGEFFBDBhII<;FIuECkxXKfpmxcKuisYI_X_qC<iXkOHUEep]X`kC>ghBCFKYcE]fyexYCT_QCKqtPdWlAs:mqdymI=yqxWIduQxRALyKLj^tLKDmiDUZ@J_QKpymvTrCxRxps[iuYAJlHsgml\\QPAxwOQpClovulK@RklTE@lpPs^avnLPwhSTpuFQTj]U;xMBMuGdsTQSFup]HO]@S\\URT`ViIMNhL]YTXdpKuVJeJcLwSLQGdSahlSHkaqx@\\T@Mxh]skHnMQSSUUH=When:\\sfQxSdMq=XwDSLLWthMGpUF=KPeKx@LfljctMnPvgAS;<LrLlQlnDaMh@Y>LSLPUExN?mmd\\J<mvmdx^lrf\\u\\dUUEr>ENBhmXXjx@ObYm?yJqIVm@KHTRX`J]=L<MNKauveyaaWglu`MVYIJv@nn<LHdjf<qyIO>HR;ER;EBxNAhpBtr_`Y\\aOMuqmyUmpximyA\\kH=Sk=p<MVj@ovDt>=J^HOnLmRisg\\oN@M>AVlMm`Il<`rLXK;pq:=s?Ej;`RaET<`NqyMR]JDMS^Ht^duhTyHeQ@yoxyPyiOAumvmJeeXhaUJ<VmpnUUVOXvvlXjyUjMYy]Jsxw;MKA\\j[UpuqKihUsyTn\\uEAY_alleSmpqXanUITnPmXlLY`N<TV:Yx?DRsTUwuk=UkkLj^^[<Ad]h`rGj\\pa`Q^_ov;@ktojHWcmHqTVh]YrXVqpiZFxcu_kIWibatJvn@psDObgqdD?p[?empjqp`u?]EFbh^pdqk^IycP[AP_XNd^wr:IsUY\\BGlGov;?fFH^Voe`NyypyqO\\]?kFhbvyygiuw?hWgdwywkyxTYyvn^aFgLpncOta@tLplPN[GyoZf_n_o:@eT_oI^dvi\\iNarV^HidSfmeArFNwbWwo?dey]Tof:wrcAaFAaHAaDxtexpXof^qeefplY_rY\\JQZLGnVOccGwmHgEWm^aagiphy]uwwMXlnI_cWllOtxoeHoncIsHquaad`otxawopqeYwuAmb@vunoWAoh>yX^drngWnttHb?_vHA]VH`V@wsy\\uyeygkCYhh`n_XfdgdjQlTwnZ?^\\N^\\VniPqmhom?yMNmc?enW```e^AuyaiF@vJqeVxZ_ws]>[\\hv=_dpWsAI]i?ttvxZn_TopOY`<>dFXwDNnQYjbxw;_e:Xmjaa<@^:@n>O_UHf[QsO_cXHu?xwaVrTvZ]idhP]XGuaFvQYljYw=y\\\\pgwp[EWg=QbhHmkw]ggxUAuWXi?pt@Y^nwsUhrFIwQAlV@x`faww_JO[pGvaNdNyvLa]w^]j_yRGl]vjmacdwcKOsAgqM^]^X`@`dDynch`;Xh@@n^A_N^_wgq[ag<wii?jY``[q`dpa^YyVfywGZanyOonhAq_@dj`]hnlkA`^`a=Gusn^_hihHmJHfpo_OGy>Gkbxo>_aU>b_hnV_\\:^oGpfN?rAAfG_p?Y_=VpAfltq[uOhwwbrViJgdj`kAGnqxlwxowPsFYwIFtVvZ=HptywFobOPj;@kB@kFhmb>^R`bL`BqR=YYQ`YYdqUxyqdnWuo[=XZIiKgc<_qVfqtWcLAyc`hsnoc>k=HbvQeOG`f_iCw[=xwu_lDg^jokCf]MIqvqlO^eoWtA>so`p@w`=quJx^SIhanvrnm>WumOqjpZ\\fvqN`_HgCV\\lXhbAgXYcyoqQ`glXj@QyHN:[VquSECyxyFcywUYRpGFIUVEWFOOSL]saCweihNKC[aS;weBSQjlrJyueAKD]Tp]Pdlv=Qv`uuA`U=xStTVjmLDiREIxxAJyAR:dQ;tNDDJiaJP`oiILrtRMMr]QptaLWEqN=ue@nlUPXdtP\\rcEs?ewEXvQiqbHsVDV]QPYARZMr<@xr`T^=Xb<k`eKbPyxPW`Er[AK<@jlEPIhKDYVpymO`kGdJ=DLKDLSTUk=QjiYLdogaPVay[=p;dYyMpNxxfaJU<jkQrW`kBxtpXqDQLPHR?urkyuS<UYqMYMb;yx\\xuC^_p@d^fme_nootVnngniYVxhWyBVlhVqVvaS`[QaqY`pvh^H`Zh?wEil>@lHoc^fmfGnspipn[EH`kQbbp[vw_CxbP`g\\yo^_yqHmXqtFWfWa`TPeM^^Ribs>yan[EO_g?c__[sqq:XrANicywIAvf^lDHvP>orGvl^ntqbY`fLYnVOhNPkHpux@j>Il:@vr?bx@]XAwaha=xgFVteQlFQoEOlmiafXZYarmQZ>wmbPoIIpm>AGV:yFH;V[QT]ss?WHgkpFDkryvOUSsPr_\\U=DRglKeEX:=PxxRxxoQPT[@LxYMeEMKAq[@VZLN\\LN]msRTjmaQBLJLdwMIcyi]rGuVv^xywiH[piw<PdcNejX\\XAttor>xcoYnavukikyhhHvsRPsMngIA]vV\\hWidyb[O^viiIvaSpflitQQh_yrhqneqlUIxvwqlWntovovw`aviacVaxq^w:^gFxj;yrtHj@iegFqe@s_ofJItnW^uYuXGf<s^ghcmGreBXQInaFwebXKxSqEdYEfccGESFGxbcDL]xY?hRsGVqSO;CuCHQIyrqYRuUKMGsKc?AhkKU\\?VccdWCSZSvu=IESteQDVEuJoVlmFKkwnaDwwWMcyUKv<iEZoBxCd=IIMcYH?yYqHFcBXkBiKcKkE[=UjkVZws;=IUUrCebYIROYw`Ce\\uuUWIsKYbAVr_cbKG<uTgGRgYTj;DKn_BVfF^^L>fgFopIw^vatw[Syxvxk]xawIZwyshOrpq]Aa^L?iCa\\HykhGd<@^X_]I^jIOrCP[^gmQfufx^v_gs^o]>_aYxN`o]FacXjEyguXjsv]vXlCwdFyrEo^kotHV^N^m_iyIFmO?xG_ief\\@njNOp;pXQITYeiWgvOCjsVDyY[Gi[mGIYeAEHhiSlGWEcvC_XGAUDEtwcRx?XJSWgkiY_FUuDZIY;swVcGk]yREeCcsCMS??bZ_wj<Y_aRnutX@xZmU=MmCEWYtOtAUX]Q=UrZqmLDX]nr>x`yIxlYojon:ajInxG?qRP_H^Z@IdCN[Jg\\HNvXA\\h?nxY^hhyZFm\\iwqneaAtUYibnvmanmHumOyqqlEvc;ABL^f@ikQqaIlfwmHWsawqDoywX_bYi`W\\?hwi>dx^pIVivA_PQeBon;yx]pgTogZXoP?qxhZQ^ZNVytApCa`XgeHptenOeYIQT`_iqYBNiSXOR`Gg?SvuIv_Ufast]=y;QrOOIR]em?bc_sJ]Fv_CMOXWaGSWyYIGXmea;CV;i^cxSGcnaviovyiEryEfqGv?RlSYV_S=uIsov\\;t>uwkQHiaEEYTdKq_AwmXmj<N_hY=aot`LGDKiLw`]MhTJDpuCexuPojQnoiRkErkHkdyNFHk`EK\\QmDPoS`jrmr`lsMmljEOKEs?UQ:eRYevdxQEilSlLStSN\\K>]R>]v<QovDtp<m^MKiMxn\\qt`MCIcKOevW[_hiuHsyPqGVef>lYiy@fn]gaR@r@xcvXnoqwXh[Y@jaVtSOhEn_aVusVmtpshNw`xs^pgDa[TnnoojUygTvgZQi]PqFhvNixCFxpyn`PgqXnjihI`jYwcMgiQVZmA[:n]casG^nMfkn`fuHaJAq=H]MPxnqsnAmlFgxFmCvy\\AijymvXdxWZ]y^kiiAOr>XuMp```itN`CNlX_qvNk;gy<NvIX]pH\\R>eP_htycjOkyf[KqkKWZEOqZn[AFhK>ivi\\Hq^ny\\D``WotCWv^Hc^VdcXhsyrOxhCPj;@kBDQkUvSWJcycyHpCv_qDJOwtOCu]ybCwseurOVK_yhgENocVkrSABQcxn;h>UYbYE=CutKXmovKgeLISpWVTCcVURrarUYxdsH;qFxou?CyRURiug]EtuEHxAfUkXaaGS_VEXmh=n[TXSTlUpu``TdTV=tkChkQXTnuJsUyBUPRynBYqwAYsTSdFlkQZTPlxFeYabo>Z=VaGf[w`hV_jf?a?isygfPA^v>_xqyfwyTGxhgb_v\\IA]>X`BfbAfq?P\\mPaaOtVq`SvsqY_ohZdx_bhiDnZ\\N>_iuKvUcR]=r@eiFKdc[SEUEoeGg=vVcXEsd>gh;SRqMCDwd=AY@sGSogtGxIOc=WvmqtBisb]UY?TwII<yhPkgvyxFMd@_wFKElWH\\we@iyMkFKgSqSdEuS[SeumdZmSIkxgwtCuEUYSwwEieRDAvuCyDqTGUbyQsckCS[xXsbmIRVexqoFdqHw;tNmg^Efy?WCiSfUFMWW:IIAWhpOhVWSdUe<N>VkQyyu@qcFbrXbIHc`FxHAhEQwZ^_Jo`[Ia<qu>VfxqgIYrZy`aOvoQar^mmHfyHjdXfGHxBinaHtOqyiasdwq=PtnXvfaws_lqouxIacOs>n[vV\\iQ`>?iX@iePtdYmrAoA_boIuW?u?Onl@pCIm;pqGfl]geoyw@XaSfdqakj_j?wr?Ww\\pfm?dF>nN__]WZUghN`kAN[@N>Doglr:HM;YL`Yk`IWnIw<eSRLMvTl^DldXNSps\\yNM@ul=MF\\yjhP;DVsXXrtJ;TJK\\rWHwelu<hPDYVO@TJtvmPwm]Txqw@lyaAr@eYFLK;XNY<ULhxclVFiq<pnpppbmv`]oEpq_]pbyycDLKD\\uNno@wOxomh]XviGXyo^w=oaqgvenySxZPQv_Vd^qfFQ^ufpMPfxxm:AmbHwU?uNn_hnshpm[>]T^Z@niPnying^vvBvynhl]YnYxryx\\AFZQGuNNoLAkh`vVfj:QdBNZdY]UFmpVyDn^F_ggHo_aelohDnZ\\ZuPvUVsmhiW_p\\ArMfwj_vs_fape@of@iv[qtZpkDwr[Ww\\AjJfuZydt>cu^oo@uZ>rtV]WAwuHbmPZk?bjGtIQ_Wxn]A\\:flyxj[IrK^b[H^Fn^@Pno?eaY`aGvu?mVIiSFwfgmTPmGX`TOc^N^\\N^ln]>GZ[fasO_SIemGwg_g`@edNva^ivv_fOe@_eA>r:qZd@]=Hc`Vr_fa_Q`h>p=pmpy[>>jd@b:Aliv\\@Fj:vbZae_^kNX_Yyj;W^UXg^Gxgy]_hnwXnLy`<GrZ_yJak;@kBDLUvFGHRssAABSohHKXQmG^cuosexqyxMckqc:mcMoWVigo=va;xUUuB]sSWcS?t>WxF=Im?RnahY?wrmbFQIFce??cxwCV=u=AFBoVfKsHKbZ;FOoSlSVHaWhwUxUIGgGMsG<gvWudXcB=CDKCDKGx\\Kud=GmcV@csEmI:=vZ?E>[dfgCqoCo_RqSwh[icyhPSeBMVh?iDswXyy@MvTiRJuTIgGUMsHaTP?F?YSHOG;GrsOgikB<Ab]OD@KSp[YGYxw;C<KeUUuR]hveFsofP;rFCu[ES@YB?SBK^b@EtMBY?WT?ShEr\\MwQ\\jG]NclJPPj?PnoHVgIj?Plo`lj\\LE^vq_yMPxiyyQfrqvuZ`dfNdpVjioyEqgZpe[P\\fNvQYnWwj<@oYGbSQeDq`F>\\Xxv[Qs_OlCa\\MQq`AhgQpO^^MG_FxvcCRsbN[C>]R>]R@YcbqRUYS_GSIUw^gx]wxJ?WguCiMvggctEC>gY?Kv`WV?QTCoywwWmMvyke\\wWQYeNSx?MsHaTh=yEqXZmRZ_EyIW]IE;KGG[sDoWZAYA]hvGGVygNossyTm?XSyBcuwVgf:=HHGgrAU>]R>]VVKxlGITsdfSfyyEIYtqgxC]WIIFjCCVGH>kt[IedwF:iv\\kgiADHAYRUVj=edGu<GbJ=D@GCQcXnkcxOfQQv_cRR;xFGrAQbG;elSYhsypIru;UjUslKDc_V_Gy;Or;Ay]?VZKN>]VvDP@\\mEtXdes^EWtAvW=tq]mxyVqDvliYrtuIPwE\\MkUV_UJrtQSepmAlg`LMtrEujDmlD=Lb`sr<u;Pq=tv<ARJ@xFDjm@MeAso`S^qrupw[myguM\\HYDatbUYLuS[@VVPTj<LKDLKD]Sv[VX^mVhhfsqouExmGQhvWvIA`?VkcxgBVb:h[=>Z:Xpp^[?^bUykPOiZ^[fF\\dfdOQ]>ip=IhqffYAZXxkGNZjhfLGmtouywyTnfyxw=^v`np\\ao?AiQVcQNwEWl<HjB<aRmoB[es;WFocW`ccEyTM?WX_RYYtIMTtUVu;YXkUlcb;[goGvDsebgh;]uCCYjII;Aib;CR?xEyXZec;QYXktrKcwHOQXJTXQu@wxavyeVpYYYySWUTm]Tf]oSPjkqS;AR>[Nvu>Xa=HcaGcoos@Yoi?^sfh`fyUwyIfjgyi]teAF@qBrEc^;yX]t@AuOMb;Wr[=Hr]bmOB[eU<WrAAvvAHF;Y_QHh?T:QIbWeRqRuaweCep_vPkgruygatqoS<Ayx\\MY]NN\\;KN@IP]IYZaO`dm_DQoQPLTlt<Snpp]ypGeNyQvm`lpqw<iLlAmLEK==UN\\w?US?`mEPR<XXrmOFdJX<LRAJQ<ujpV:YSJhmRqREuVQdsQmXMqxiUkbUqdXmVUUulsdpnZQV\\]mtxSB@kBF]yam=IaUfdCViNx[finyywUGwyowIalpaq;GwJqa<`iYnpVo[Uvmk>d]?`jhec_tq@rI?d@Nj^Om>WgAfsQaqAHwq`o^hfhaiLgkGGd;Nj=fj<XkDPj;@K\\v\\EvV=uk=uSAprDMjer<DrutRbYYhUKwxOwyNwyyVqRcAtx\\U\\dTcqXVmp[un^Qpo]LliyNyUk@jfivmAoUHY?dkmmo^hxdYw<YXSUUcPSplqDdkilPDlJ\\BKWc?]hn;GxqiLEWfeGpwy>CrCWv>ciiAvDgBjaijEIK]xUkGtiDeeGCOy@[yt_EXmFEweHAvaWH=crHItFCb`MChkIDkZBDQSfdWUvsBZeWriemedu]yMmu>kbgec=iUD_c[Ky`ODF[DBkGXMC@KF\\KNhlVkaO<]q><odIoyIwyerOetK<MFHxHAYv`UV\\LFB\\>[Dxi\\N^\\N>?GR;cBDLKN[@N>?cBDR;AR>C\\<Tj<LKbB\\LFB\\>[DnZ\\JKNJJ>?NJK>?>K\\:bBDBB\\<DbB\\<\\BK:N>?>>K;?N>K;K^BJcHXUxPimvQxqvivb`meurHhMfxUypYNms_LN\\tLHAWHhJkdkCLNaTTj<lThpkUv@mMv=x;mQlIlI`kDIy`usXhs[YrAHqyqyuyR_aY\\LNllxHaPP<UeEwcIw[urHhM]lQipr>DlMHMaamuupYajBATyuyuyuSmqvEQUmpfEVHamsTnpmuZ<KRmpfEMepTgPvxXyhYMoXxD@kBAwuduR=xDYOi@pnEwLmkVDQ<hpP<jmEqWHtR@Nl<m<HjNamXquXmvIymIQqoUwReqtexbxmyAv;YjnuXqUpkUv@moupwtHTytqB@kVxqmdk?lsslkWTQ@YtIuQGyjx\\x[Pseuv<UV<@s:dJ=DostUyQyQIuvHYmtSydynAmWUv[xjXLvququiMIqQuaO@AmkTqH@kB`mUHvHhJGeSG]MulXfam=HJb]SJDkcpr:MWDqoWUqrqyqyqIylx`x_HPwpsQlqjiJXmYsiVxMyMymHHwo]R>]V^qRllL^TlCYxxpm@aJK@l<HjNalYlyjyjnFg[gtdhd]OiWplPp\\xfycycmAx=y[IHwo_b>_f^q_NAeJVtR@^LNdj>lTHdhvlsIuIqi@y^yFyCO\\C`rRxeigvDilfWuphkaymyoiFyo_N^\\VrmGnAQjRpr>F\\?V:=sPgGU=uywYysHXAY]AcxuwVutOourUvG?YXwHdYY]UcB?ssWIQIhZaYc]SJCbEsD?iRHQvIuYtYD:stYuYwIUIgyAyIxIrtixeIIkMv>Cc>MbXoeXKItKIr=w[wbbAwbAEPix`[SR?rostVUrPgGUmseiYE?cBAwSCsR=HNqhgUurItIoY>uWiuGwgiw_HocHkIuIqYp=U[SR]MbBOb;_tJggUuhlcYtaxmouRyWWQiOgheutlGV=qB`msVGC:EhR]vxWyhYVXais]IpAu]UrXudteyoytmAu]ucKwsaIs^MHaiyS[R>]vvaCq]GRKwAsIrIBusXhavUyuxqHgggg?RRaEgEulgVvExEwU^YUYQyPIUEcdokFBifHUSC_f`]wSYhaOX]wY`SWPag[UsPgGfMunGglQUdcd\\IdAmE[Gf[GbIeYdYTfyuywYRutV_IsMH_QXSwHYaYmaUYqhB?cFOf[qc?SRwgxPYUvKxBYFO?T:;x[yCy=eYeydyTfWUqoWReCFaH`Xc?VZcH]An[V>ncHocaoAi]v>iJPfk@iLquPImFoj_VcP@tQytAy]xAxAHfWWp_hn?>jWXaqokvi[E@kBAoUnwR?`NiyqyuyOsQydf@e;whqw`yFyCycRaqsWxSvs[H`;o_oO[@NdMNc_P\\AokVFf<ajCvfwnh=qjG^ioYOEUuoXgISySeoSWP;BAoCWKEPiX]IRZAsKWF];YqOF\\KHPkRlkDFcdDefHUymwcy]y]AIaAyhyXyWY@YXbJOAMBeSr\\YrAP:dkGhkaeQpEx\\irflUv@M:@NB<Y`Ima=YcinQ@Qj=v:eV`@nixoi=UQiWhmWXDtkQN\\LPpmRllLF`RvAtbijQlUrTvkMMM\\vLunSTJcHKkUKtQVk@QfXvY]YkiRxDxCxSjtVHaMxUxUxuJitOiramQmIMhmqsqvKdUq@Tb<J]xQBDkB@sBikn]ORlormJ\\Ax[YrfYuqxwnxrc]SJNaGA]BgcbxoixZZAukXfagapIvAx]`IjAn]ZGsLh^viviviS^dboh`Ho^YdCxoqFilavKfyX@kB`kxHlFhZ]FtYyuYGyxfmHwmpAaGH[lGoMak;`t>pj@d@qr@dMFlPgMu>yly`in`pn@xrYvIx[DfZjOhmXp=wjHFtMYtmOumi]wNiN>jppppXhvwv\\N^lNe@XaP^kNIr=xZ;>mkVf@gnH@vN_``>S@VZdP]mtfHUfiuuxxFxrf=ujHJ:xkw]w]unvMnmXYqqw;uYYAqkUNIeQoatcusQtLcTwcAlB@Sg=MHAUjMOPQuMqyfIkalm:<vXYYiiQ]IQnlNBinHEr:MW@Qr?XKSqqwUyZHOYIn\\iXaxntMv]ame`LPhrmtJ?QVK`WpTYTYxwiwiuY]MwNIoa]Y<`N\\LNQlsjmr<XTsdU[Ex;XJA<YlIsaDwhqw`YOYEyDIMIInkDRhdXDlJLUPPpOWMSs`U`irQtUvdwktXWiXQ<JypyoyoIMMnltgXUAQuoXWCqVmhlm]qnQtE]XquXYPxVmsslytytyPpnEwLITtaJ\\LNlmq@XPP\\Ko`YsQXxxxwxwkQxEyOILYwAwKYnf`UsPlHqsHmYxYxYxmkXxkpr>DLOtMEeKshxPYUkaQIxvXXYHhREpLWPxRhtexTM]OPDUmpVGTkPdO\\YXYXyVDwnMmytysysftUx`mutwvXlQuUweli]Y]YMnuh`qwuxw`OsNH_a`aQYwixqHIl]vbRGp\\grRoifF\\KF];HvFhZOQtca`IpatA_s`eHxZY^iJ`htfsLh^E?umxfIvkynyrv`WahMvusqsq?oeXouVvs_``>k:Hh=WoofbXibqxuxWawgiwwfgqcC>pwWypohiquGWf]W^En\\f>]n`fbxnaxZaa]Mv^H_agywixeypmoXG_wUyhiOhMkbB?cvWy@MHP[CoWYqqWXeYoiTtSIuCwdQwd_W;OYpKEM[RN[C^orvqxqwi_qcukwZUypiwFieusXFqg]ae]mxfIuVQYeigvAyAyIXSheAcB?sBiUbGhZkfk@SBEr:MWDXXHXMh=q;XMh=aeytix]mDI]IkaBewTiovowtXUIgQT]CDKCYq]UbGhZ:^maymyom_WsPHpgWupnnGWmpNwayhHIhMicqFhUigqHxoxowggNysiN>IyUSwk?F`R:oX_KdTWXgihQQxsysymeuwwxWeZ;C@eyvYwPiOs`U`IjAlMRdxmUkB@sbAMeIpZlnkDR^=j`]K^NhHIpdgtdn\\f>e:y`yHyGIduvwPh_U?qaqmu?i`Ima?giwgYfpmQkB@sbY]eHpZnnkFb^?`GA=DM]=y?yOxEretovPriyYyYyKEQaqqwUyRUp`eKy]y]yMo<JB@kFXJ]EPP\\rnlNB`mFUP@LTMamm]Mv<Yj]TTYtY@QkMJ]]kpH^\\N`Hak`AeJVtR@^lO`?VZKF<]jbEOK@kB@kBFdj>\\KF<]JDlJ\\BKLj<HjBR>@nZ=N\\LN\\L^J?`JF<@[N:CL<:]jZ:CLb:]JDZ>C;ZKRJZ>CNZKB?J\\^:jBFBJ\\>DjB>vyYZwosdqeHxtCFv:>Z:>ZCgbH_bhPbZOJ::1:\"\{\}<Drawing-Root>LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIjNSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlZ1tGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiU/RkYqLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image><Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="10" readonly="false" background="[255,255,255]" placeholder="false" family="P052">
Fig 2: Quantum-classical isomorphism - (a) Interatomic potential (blue and white curly
<Font encoding="UTF-8">bonds) between two atoms (in green and orange) (b) The \342\200\230ring polymer\342\200\231 molecule with P = 5
</Font>(or 5 beads/replicas of (a)) connected by harmonic springs
(figures taken from </Font><Hyperlink linktarget="http://www.sklogwiki.org/SklogWiki/index.php/Path_integral_formulation" hyperlink="true"><Font size="10" style="Hyperlink" family="P052">Ref 5</Font></Hyperlink><Font opaque="false" subscript="false" underline="false" superscript="false" bold="false" foreground="[0,0,0]" italic="false" executable="false" selection-placeholder="false" size="10" readonly="false" background="[255,255,255]" placeholder="false" family="P052">)</Font></Text-field>
</Group>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" size="10" family="P052" layout="Heading 2"><Font size="12" family="P052">PIMD using the Harmonic Oscillator model</Font></Text-field></Title><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">As an illustration of PIMD, we will consider a particular moving under a harmonic oscillator potential. The potential term in Eq (2) is given by</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">Thus, the partition function can be written as,
</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">and the classical Hamiltonian can be written as,
</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">subject to the constraint that </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EieEYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNistRi82J1EiUEYnRjJGNUY4RjstSSNtb0dGJDYvUSIrRidGMkY1L0Y8USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSy8lKXN0cmV0Y2h5R0ZLLyUqc3ltbWV0cmljR0ZLLyUobGFyZ2VvcEdGSy8lLm1vdmFibGVsaW1pdHNHRksvJSdhY2NlbnRHRksvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZaLUkjbW5HRiQ2JlEiMUYnRjJGNUZHRjJGNUY4LyUrZm9yZWdyb3VuZEdRLFsyMDAsMCwyMDBdRicvJSxwbGFjZWhvbGRlckdGOkY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkQ2L1EiPUYnRjJGNUZHRklGTEZORlBGUkZURlYvRllRLDAuMjc3Nzc3OGVtRicvRmZuRmdvLUYsNiVGLi1GIzYpRkBGMkY1RjhGW29GXm9GO0Zgby1GRDYvUSJ+RidGMkY1RkdGSUZMRk5GUEZSRlRGVi9GWVEmMC4wZW1GJy9GZm5GYXAtRkQ2L1EiLkYnRjJGNUZHRklGTEZORlBGUkZURlZGYHBGYnBGMkY1Rkc=">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</Equation><Font size="10" family="P052"> Now, using Hamilton's equations of motion, the equations of motion can be derived as</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">and</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052">= </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">where </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052">is the force acting on the </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" family="P052">bead. These equations can be conveniently written in the form of a Velocity Verlet loop, and the beads (and hence the original quantum particle) can be propagated accordingly. The next section demonstrates this using a small code.</Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EifkYnLyUnZmFtaWx5R1ElUDA1MkYnLyUlc2l6ZUdRIzEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRklGL0YyLyUrZXhlY3V0YWJsZUdGOkY1</Equation></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"><Equation executable="true" style="2D Math"></Equation></Text-field>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" size="10" family="P052" layout="Heading 2"><Font size="12" family="P052">Simple illustration of PIMD</Font></Text-field></Title><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">
This is a very simple illustration of PIMD using a toy system. As explained in the previous section, this code uses a particle under a harmonic oscillator potential, and its dynamics can be described using the dynamics of a collection of beads. In this example, 10 beads are used for describing one particle, over 2000 time steps. The parameters for PIMD have been chosen arbitrarily (it does not represent any real system, just highlights the method).</Font></Text-field>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" size="10" family="P052" layout="Heading 2"></Text-field></Title>
<Group labelreference="L14546" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" style="Text" family="P052" italic="true">Initialising/declaring the PIMD parameters. For simplicity, all masses and force constants have been taken as 1</Font><Font size="10" family="P052">
pp := 10: </Font><Font style="Text" italic="true">(number of beads)</Font><Font size="10" family="P052">
nstep := 2000: </Font><Font style="Text" italic="true">(number of time steps)</Font><Font size="10" family="P052">
dt := 0.05: </Font><Font style="Text" italic="true">(time step)</Font><Font size="10" family="P052">
kk := 1: </Font><Font style="Text" italic="true">(force constant in the harmonic potential)</Font><Font size="10" family="P052" italic="true">
</Font><Font size="10" family="P052">m :=1:
omegap :=1:
<Font style="Text" italic="true">Defining a random number generator and initialising the coordinates, momenta and forces</Font></Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14544" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">randno := rand(0.0..1.0):</Font></Text-field>
</Input>
</Group>
<Group labelreference="L14545" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">x := array(1..pp,1..nstep):
p := array(1..pp,1..nstep):
F := array(1..pp,1..nstep):
for k from 1 to pp do
for i from 1 to (nstep-1) do
x[k,i] := 0.0:
p[k,i] := m*randno():
F[k,i] := 0.0:
end do:
end do:
</Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14551" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">for k from 1 to pp do
kp := k+1:
km := k-1:
if k = pp then kp:=1:
end if:
if k = 1 then km:=pp:
end if:
<Font style="Text" italic="true">Velocity Verlet loop for all the beads</Font><Font italic="true">
</Font> for i from 1 to (nstep-1) do
F[k,i] := -m*omegap^2*(2*x[k,i]-x[km,i]-x[kp,i])-(kk*x[k,i])/pp:
x[k,i+1] := x[k,i] + dt*p[k,i]/m + (0.5*F[k,i]*dt^2)/m:
F[k,i+1] := -m*omegap^2*(2*x[k,i+1]-x[km,i+1]-x[kp,i+1])-(kk*x[k,i+1])/pp:
p[k,i+1] := p[k,i] + 0.5*dt*F[k,i] + 0.5*dt*F[k,i+1]:
<Font italic="true"> <Font style="Text">Berendsen thermostat (standard velocity rescaling used here)</Font>
</Font> tactual := (0.5*p[k,i]^2)/m:
lambda := sqrt(1.0 + (dt/0.05)*((300.0/tactual)-1.0)):
p[k,i] := p[k,i]*lambda:
end do:
end do:
</Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14549" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">tempv := []:
timev := []:
<Font style="Text" italic="true">Plotting the evolution of temperature (NVT simulation)</Font></Font></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L14550" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">t := 0.0:
temp := 0.0:
for i from 1 to (nstep-1) do
for k from 1 to pp do
kp := (k+1):
if k = (pp+1) then kp:=1:
end if:
temp := temp + 0.5*p[k,i]^2:
end do:
t := t + dt;
tempv := [op(tempv),temp/pp]:
timev := [op(timev),t]:
temp := 0.0;
end do:</Font></Text-field>
</Input>
<Input><Text-field style="Text" family="P052" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"></Text-field>
</Input>
</Group>
<Group labelreference="L14548" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" size="10" family="P052" layout="Normal"><Font size="10" family="P052">plot(timev,tempv,axes = boxed, labels = ['time', 'temperature'], color = red, thickness = 3);</Font></Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" type="two-dimensional" width="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">6,-%'CURVESG6#7[hr7$$""&!"#$"%+I!""7$$"""!""$"%+I!""7$$"#:!"#$"%+I!""7$$""#!""$"%+I!""7$$"#D!"#$"%+I!""7$$""$!""$"%+I!""7$$"#N!"#$"%+I!""7$$""%!""$"%+I!""7$$"#X!"#$"%+I!""7$$""&!""$"%+I!""7$$"#b!"#$"%+I!""7$$""'!""$"%+I!""7$$"#l!"#$"%+I!""7$$""(!""$"%+I!""7$$"#v!"#$"%+I!""7$$"")!""$"%+I!""7$$"#&)!"#$"%+I!""7$$""*!""$"%+I!""7$$"#&*!"#$"%+I!""7$$"#5!""$"%+I!""7$$"$0"!"#$"%+I!""7$$"#6!""$"%+I!""7$$"$:"!"#$"%+I!""7$$"#7!""$"%+I!""7$$"$D"!"#$"0*************H!#77$$"#8!""$"%+I!""7$$"$N"!"#$"%+I!""7$$"#9!""$"%+I!""7$$"$X"!"#$"%+I!""7$$"#:!""$"%+I!""7$$"$b"!"#$"%+I!""7$$"#;!""$"%+I!""7$$"$l"!"#$"%+I!""7$$"#<!""$"%+I!""7$$"$v"!"#$"%+I!""7$$"#=!""$"%+I!""7$$"$&=!"#$"%+I!""7$$"#>!""$"%+I!""7$$"$&>!"#$"%+I!""7$$"#?!""$"%+I!""7$$"$0#!"#$"%+I!""7$$"#@!""$"%+I!""7$$"$:#!"#$"%+I!""7$$"#A!""$"%+I!""7$$"$D#!"#$"%+I!""7$$"#B!""$"%+I!""7$$"$N#!"#$"%+I!""7$$"#C!""$"0*************H!#77$$"$X#!"#$"%+I!""7$$"#D!""$"%+I!""7$$"$b#!"#$"%+I!""7$$"#E!""$"%+I!""7$$"$l#!"#$"%+I!""7$$"#F!""$"%+I!""7$$"$v#!"#$"%+I!""7$$"#G!""$"%+I!""7$$"$&G!"#$"%+I!""7$$"#H!""$"%+I!""7$$"$&H!"#$"%+I!""7$$"#I!""$"%+I!""7$$"$0$!"#$"%+I!""7$$"#J!""$"0,++++++$!#77$$"$:$!"#$"%+I!""7$$"#K!""$"%+I!""7$$"$D$!"#$"0*************H!#77$$"#L!""$"%+I!""7$$"$N$!"#$"%+I!""7$$"#M!""$"%+I!""7$$"$X$!"#$"%+I!""7$$"#N!""$"%+I!""7$$"$b$!"#$"%+I!""7$$"#O!""$"0,++++++$!#77$$"$l$!"#$"0*************H!#77$$"#P!""$"%+I!""7$$"$v$!"#$"%+I!""7$$"#Q!""$"%+I!""7$$"$&Q!"#$"%+I!""7$$"#R!""$"%+I!""7$$"$&R!"#$"%+I!""7$$"#S!""$"%+I!""7$$"$0%!"#$"%+I!""7$$"#T!""$"%+I!""7$$"$:%!"#$"%+I!""7$$"#U!""$"%+I!""7$$"$D%!"#$"%+I!""7$$"#V!""$"%+I!""7$$"$N%!"#$"%+I!""7$$"#W!""$"%+I!""7$$"$X%!"#$"%+I!""7$$"#X!""$"%+I!""7$$"$b%!"#$"%+I!""7$$"#Y!""$"%+I!""7$$"$l%!"#$"%+I!""7$$"#Z!""$"%+I!""7$$"$v%!"#$"0*************H!#77$$"#[!""$"%+I!""7$$"$&[!"#$"%+I!""7$$"#\!""$"%+I!""7$$"$&\!"#$"%+I!""7$$"#]!""$"%+I!""7$$"$0&!"#$"%+I!""7$$"#^!""$"%+I!""7$$"$:&!"#$"%+I!""7$$"#_!""$"0*************H!#77$$"$D&!"#$"%+I!""7$$"#`!""$"%+I!""7$$"$N&!"#$"0*************H!#77$$"#a!""$"%+I!""7$$"$X&!"#$"%+I!""7$$"#b!""$"%+I!""7$$"$b&!"#$"%+I!""7$$"#c!""$"%+I!""7$$"$l&!"#$"%+I!""7$$"#d!""$"%+I!""7$$"$v&!"#$"%+I!""7$$"#e!""$"%+I!""7$$"$&e!"#$"%+I!""7$$"#f!""$"%+I!""7$$"$&f!"#$"%+I!""7$$"#g!""$"%+I!""7$$"$0'!"#$"%+I!""7$$"#h!""$"%+I!""7$$"$:'!"#$"%+I!""7$$"#i!""$"%+I!""7$$"$D'!"#$"%+I!""7$$"#j!""$"%+I!""7$$"$N'!"#$"%+I!""7$$"#k!""$"%+I!""7$$"$X'!"#$"%+I!""7$$"#l!""$"%+I!""7$$"$b'!"#$"%+I!""7$$"#m!""$"%+I!""7$$"$l'!"#$"%+I!""7$$"#n!""$"%+I!""7$$"$v'!"#$"0*************H!#77$$"#o!""$"%+I!""7$$"$&o!"#$"%+I!""7$$"#p!""$"%+I!""7$$"$&p!"#$"%+I!""7$$"#q!""$"%+I!""7$$"$0(!"#$"%+I!""7$$"#r!""$"%+I!""7$$"$:(!"#$"%+I!""7$$"#s!""$"%+I!""7$$"$D(!"#$"%+I!""7$$"#t!""$"%+I!""7$$"$N(!"#$"%+I!""7$$"#u!""$"%+I!""7$$"$X(!"#$"%+I!""7$$"#v!""$"%+I!""7$$"$b(!"#$"%+I!""7$$"#w!""$"%+I!""7$$"$l(!"#$"%+I!""7$$"#x!""$"%+I!""7$$"$v(!"#$"%+I!""7$$"#y!""$"%+I!""7$$"$&y!"#$"%+I!""7$$"#z!""$"%+I!""7$$"$&z!"#$"%+I!""7$$"#!)!""$"%+I!""7$$"$0)!"#$"0,++++++$!#77$$"#")!""$"%+I!""7$$"$:)!"#$"%+I!""7$$"##)!""$"%+I!""7$$"$D)!"#$"%+I!""7$$"#$)!""$"%+I!""7$$"$N)!"#$"%+I!""7$$"#%)!""$"%+I!""7$$"$X)!"#$"%+I!""7$$"#&)!""$"%+I!""7$$"$b)!"#$"%+I!""7$$"#')!""$"%+I!""7$$"$l)!"#$"%+I!""7$$"#()!""$"%+I!""7$$"$v)!"#$"%+I!""7$$"#))!""$"%+I!""7$$"$&))!"#$"0,++++++$!#77$$"#*)!""$"%+I!""7$$"$&*)!"#$"%+I!""7$$"#!*!""$"%+I!""7$$"$0*!"#$"%+I!""7$$"#"*!""$"%+I!""7$$"$:*!"#$"%+I!""7$$"##*!""$"%+I!""7$$"$D*!"#$"%+I!""7$$"#$*!""$"%+I!""7$$"$N*!"#$"%+I!""7$$"#%*!""$"%+I!""7$$"$X*!"#$"%+I!""7$$"#&*!""$"%+I!""7$$"$b*!"#$"0,++++++$!#77$$"#'*!""$"%+I!""7$$"$l*!"#$"%+I!""7$$"#(*!""$"0*************H!#77$$"$v*!"#$"%+I!""7$$"#)*!""$"%+I!""7$$"$&)*!"#$"%+I!""7$$"#**!""$"%+I!""7$$"$&**!"#$"%+I!""7$$"$+"!""$"%+I!""7$$"%05!"#$"%+I!""7$$"$,"!""$"%+I!""7$$"%:5!"#$"%+I!""7$$"$-"!""$"%+I!""7$$"%D5!"#$"%+I!""7$$"$."!""$"%+I!""7$$"%N5!"#$"%+I!""7$$"$/"!""$"%+I!""7$$"%X5!"#$"%+I!""7$$"$0"!""$"%+I!""7$$"%b5!"#$"%+I!""7$$"$1"!""$"%+I!""7$$"%l5!"#$"%+I!""7$$"$2"!""$"%+I!""7$$"%v5!"#$"%+I!""7$$"$3"!""$"%+I!""7$$"%&3"!"#$"0,++++++$!#77$$"$4"!""$"0*************H!#77$$"%&4"!"#$"%+I!""7$$"$5"!""$"%+I!""7$$"%06!"#$"%+I!""7$$"$6"!""$"%+I!""7$$"%:6!"#$"%+I!""7$$"$7"!""$"%+I!""7$$"%D6!"#$"%+I!""7$$"$8"!""$"%+I!""7$$"%N6!"#$"%+I!""7$$"$9"!""$"%+I!""7$$"%X6!"#$"%+I!""7$$"$:"!""$"%+I!""7$$"%b6!"#$"%+I!""7$$"$;"!""$"%+I!""7$$"%l6!"#$"%+I!""7$$"$<"!""$"%+I!""7$$"%v6!"#$"%+I!""7$$"$="!""$"0*************H!#77$$"%&="!"#$"0,++++++$!#77$$"$>"!""$"%+I!""7$$"%&>"!"#$"%+I!""7$$"$?"!""$"%+I!""7$$"%07!"#$"%+I!""7$$"$@"!""$"%+I!""7$$"%:7!"#$"%+I!""7$$"$A"!""$"%+I!""7$$"%D7!"#$"%+I!""7$$"$B"!""$"%+I!""7$$"%N7!"#$"%+I!""7$$"$C"!""$"%+I!""7$$"%X7!"#$"%+I!""7$$"$D"!""$"%+I!""7$$"%b7!"#$"%+I!""7$$"$E"!""$"%+I!""7$$"%l7!"#$"%+I!""7$$"$F"!""$"%+I!""7$$"%v7!"#$"%+I!""7$$"$G"!""$"0*************H!#77$$"%&G"!"#$"%+I!""7$$"$H"!""$"0*************H!#77$$"%&H"!"#$"%+I!""7$$"$I"!""$"%+I!""7$$"%08!"#$"0*************H!#77$$"$J"!""$"%+I!""7$$"%:8!"#$"%+I!""7$$"$K"!""$"%+I!""7$$"%D8!"#$"%+I!""7$$"$L"!""$"0,++++++$!#77$$"%N8!"#$"%+I!""7$$"$M"!""$"0*************H!#77$$"%X8!"#$"%+I!""7$$"$N"!""$"%+I!""7$$"%b8!"#$"%+I!""7$$"$O"!""$"%+I!""7$$"%l8!"#$"0*************H!#77$$"$P"!""$"%+I!""7$$"%v8!"#$"%+I!""7$$"$Q"!""$"%+I!""7$$"%&Q"!"#$"%+I!""7$$"$R"!""$"%+I!""7$$"%&R"!"#$"%+I!""7$$"$S"!""$"%+I!""7$$"%09!"#$"0*************H!#77$$"$T"!""$"%+I!""7$$"%:9!"#$"%+I!""7$$"$U"!""$"%+I!""7$$"%D9!"#$"%+I!""7$$"$V"!""$"%+I!""7$$"%N9!"#$"%+I!""7$$"$W"!""$"%+I!""7$$"%X9!"#$"%+I!""7$$"$X"!""$"0*************H!#77$$"%b9!"#$"%+I!""7$$"$Y"!""$"%+I!""7$$"%l9!"#$"%+I!""7$$"$Z"!""$"0*************H!#77$$"%v9!"#$"%+I!""7$$"$["!""$"%+I!""7$$"%&["!"#$"%+I!""7$$"$\"!""$"0,++++++$!#77$$"%&\"!"#$"%+I!""7$$"$]"!""$"%+I!""7$$"%0:!"#$"0*************H!#77$$"$^"!""$"%+I!""7$$"%::!"#$"0*************H!#77$$"$_"!""$"0,++++++$!#77$$"%D:!"#$"%+I!""7$$"$`"!""$"%+I!""7$$"%N:!"#$"%+I!""7$$"$a"!""$"%+I!""7$$"%X:!"#$"%+I!""7$$"$b"!""$"%+I!""7$$"%b:!"#$"%+I!""7$$"$c"!""$"%+I!""7$$"%l:!"#$"%+I!""7$$"$d"!""$"%+I!""7$$"%v:!"#$"%+I!""7$$"$e"!""$"%+I!""7$$"%&e"!"#$"%+I!""7$$"$f"!""$"%+I!""7$$"%&f"!"#$"%+I!""7$$"$g"!""$"%+I!""7$$"%0;!"#$"%+I!""7$$"$h"!""$"%+I!""7$$"%:;!"#$"0*************H!#77$$"$i"!""$"%+I!""7$$"%D;!"#$"%+I!""7$$"$j"!""$"%+I!""7$$"%N;!"#$"%+I!""7$$"$k"!""$"%+I!""7$$"%X;!"#$"%+I!""7$$"$l"!""$"%+I!""7$$"%b;!"#$"%+I!""7$$"$m"!""$"%+I!""7$$"%l;!"#$"%+I!""7$$"$n"!""$"%+I!""7$$"%v;!"#$"%+I!""7$$"$o"!""$"%+I!""7$$"%&o"!"#$"%+I!""7$$"$p"!""$"%+I!""7$$"%&p"!"#$"0*************H!#77$$"$q"!""$"%+I!""7$$"%0<!"#$"%+I!""7$$"$r"!""$"%+I!""7$$"%:<!"#$"%+I!""7$$"$s"!""$"%+I!""7$$"%D<!"#$"0,++++++$!#77$$"$t"!""$"%+I!""7$$"%N<!"#$"%+I!""7$$"$u"!""$"%+I!""7$$"%X<!"#$"%+I!""7$$"$v"!""$"%+I!""7$$"%b<!"#$"%+I!""7$$"$w"!""$"%+I!""7$$"%l<!"#$"%+I!""7$$"$x"!""$"%+I!""7$$"%v<!"#$"%+I!""7$$"$y"!""$"%+I!""7$$"%&y"!"#$"%+I!""7$$"$z"!""$"%+I!""7$$"%&z"!"#$"%+I!""7$$"$!=!""$"%+I!""7$$"%0=!"#$"%+I!""7$$"$"=!""$"%+I!""7$$"%:=!"#$"%+I!""7$$"$#=!""$"%+I!""7$$"%D=!"#$"0*************H!#77$$"$$=!""$"%+I!""7$$"%N=!"#$"%+I!""7$$"$%=!""$"%+I!""7$$"%X=!"#$"%+I!""7$$"$&=!""$"%+I!""7$$"%b=!"#$"%+I!""7$$"$'=!""$"%+I!""7$$"%l=!"#$"%+I!""7$$"$(=!""$"%+I!""7$$"%v=!"#$"%+I!""7$$"$)=!""$"%+I!""7$$"%&)=!"#$"%+I!""7$$"$*=!""$"%+I!""7$$"%&*=!"#$"%+I!""7$$"$!>!""$"%+I!""7$$"%0>!"#$"%+I!""7$$"$">!""$"%+I!""7$$"%:>!"#$"%+I!""7$$"$#>!""$"%+I!""7$$"%D>!"#$"%+I!""7$$"$$>!""$"%+I!""7$$"%N>!"#$"0*************H!#77$$"$%>!""$"%+I!""7$$"%X>!"#$"%+I!""7$$"$&>!""$"%+I!""7$$"%b>!"#$"%+I!""7$$"$'>!""$"%+I!""7$$"%l>!"#$"%+I!""7$$"$(>!""$"%+I!""7$$"%v>!"#$"%+I!""7$$"$)>!""$"%+I!""7$$"%&)>!"#$"%+I!""7$$"$*>!""$"%+I!""7$$"%&*>!"#$"%+I!""7$$"$+#!""$"%+I!""7$$"%0?!"#$"%+I!""7$$"$,#!""$"%+I!""7$$"%:?!"#$"%+I!""7$$"$-#!""$"%+I!""7$$"%D?!"#$"%+I!""7$$"$.#!""$"%+I!""7$$"%N?!"#$"%+I!""7$$"$/#!""$"%+I!""7$$"%X?!"#$"%+I!""7$$"$0#!""$"%+I!""7$$"%b?!"#$"%+I!""7$$"$1#!""$"%+I!""7$$"%l?!"#$"%+I!""7$$"$2#!""$"%+I!""7$$"%v?!"#$"%+I!""7$$"$3#!""$"0,++++++$!#77$$"%&3#!"#$"%+I!""7$$"$4#!""$"%+I!""7$$"%&4#!"#$"0,++++++$!#77$$"$5#!""$"0,++++++$!#77$$"%0@!"#$"%+I!""7$$"$6#!""$"%+I!""7$$"%:@!"#$"%+I!""7$$"$7#!""$"%+I!""7$$"%D@!"#$"%+I!""7$$"$8#!""$"%+I!""7$$"%N@!"#$"%+I!""7$$"$9#!""$"0,++++++$!#77$$"%X@!"#$"0*************H!#77$$"$:#!""$"%+I!""7$$"%b@!"#$"0,++++++$!#77$$"$;#!""$"%+I!""7$$"%l@!"#$"0,++++++$!#77$$"$<#!""$"%+I!""7$$"%v@!"#$"%+I!""7$$"$=#!""$"%+I!""7$$"%&=#!"#$"%+I!""7$$"$>#!""$"%+I!""7$$"%&>#!"#$"%+I!""7$$"$?#!""$"%+I!""7$$"%0A!"#$"0*************H!#77$$"$@#!""$"%+I!""7$$"%:A!"#$"%+I!""7$$"$A#!""$"%+I!""7$$"%DA!"#$"%+I!""7$$"$B#!""$"%+I!""7$$"%NA!"#$"0*************H!#77$$"$C#!""$"0*************H!#77$$"%XA!"#$"%+I!""7$$"$D#!""$"%+I!""7$$"%bA!"#$"%+I!""7$$"$E#!""$"%+I!""7$$"%lA!"#$"%+I!""7$$"$F#!""$"0-++++++$!#77$$"%vA!"#$"0)************H!#77$$"$G#!""$"%+I!""7$$"%&G#!"#$"0,++++++$!#77$$"$H#!""$"%+I!""7$$"%&H#!"#$"0-++++++$!#77$$"$I#!""$"0,++++++$!#77$$"%0B!"#$"0,++++++$!#77$$"$J#!""$"0*************H!#77$$"%:B!"#$"0*************H!#77$$"$K#!""$"0*************H!#77$$"%DB!"#$"0-++++++$!#77$$"$L#!""$"0,++++++$!#77$$"%NB!"#$"0-++++++$!#77$$"$M#!""$"0*************H!#77$$"%XB!"#$"0,++++++$!#77$$"$N#!""$"0*************H!#77$$"%bB!"#$"0,++++++$!#77$$"$O#!""$"%+I!""7$$"%lB!"#$"0*************H!#77$$"$P#!""$"0*************H!#77$$"%vB!"#$"0)************H!#77$$"$Q#!""$"0-++++++$!#77$$"%&Q#!"#$"%+I!""7$$"$R#!""$"%+I!""7$$"%&R#!"#$"%+I!""7$$"$S#!""$"%+I!""7$$"%0C!"#$"0,++++++$!#77$$"$T#!""$"0*************H!#77$$"%:C!"#$"0*************H!#77$$"$U#!""$"0,++++++$!#77$$"%DC!"#$"0,++++++$!#77$$"$V#!""$"0*************H!#77$$"%NC!"#$"0-++++++$!#77$$"$W#!""$"0)************H!#77$$"%XC!"#$"0,++++++$!#77$$"$X#!""$"0,++++++$!#77$$"%bC!"#$"%+I!""7$$"$Y#!""$"0*************H!#77$$"%lC!"#$"%+I!""7$$"$Z#!""$"0-++++++$!#77$$"%vC!"#$"%+I!""7$$"$[#!""$"0,++++++$!#77$$"%&[#!"#$"0)************H!#77$$"$\#!""$"0*************H!#77$$"%&\#!"#$"%+I!""7$$"$]#!""$"0-++++++$!#77$$"%0D!"#$"0,++++++$!#77$$"$^#!""$"%+I!""7$$"%:D!"#$"%+I!""7$$"$_#!""$"0(************H!#77$$"%DD!"#$"0(************H!#77$$"$`#!""$"0*************H!#77$$"%ND!"#$"0-++++++$!#77$$"$a#!""$"0/++++++$!#77$$"%XD!"#$"0%************H!#77$$"$b#!""$"%+I!""7$$"%bD!"#$"0*************H!#77$$"$c#!""$"%+I!""7$$"%lD!"#$"%+I!""7$$"$d#!""$"0%************H!#77$$"%vD!"#$"00++++++$!#77$$"$e#!""$"0*************H!#77$$"%&e#!"#$"0(************H!#77$$"$f#!""$"0,++++++$!#77$$"%&f#!"#$"0*************H!#77$$"$g#!""$"0(************H!#77$$"%0E!"#$"0,++++++$!#77$$"$h#!""$"0-++++++$!#77$$"%:E!"#$"0*************H!#77$$"$i#!""$"0,++++++$!#77$$"%DE!"#$"0)************H!#77$$"$j#!""$"0*************H!#77$$"%NE!"#$"0)************H!#77$$"$k#!""$"0*************H!#77$$"%XE!"#$"0*************H!#77$$"$l#!""$"0-++++++$!#77$$"%bE!"#$"0*************H!#77$$"$m#!""$"0,++++++$!#77$$"%lE!"#$"0*************H!#77$$"$n#!""$"0,++++++$!#77$$"%vE!"#$"0)************H!#77$$"$o#!""$"0,++++++$!#77$$"%&o#!"#$"0'************H!#77$$"$p#!""$"0)************H!#77$$"%&p#!"#$"0(************H!#77$$"$q#!""$"0*************H!#77$$"%0F!"#$"0-++++++$!#77$$"$r#!""$"0,++++++$!#77$$"%:F!"#$"0)************H!#77$$"$s#!""$"0(************H!#77$$"%DF!"#$"0)************H!#77$$"$t#!""$"03++++++$!#77$$"%NF!"#$"0*************H!#77$$"$u#!""$"%+I!""7$$"%XF!"#$"0(************H!#77$$"$v#!""$"%+I!""7$$"%bF!"#$"0*************H!#77$$"$w#!""$"0()***********H!#77$$"%lF!"#$"/************H!#67$$"$x#!""$"09++++++$!#77$$"%vF!"#$"08++++++$!#77$$"$y#!""$"08++++++$!#77$$"%&y#!"#$"0;++++++$!#77$$"$z#!""$"0)************H!#77$$"%&z#!"#$"%+I!""7$$"$!G!""$"0-++++++$!#77$$"%0G!"#$"0&************H!#77$$"$"G!""$"02++++++$!#77$$"%:G!"#$"0,++++++$!#77$$"$#G!""$"04++++++$!#77$$"%DG!"#$"01++++++$!#77$$"$$G!""$"0-++++++$!#77$$"%NG!"#$"%+I!""7$$"$%G!""$"0)************H!#77$$"%XG!"#$"%+I!""7$$"$&G!""$"0,++++++$!#77$$"%bG!"#$"0.++++++$!#77$$"$'G!""$"0,++++++$!#77$$"%lG!"#$"0,++++++$!#77$$"$(G!""$"0)************H!#77$$"%vG!"#$"0*************H!#77$$"$)G!""$"0)************H!#77$$"%&)G!"#$"%+I!""7$$"$*G!""$"%+I!""7$$"%&*G!"#$"0,++++++$!#77$$"$!H!""$"0,++++++$!#77$$"%0H!"#$"0%************H!#77$$"$"H!""$"0,++++++$!#77$$"%:H!"#$"%+I!""7$$"$#H!""$"0*************H!#77$$"%DH!"#$"0,++++++$!#77$$"$$H!""$"00++++++$!#77$$"%NH!"#$"0-++++++$!#77$$"$%H!""$"0)************H!#77$$"%XH!"#$"/,+++++I!#67$$"$&H!""$"0.++++++$!#77$$"%bH!"#$"0;++++++$!#77$$"$'H!""$"09++++++$!#77$$"%lH!"#$"0&************H!#77$$"$(H!""$"0"************H!#77$$"%vH!"#$"02++++++$!#77$$"$)H!""$"0*)***********H!#77$$"%&)H!"#$"0'************H!#77$$"$*H!""$"0#************H!#77$$"%&*H!"#$"0<++++++$!#77$$"$+$!""$"/(***********H!#67$$"%0I!"#$"0y***********H!#77$$"$,$!""$"0x***********H!#77$$"%:I!"#$"0&************H!#77$$"$-$!""$"04++++++$!#77$$"%DI!"#$"0&)***********H!#77$$"$.$!""$"06++++++$!#77$$"%NI!"#$"03++++++$!#77$$"$/$!""$"0.++++++$!#77$$"%XI!"#$"02++++++$!#77$$"$0$!""$"0'************H!#77$$"%bI!"#$"0*************H!#77$$"$1$!""$"0$************H!#77$$"%lI!"#$"00++++++$!#77$$"$2$!""$"%+I!""7$$"%vI!"#$"%+I!""7$$"$3$!""$"%+I!""7$$"%&3$!"#$"0'************H!#77$$"$4$!""$"0/++++++$!#77$$"%&4$!"#$"%+I!""7$$"$5$!""$"02++++++$!#77$$"%0J!"#$"0&************H!#77$$"$6$!""$"0(************H!#77$$"%:J!"#$"0'************H!#77$$"$7$!""$"0/++++++$!#77$$"%DJ!"#$"0,++++++$!#77$$"$8$!""$"0&************H!#77$$"%NJ!"#$"00++++++$!#77$$"$9$!""$"0*************H!#77$$"%XJ!"#$"01++++++$!#77$$"$:$!""$"00++++++$!#77$$"%bJ!"#$"0A++++++$!#77$$"$;$!""$"0H++++++$!#77$$"%lJ!"#$"/************H!#67$$"$<$!""$"0N++++++$!#77$$"%vJ!"#$"0e***********H!#77$$"$=$!""$"0X++++++$!#77$$"%&=$!"#$"0G++++++$!#77$$"$>$!""$"0G++++++$!#77$$"%&>$!"#$"/)***********H!#67$$"$?$!""$"/%***********H!#67$$"%0K!"#$"/%***********H!#67$$"$@$!""$"0[++++++$!#77$$"%:K!"#$"0#************H!#77$$"$A$!""$"0=++++++$!#77$$"%DK!"#$"/&***********H!#67$$"$B$!""$"0U++++++$!#77$$"%NK!"#$"0()***********H!#77$$"$C$!""$"0j***********H!#77$$"%XK!"#$"06++++++$!#77$$"$D$!""$"0&)***********H!#77$$"%bK!"#$"0p***********H!#77$$"$E$!""$"0E++++++$!#77$$"%lK!"#$"0#************H!#77$$"$F$!""$"03++++++$!#77$$"%vK!"#$"%+I!""7$$"$G$!""$"03++++++$!#77$$"%&G$!"#$"0-++++++$!#77$$"$H$!""$"0%************H!#77$$"%&H$!"#$"0/++++++$!#77$$"$I$!""$"0&************H!#77$$"%0L!"#$"06++++++$!#77$$"$J$!""$"/************H!#67$$"%:L!"#$"0'************H!#77$$"$K$!""$"%+I!""7$$"%DL!"#$"0-++++++$!#77$$"$L$!""$"0-++++++$!#77$$"%NL!"#$"%+I!""7$$"$M$!""$"0(************H!#77$$"%XL!"#$"0$************H!#77$$"$N$!""$"0r***********H!#77$$"%bL!"#$"0#************H!#77$$"$O$!""$"0n***********H!#77$$"%lL!"#$"0&)***********H!#77$$"$P$!""$"0v***********H!#77$$"%vL!"#$"0`++++++$!#77$$"$Q$!""$"0*)***********H!#77$$"%&Q$!"#$"/,+++++I!#67$$"$R$!""$"08++++++$!#77$$"%&R$!"#$"0:++++++$!#77$$"$S$!""$"07++++++$!#77$$"%0M!"#$"0C++++++$!#77$$"$T$!""$"0D++++++$!#77$$"%:M!"#$"0(************H!#77$$"$U$!""$"0.++++++$!#77$$"%DM!"#$"0)************H!#77$$"$V$!""$"0R***********H!#77$$"%NM!"#$"0a++++++$!#77$$"$W$!""$"0p++++++$!#77$$"%XM!"#$"0r++++++$!#77$$"$X$!""$"0T***********H!#77$$"%bM!"#$"0[***********H!#77$$"$Y$!""$"0i***********H!#77$$"%lM!"#$"0(************H!#77$$"$Z$!""$"0F++++++$!#77$$"%vM!"#$"0)************H!#77$$"$[$!""$"0$************H!#77$$"%&[$!"#$"0=++++++$!#77$$"$\$!""$"/************H!#67$$"%&\$!"#$"06++++++$!#77$$"$]$!""$"0#)***********H!#77$$"%0N!"#$"0)************H!#77$$"$^$!""$"0"************H!#77$$"%:N!"#$"0,++++++$!#77$$"$_$!""$"0*************H!#77$$"%DN!"#$"0$************H!#77$$"$`$!""$"0%)***********H!#77$$"%NN!"#$"0<++++++$!#77$$"$a$!""$"06++++++$!#77$$"%XN!"#$"0"************H!#77$$"$b$!""$"0#)***********H!#77$$"%bN!"#$"0l***********H!#77$$"$c$!""$"0z***********H!#77$$"%lN!"#$"0'************H!#77$$"$d$!""$"0[***********H!#77$$"%vN!"#$"0P++++++$!#77$$"$e$!""$"/"***********H!#67$$"%&e$!"#$"0$************H!#77$$"$f$!""$"0t***********H!#77$$"%&f$!"#$"/6+++++I!#67$$"$g$!""$"07,+++++$!#77$$"%0O!"#$"0O***********H!#77$$"$h$!""$"/*)**********H!#67$$"%:O!"#$"0$************H!#77$$"$i$!""$"%+I!""7$$"%DO!"#$"0)*)**********H!#77$$"$j$!""$"0j++++++$!#77$$"%NO!"#$"/-+++++I!#67$$"$k$!""$"0K***********H!#77$$"%XO!"#$"0e***********H!#77$$"$l$!""$"0b++++++$!#77$$"%bO!"#$"0b***********H!#77$$"$m$!""$"08++++++$!#77$$"%lO!"#$"04***********H!#77$$"$n$!""$"06++++++$!#77$$"%vO!"#$"0_++++++$!#77$$"$o$!""$"0s++++++$!#77$$"%&o$!"#$"0t***********H!#77$$"$p$!""$"0@++++++$!#77$$"%&p$!"#$"0.++++++$!#77$$"$q$!""$"0j***********H!#77$$"%0P!"#$"0P++++++$!#77$$"$r$!""$"0()***********H!#77$$"%:P!"#$"/************H!#67$$"$s$!""$"0/++++++$!#77$$"%DP!"#$"0(************H!#77$$"$t$!""$"0))***********H!#77$$"%NP!"#$"0s***********H!#77$$"$u$!""$"0[++++++$!#77$$"%XP!"#$"0e***********H!#77$$"$v$!""$"0W***********H!#77$$"%bP!"#$"03***********H!#77$$"$w$!""$"0-++++++$!#77$$"%lP!"#$"02++++++$!#77$$"$x$!""$"0"*)**********H!#77$$"%vP!"#$"0%*)**********H!#77$$"$y$!""$"0u++++++$!#77$$"%&y$!"#$"0J++++++$!#77$$"$z$!""$"0.++++++$!#77$$"%&z$!"#$"/*)**********H!#67$$"$!Q!""$"0#4+++++I!#77$$"%0Q!"#$"0C,+++++$!#77$$"$"Q!""$"0s***********H!#77$$"%:Q!"#$"0P,+++++$!#77$$"$#Q!""$"0F)**********H!#77$$"%DQ!"#$"0,)**********H!#77$$"$$Q!""$"0#y**********H!#77$$"%NQ!"#$"0o++++++$!#77$$"$%Q!""$"0N)**********H!#77$$"%XQ!"#$"0>++++++$!#77$$"$&Q!""$"0$=+++++I!#77$$"%bQ!"#$"/************H!#67$$"$'Q!""$"0&4+++++I!#77$$"%lQ!"#$"0Y,+++++$!#77$$"$(Q!""$"0^***********H!#77$$"%vQ!"#$"03,+++++$!#77$$"$)Q!""$"0y***********H!#77$$"%&)Q!"#$"0,,+++++$!#77$$"$*Q!""$"01++++++$!#77$$"%&*Q!"#$"0k,+++++$!#77$$"$!R!""$"0=++++++$!#77$$"%0R!"#$"0Y***********H!#77$$"$"R!""$"0V***********H!#77$$"%:R!"#$"/,+++++I!#67$$"$#R!""$"0F++++++$!#77$$"%DR!"#$"0T++++++$!#77$$"$$R!""$"0#4+++++I!#77$$"%NR!"#$"0;++++++$!#77$$"$%R!""$"0j)**********H!#77$$"%XR!"#$"/;+++++I!#67$$"$&R!""$"0O***********H!#77$$"%bR!"#$"0d***********H!#77$$"$'R!""$"0&)***********H!#77$$"%lR!"#$"0)=+++++I!#77$$"$(R!""$"0v***********H!#77$$"%vR!"#$"0Z(**********H!#77$$"$)R!""$"0t,+++++$!#77$$"%&)R!"#$"07)**********H!#77$$"$*R!""$"00'**********H!#77$$"%&*R!"#$"0-***********H!#77$$"$+%!""$"0,-+++++$!#77$$"%0S!"#$"0X,+++++$!#77$$"$,%!""$"07(**********H!#77$$"%:S!"#$"0*************H!#77$$"$-%!""$"0*G+++++I!#77$$"%DS!"#$"0^)**********H!#77$$"$.%!""$"0B/+++++$!#77$$"%NS!"#$"0C(**********H!#77$$"$/%!""$"0/.+++++$!#77$$"%XS!"#$"0&))**********H!#77$$"$0%!""$"0-++++++$!#77$$"%bS!"#$"0%4+++++I!#77$$"$1%!""$"0a.+++++$!#77$$"%lS!"#$"0*H+++++I!#77$$"$2%!""$"0.(**********H!#77$$"%vS!"#$"0J++++++$!#77$$"$3%!""$"0l)**********H!#77$$"%&3%!"#$"0j++++++$!#77$$"$4%!""$"/&***********H!#67$$"%&4%!"#$"0%*)**********H!#77$$"$5%!""$"0c.+++++$!#77$$"%0T!"#$"/$)**********H!#67$$"$6%!""$"0F(**********H!#77$$"%:T!"#$"0Q++++++$!#77$$"$7%!""$"0t***********H!#77$$"%DT!"#$"0@-+++++$!#77$$"$8%!""$"0c++++++$!#77$$"%NT!"#$"/7+++++I!#67$$"$9%!""$"0*=+++++I!#77$$"%XT!"#$"/C+++++I!#67$$"$:%!""$"0G++++++$!#77$$"%bT!"#$"0b++++++$!#77$$"$;%!""$"0/++++++$!#77$$"%lT!"#$"0'p**********H!#77$$"$<%!""$"0^.+++++$!#77$$"%vT!"#$"0@(**********H!#77$$"$=%!""$"0L$**********H!#77$$"%&=%!"#$"0,-+++++$!#77$$"$>%!""$"0=-+++++$!#77$$"%&>%!"#$"/d+++++I!#67$$"$?%!""$"094+++++$!#77$$"%0U!"#$"0_.+++++$!#77$$"$@%!""$"0j&**********H!#77$$"%:U!"#$"0H7+++++$!#77$$"$A%!""$"0Q***********H!#77$$"%DU!"#$"0,&**********H!#77$$"$B%!""$"0p4+++++$!#77$$"%NU!"#$"06#**********H!#77$$"$C%!""$"0^5+++++$!#77$$"%XU!"#$"0j6+++++$!#77$$"$D%!""$"0-!**********H!#77$$"%bU!"#$"0Q(**********H!#77$$"$E%!""$"0z++++++$!#77$$"%lU!"#$"0T'**********H!#77$$"$F%!""$"0K'**********H!#77$$"%vU!"#$"0>)**********H!#77$$"$G%!""$"0V&**********H!#77$$"%&G%!"#$"0(o+++++I!#77$$"$H%!""$"/0+++++I!#67$$"%&H%!"#$"0'H**********H!#77$$"$I%!""$"0**4+++++$!#77$$"%0V!"#$"/P+++++I!#67$$"$J%!""$"0N,+++++$!#77$$"%:V!"#$"0k3+++++$!#77$$"$K%!""$"0r$**********H!#77$$"%DV!"#$"0c"**********H!#77$$"$L%!""$"/H**********H!#67$$"%NV!"#$"0&*)**********H!#77$$"$M%!""$"0&Q**********H!#77$$"%XV!"#$"0F++++++$!#77$$"$N%!""$"/&***********H!#67$$"%bV!"#$"0@6+++++$!#77$$"$O%!""$"0#*))*********H!#77$$"%lV!"#$"0f$**********H!#77$$"$P%!""$".***********H!#57$$"%vV!"#$"0R$**********H!#77$$"$Q%!""$"00!)*********H!#77$$"%&Q%!"#$"07=+++++$!#77$$"$R%!""$"/>+++++I!#67$$"%&R%!"#$"0'Q,++++I!#77$$"$S%!""$"0k1+++++$!#77$$"%0W!"#$"0u'**********H!#77$$"$T%!""$"0RJ+++++$!#77$$"%:W!"#$"079+++++$!#77$$"$U%!""$"0/,+++++$!#77$$"%DW!"#$"0G'**********H!#77$$"$V%!""$"0l***********H!#77$$"%NW!"#$"0=&**********H!#77$$"$W%!""$"0`8+++++$!#77$$"%XW!"#$"0V@+++++$!#77$$"$X%!""$"01#**********H!#77$$"%bW!"#$"0_s*********H!#77$$"$Y%!""$"0&)3+++++$!#77$$"%lW!"#$"0b)**********H!#77$$"$Z%!""$"0b/+++++$!#77$$"%vW!"#$"/#4+++++$!#67$$"$[%!""$"0)R**********H!#77$$"%&[%!"#$"0T3+++++$!#77$$"$\%!""$"012+++++$!#77$$"%&\%!"#$"0.(**********H!#77$$"$]%!""$"0h")*********H!#77$$"%0X!"#$"0#Q-++++I!#77$$"$^%!""$"0P.+++++$!#77$$"%:X!"#$"0[')*********H!#77$$"$_%!""$"0(G+++++I!#77$$"%DX!"#$"0Tx*********H!#77$$"$`%!""$"0")***********H!#77$$"%NX!"#$"0Py*********H!#77$$"$a%!""$"/\,++++I!#67$$"%XX!"#$"0'y**********H!#77$$"$b%!""$"0i7+++++$!#77$$"%bX!"#$"0w!**********H!#77$$"$c%!""$"0G,+++++$!#77$$"%lX!"#$"01,+++++$!#77$$"$d%!""$"0e)**********H!#77$$"%vX!"#$"0RI+++++$!#77$$"$e%!""$"0k.+++++$!#77$$"%&e%!"#$"0@p*********H!#77$$"$f%!""$"0A]*********H!#77$$"%&f%!"#$"0M4+++++$!#77$$"$g%!""$"0%[+++++I!#77$$"%0Y!"#$"0N\*********H!#77$$"$h%!""$"0Cy*********H!#77$$"%:Y!"#$"0D$**********H!#77$$"$i%!""$"0/L*********H!#77$$"%DY!"#$"/y-++++I!#67$$"$j%!""$"0D!)*********H!#77$$"%NY!"#$"0$z#*********H!#77$$"$k%!""$"0c9+++++$!#77$$"%XY!"#$"0MV*********H!#77$$"$l%!""$"0Ek*********H!#77$$"%bY!"#$"/"[*********H!#67$$"$m%!""$"0jd+++++$!#77$$"%lY!"#$"0aV*********H!#77$$"$n%!""$"0>/+++++$!#77$$"%vY!"#$"08^+++++$!#77$$"$o%!""$"0X()*********H!#77$$"%&o%!"#$"0CH+++++$!#77$$"$p%!""$"0ap*********H!#77$$"%&p%!"#$"0O%**********H!#77$$"$q%!""$"0:1+++++$!#77$$"%0Z!"#$"0$=.++++I!#77$$"$r%!""$"0HT*********H!#77$$"%:Z!"#$"0UE+++++$!#77$$"$s%!""$"08Q*********H!#77$$"%DZ!"#$"0B)**********H!#77$$"$t%!""$"0h)**********H!#77$$"%NZ!"#$"03P*********H!#77$$"$u%!""$"0cd*********H!#77$$"%XZ!"#$"07g*********H!#77$$"$v%!""$"0'*f*********H!#77$$"%bZ!"#$"0ai*********H!#77$$"$w%!""$"0:i+++++$!#77$$"%lZ!"#$"0u1+++++$!#77$$"$x%!""$"/<)*********H!#67$$"%vZ!"#$"0=,+++++$!#77$$"$y%!""$"0P++++++$!#77$$"%&y%!"#$"0<&)*********H!#77$$"$z%!""$"/O**********H!#67$$"%&z%!"#$"0MM*********H!#77$$"$![!""$"001+++++$!#77$$"%0[!"#$"0=[+++++$!#77$$"$"[!""$"0/()*********H!#77$$"%:[!"#$"0#*3,++++$!#77$$"$#[!""$"0*\2++++I!#77$$"%D[!"#$"0F%**********H!#77$$"$$[!""$"0w5)********H!#77$$"%N[!"#$"0_0*********H!#77$$"$%[!""$"04*y********H!#77$$"%X[!"#$"/KC++++I!#67$$"$&[!""$"0*)4*********H!#77$$"%b[!"#$"0L7)********H!#77$$"$'[!""$"//3++++I!#67$$"%l[!"#$"028+++++$!#77$$"$([!""$"0_e,++++$!#77$$"%v[!"#$"0(Q4++++I!#77$$"$)[!""$"0EX*********H!#77$$"%&)[!"#$"0@[+++++$!#77$$"$*[!""$"0z/+++++$!#77$$"%&*[!"#$"0hQ*********H!#77$$"$!\!""$"0`w+++++$!#77$$"%0\!"#$"0<@+++++$!#77$$"$"\!""$"0NN+++++$!#77$$"%:\!"#$"/=2++++I!#67$$"$#\!""$"0k#))********H!#77$$"%D\!"#$"0%y.++++I!#77$$"$$\!""$"0W]+++++$!#77$$"%N\!"#$"0TU*********H!#77$$"$%\!""$"0mr)********H!#77$$"%X\!"#$"0$3**********H!#77$$"$&\!""$"0G=+++++$!#77$$"%b\!"#$"0'*G+++++$!#77$$"$'\!""$"0\q+++++$!#77$$"%l\!"#$"0nM+++++$!#77$$"$(\!""$"0C/,++++$!#77$$"%v\!"#$"0<3+++++$!#77$$"$)\!""$"01h+++++$!#77$$"%&)\!"#$"0hN*********H!#77$$"$*\!""$"0#[%*********H!#77$$"%&*\!"#$"0R,,++++$!#77$$"$+&!""$"0Y3-++++$!#77$$"%0]!"#$"0**)z********H!#77$$"$,&!""$"0_j+++++$!#77$$"%:]!"#$"0JO+++++$!#77$$"$-&!""$"0Nv&********H!#77$$"%D]!"#$"0;%>++++I!#77$$"$.&!""$"0)R7++++I!#77$$"%N]!"#$"0YO&********H!#77$$"$/&!""$"0bG'********H!#77$$"%X]!"#$"/C()********H!#67$$"$0&!""$"0C$3++++I!#77$$"%b]!"#$"0W7(********H!#77$$"$1&!""$"0xv+++++$!#77$$"%l]!"#$"0v6-++++$!#77$$"$2&!""$"0#4*)********H!#77$$"%v]!"#$"0`,&********H!#77$$"$3&!""$"0C*\********H!#77$$"%&3&!"#$"0t_*********H!#77$$"$4&!""$"0$>1++++I!#77$$"%&4&!"#$"0z,+++++$!#77$$"$5&!""$"0$HA++++I!#77$$"%0^!"#$"/EE++++I!#67$$"$6&!""$"09s+++++$!#77$$"%:^!"#$"0c!)*********H!#77$$"$7&!""$"0L1*********H!#77$$"%D^!"#$"0#\0++++I!#77$$"$8&!""$"0WN*********H!#77$$"%N^!"#$"//#*********H!#67$$"$9&!""$"0[:+++++$!#77$$"%X^!"#$"/eE++++I!#67$$"$:&!""$"0Xd,++++$!#77$$"%b^!"#$"/>3++++I!#67$$"$;&!""$"0l0(********H!#77$$"%l^!"#$"0&>')********H!#77$$"$<&!""$"/iA++++I!#67$$"%v^!"#$"0%QG++++I!#77$$"$=&!""$"0Q!o********H!#77$$"%&=&!"#$"0wZ'********H!#77$$"$>&!""$"0yJ.++++$!#77$$"%&>&!"#$"08,'********H!#77$$"$?&!""$"0da*********H!#77$$"%0_!"#$"0QA-++++$!#77$$"$@&!""$"0z2/++++$!#77$$"%:_!"#$"0WT/++++$!#77$$"$A&!""$"0#)o1++++$!#77$$"%D_!"#$"00Y'********H!#77$$"$B&!""$"0o-'********H!#77$$"%N_!"#$"0cz+++++$!#77$$"$C&!""$"0s$*4++++$!#77$$"%X_!"#$"0Hz(********H!#77$$"$D&!""$"0iz#********H!#77$$"%b_!"#$"/P")********H!#67$$"$E&!""$"/4z********H!#67$$"%l_!"#$"0Xf"********H!#77$$"$F&!""$"0s"y)*******H!#77$$"%v_!"#$"/t:********H!#67$$"$G&!""$"01M-++++$!#77$$"%&G&!"#$"0(e')********H!#77$$"$H&!""$"0X")))*******H!#77$$"%&H&!"#$"0,Y,++++$!#77$$"$I&!""$"0(z#)********H!#77$$"%0`!"#$"0x)=********H!#77$$"$J&!""$"0^j,++++$!#77$$"%:`!"#$"0kw*********H!#77$$"$K&!""$"0RQ-++++$!#77$$"%D`!"#$"0'fZ++++I!#77$$"$L&!""$"0kC)********H!#77$$"%N`!"#$"0%pF++++I!#77$$"$M&!""$"0`9+++++$!#77$$"%X`!"#$"0Au)********H!#77$$"$N&!""$"07)H++++I!#77$$"%b`!"#$"0#f.++++I!#77$$"$O&!""$"0_v0++++$!#77$$"%l`!"#$"0Um+++++$!#77$$"$P&!""$"0GU$********H!#77$$"%v`!"#$"0"=N++++I!#77$$"$Q&!""$"0#Q%*********H!#77$$"%&Q&!"#$"0A>'********H!#77$$"$R&!""$"0)*=+++++$!#77$$"%&R&!"#$"0u='********H!#77$$"$S&!""$"0R[/++++$!#77$$"%0a!"#$"0j4,++++$!#77$$"$T&!""$"0#py********H!#77$$"%:a!"#$"0"z#*)*******H!#77$$"$U&!""$"0a?#********H!#77$$"%Da!"#$"0`7*********H!#77$$"$V&!""$"0'3s++++I!#77$$"%Na!"#$"0t;+++++$!#77$$"$W&!""$"0Y!z,+++I!#77$$"%Xa!"#$"0Jw(********H!#77$$"$X&!""$"0r+0++++$!#77$$"%ba!"#$"0bc0++++$!#77$$"$Y&!""$"06q"********H!#77$$"%la!"#$"0CnH++++$!#77$$"$Z&!""$"0"y3++++I!#77$$"%va!"#$"0BS:++++$!#77$$"$[&!""$"0zLH++++$!#77$$"%&[&!"#$"0#)\A++++$!#77$$"$\&!""$"/&)p********H!#67$$"%&\&!"#$"0Au*********H!#77$$"$]&!""$"0QSE++++$!#77$$"%0b!"#$"0yE*)*******H!#77$$"$^&!""$"0&\y********H!#77$$"%:b!"#$"0f1z*******H!#77$$"$_&!""$"0D=!)*******H!#77$$"%Db!"#$"0EE(********H!#77$$"$`&!""$"0\'*))*******H!#77$$"%Nb!"#$"0<T5++++$!#77$$"$a&!""$"0YT2++++$!#77$$"%Xb!"#$"/)R))*******H!#67$$"$b&!""$"0F.)********H!#77$$"%bb!"#$"0AN&********H!#77$$"$c&!""$"0u*Q********H!#77$$"%lb!"#$"0MC(********H!#77$$"$d&!""$"0fX(********H!#77$$"%vb!"#$"0sV%********H!#77$$"$e&!""$"0GS,++++$!#77$$"%&e&!"#$"02q))*******H!#77$$"$f&!""$"0*H>++++I!#77$$"%&f&!"#$"0(QY********H!#77$$"$g&!""$"0%*o-++++$!#77$$"%0c!"#$"0,%Q********H!#77$$"$h&!""$"0O_8++++$!#77$$"%:c!"#$"/)R<++++$!#67$$"$i&!""$"0Y3%********H!#77$$"%Dc!"#$"0se"********H!#77$$"$j&!""$"0)Gu++++I!#77$$"%Nc!"#$"0hu*)*******H!#77$$"$k&!""$"0V.(********H!#77$$"%Xc!"#$"0c?H++++$!#77$$"$l&!""$"0"HJ********H!#77$$"%bc!"#$"0$=$=++++$!#77$$"$m&!""$"0@4*********H!#77$$"%lc!"#$"0w?4++++$!#77$$"$n&!""$"0-"y-+++I!#77$$"%vc!"#$"0AlC++++$!#77$$"$o&!""$"0xm-++++$!#77$$"%&o&!"#$"0=.$)*******H!#77$$"$p&!""$"0EO4++++$!#77$$"%&p&!"#$"/uK$*******H!#67$$"$q&!""$"0NV$)*******H!#77$$"%0d!"#$"/D*>++++$!#67$$"$r&!""$"0"f()********H!#77$$"%:d!"#$"0H@#********H!#77$$"$s&!""$"0h5h++++$!#77$$"%Dd!"#$"0U0))*******H!#77$$"$t&!""$"01]@++++$!#77$$"%Nd!"#$"0rL0++++$!#77$$"$u&!""$"0_Hm*******H!#77$$"%Xd!"#$"0p'\.+++I!#77$$"$v&!""$"0[Nf*******H!#77$$"%bd!"#$"0\c))*******H!#77$$"$w&!""$"0eb,++++$!#77$$"%ld!"#$"0HS+++++$!#77$$"$x&!""$"0j+%********H!#77$$"%vd!"#$"00P2++++$!#77$$"$y&!""$"0Zm)********H!#77$$"%&y&!"#$"0x'H,+++I!#77$$"$z&!""$"0tg:++++$!#77$$"%&z&!"#$"0^[#********H!#77$$"$!e!""$"0r:1++++$!#77$$"%0e!"#$"0R!H********H!#77$$"$"e!""$"/9H)*******H!#67$$"%:e!"#$"0(fa++++I!#77$$"$#e!""$".N')*******H!#57$$"%De!"#$"0aT2++++$!#77$$"$$e!""$"/O8++++I!#67$$"%Ne!"#$"0>1+++++$!#77$$"$%e!""$"0[;v*******H!#77$$"%Xe!"#$"0n!3++++I!#77$$"$&e!""$"0%=$z*******H!#77$$"%be!"#$"0'o6,+++I!#77$$"$'e!""$"0Wuu++++$!#77$$"%le!"#$"0$>X-+++I!#77$$"$(e!""$"0(H&e++++$!#77$$"%ve!"#$"0TCn*******H!#77$$"$)e!""$"0'e&)*)******H!#77$$"%&)e!"#$"0Y#R-+++I!#77$$"$*e!""$"0bG"))******H!#77$$"%&*e!"#$"0/9z++++$!#77$$"$!f!""$"0m0#)*******H!#77$$"%0f!"#$"0z#3(*******H!#77$$"$"f!""$"/;!4++++$!#67$$"%:f!"#$"0R#*\)******H!#77$$"$#f!""$"0A*\5+++I!#77$$"%Df!"#$"0$3G++++I!#77$$"$$f!""$"0"*)46+++I!#77$$"%Nf!"#$"0DfQ*******H!#77$$"$%f!""$"0z?%********H!#77$$"%Xf!"#$"0:w8,+++$!#77$$"$&f!""$"0jy*))******H!#77$$"%bf!"#$"0*4u1+++I!#77$$"$'f!""$"0$H*=*******H!#77$$"%lf!"#$"0)>R/+++I!#77$$"$(f!""$"0;"\++++I!#77$$"%vf!"#$"0E5j++++$!#77$$"$)f!""$"0l'>.+++I!#77$$"%&)f!"#$"08J,++++$!#77$$"$*f!""$"0*43(*******H!#77$$"%&*f!"#$"/CA)*******H!#67$$"$+'!""$"0p0<++++$!#77$$"%0g!"#$"0,yr*******H!#77$$"$,'!""$"0%)G$)*******H!#77$$"%:g!"#$"0P#z)*******H!#77$$"$-'!""$"/PU)*******H!#67$$"%Dg!"#$"0e'G(*******H!#77$$"$.'!""$"0@39++++$!#77$$"%Ng!"#$"/^A********H!#67$$"$/'!""$"/:C++++I!#67$$"%Xg!"#$"0V<O++++$!#77$$"$0'!""$"0yi%********H!#77$$"%bg!"#$"0:jz*******H!#77$$"$1'!""$"0-6P++++$!#77$$"%lg!"#$"0d'z********H!#77$$"$2'!""$"0v^,++++$!#77$$"%vg!"#$"0-(*p*******H!#77$$"$3'!""$"0'Ql********H!#77$$"%&3'!"#$"0k'f"*******H!#77$$"$4'!""$"/tv:+++I!#67$$"%&4'!"#$"0Y]L)******H!#77$$"$5'!""$"/wB(*******H!#67$$"%0h!"#$"0W'eD+++I!#77$$"$6'!""$"0s(R&)******H!#77$$"%:h!"#$"0*[5v******H!#77$$"$7'!""$"0y)*R*******H!#77$$"%Dh!"#$"/X_3+++I!#67$$"$8'!""$"04A#G+++I!#77$$"%Nh!"#$"0:72++++$!#77$$"$9'!""$"0rZq++++$!#77$$"%Xh!"#$"0t`\*******H!#77$$"$:'!""$"03N/,+++$!#77$$"%bh!"#$"00`I*******H!#77$$"$;'!""$"0W<+,+++$!#77$$"%lh!"#$"0M*oC+++I!#77$$"$<'!""$"/1y.+++I!#67$$"%vh!"#$"0lHH,+++$!#77$$"$='!""$"/cN;+++I!#67$$"%&='!"#$"01-1*******H!#77$$"$>'!""$"/1]********H!#67$$"%&>'!"#$"0jZI*******H!#77$$"$?'!""$"06L,*******H!#77$$"%0i!"#$"03dZ*******H!#77$$"$@'!""$"0lUz*******H!#77$$"%:i!"#$"0tgh++++$!#77$$"$A'!""$"0)y!y*******H!#77$$"%Di!"#$"0(\+)*******H!#77$$"$B'!""$"0"\u$*******H!#77$$"%Ni!"#$"0%>&=*******H!#77$$"$C'!""$"0fh=*******H!#77$$"%Xi!"#$"/())o++++$!#67$$"$D'!""$"0s&31+++I!#77$$"%bi!"#$"0Tas*******H!#77$$"$E'!""$"/)H"))******H!#67$$"%li!"#$"0P(31+++I!#77$$"$F'!""$"0t!p&*******H!#77$$"%vi!"#$"0tGq++++$!#77$$"$G'!""$"0=RU++++$!#77$$"%&G'!"#$"0HBD,+++$!#77$$"$H'!""$"0;f)z******H!#77$$"%&H'!"#$"0)z/=+++I!#77$$"$I'!""$"0TDl++++$!#77$$"%0j!"#$"0T^?*******H!#77$$"$J'!""$"0w![$*******H!#77$$"%:j!"#$"0sH&)*******H!#77$$"$K'!""$"0>m*>+++I!#77$$"%Dj!"#$"0wZV(******H!#77$$"$L'!""$"0J#Q<+++I!#77$$"%Nj!"#$"/T=X******H!#67$$"$M'!""$"0ja6.+++$!#77$$"%Xj!"#$"0lsj)******H!#77$$"$N'!""$"0XqC++++$!#77$$"%bj!"#$"0jhG/+++$!#77$$"$O'!""$"0&o(3*******H!#77$$"%lj!"#$"04a?/+++$!#77$$"$P'!""$"0cIj&******H!#77$$"%vj!"#$"0U!*>,+++$!#77$$"$Q'!""$"07%G!*******H!#77$$"%&Q'!"#$"0PW5,+++$!#77$$"$R'!""$"/-xl******H!#67$$"%&R'!"#$"0wW#=+++I!#77$$"$S'!""$"0GQw*******H!#77$$"%0k!"#$"0=/,-+++$!#77$$"$T'!""$"0D>Z(******H!#77$$"%:k!"#$"03%*)*)******H!#77$$"$U'!""$"0%3,3+++I!#77$$"%Dk!"#$"0%=7,+++I!#77$$"$V'!""$"0>j,,+++$!#77$$"%Nk!"#$"/2R++++I!#67$$"$W'!""$"0CRF*******H!#77$$"%Xk!"#$"0U^^++++$!#77$$"$X'!""$"0hlX*******H!#77$$"%bk!"#$"0K3M++++$!#77$$"$Y'!""$"0e&f"*******H!#77$$"%lk!"#$"0FX9++++$!#77$$"$Z'!""$"0UR6++++$!#77$$"%vk!"#$"0p2*3+++I!#77$$"$['!""$"0j*)[*******H!#77$$"%&['!"#$"0\=4++++$!#77$$"$\'!""$"0u,"4+++I!#77$$"%&\'!"#$"09!=z******H!#77$$"$]'!""$"0/0a'******H!#77$$"%0l!"#$"0%)**4*******H!#77$$"$^'!""$"0A[L'******H!#77$$"%:l!"#$"0H)=T+++I!#77$$"$_'!""$"0'4hI+++I!#77$$"%Dl!"#$"0T,i-+++$!#77$$"$`'!""$"0mB#H******H!#77$$"%Nl!"#$"07&[E******H!#77$$"$a'!""$"0ZKY,+++$!#77$$"%Xl!"#$"0TDr!******H!#77$$"$b'!""$"0o>z*******H!#77$$"%bl!"#$"0B`")))*****H!#77$$"$c'!""$"0J%*)*)******H!#77$$"%ll!"#$"0Hfs(******H!#77$$"$d'!""$"0#[;s******H!#77$$"%vl!"#$"0'Q-0,++I!#77$$"$e'!""$"0>!=u******H!#77$$"%&e'!"#$"0Fv?++++$!#77$$"$f'!""$"0&>rz+++I!#77$$"%&f'!"#$"0hV`*******H!#77$$"$g'!""$"0m[H(******H!#77$$"%0m!"#$"0zgG2+++$!#77$$"$h'!""$"0R[,)******H!#77$$"%:m!"#$"0NW%Q+++I!#77$$"$i'!""$"0zsM'******H!#77$$"%Dm!"#$"0W`'y******H!#77$$"$j'!""$"0^PN*******H!#77$$"%Nm!"#$"0#Q*4)******H!#77$$"$k'!""$"0#4*H++++$!#77$$"%Xm!"#$"0rc#4+++I!#77$$"$l'!""$"0HMb*******H!#77$$"%bm!"#$"/O)o++++$!#67$$"$m'!""$"0X]b*******H!#77$$"%lm!"#$"0l9-*******H!#77$$"$n'!""$"0OTy*******H!#77$$"%vm!"#$"0m3`-+++$!#77$$"$o'!""$"0:1U(******H!#77$$"%&o'!"#$"0Ow!3+++I!#77$$"$p'!""$"0i!*Q)******H!#77$$"%&p'!"#$"0PIA(******H!#77$$"$q'!""$"0$y[.+++I!#77$$"%0n!"#$"0Ks.(******H!#77$$"$r'!""$"0D4H)******H!#77$$"%:n!"#$"0#**>7+++I!#77$$"$s'!""$"/(*)z/+++$!#67$$"%Dn!"#$"0f]e$******H!#77$$"$t'!""$"0aeW.+++$!#77$$"%Nn!"#$"0-P1&******H!#77$$"$u'!""$"0X$[M+++I!#77$$"%Xn!"#$"0xH*y******H!#77$$"$v'!""$"0"ezy+++I!#77$$"%bn!"#$"0_(3i)*****H!#77$$"$w'!""$"0ng$)4+++$!#77$$"%ln!"#$"03[%=)*****H!#77$$"$x'!""$"0UIY*)*****H!#77$$"%vn!"#$"0_Ni-+++$!#77$$"$y'!""$"0%RjJ)*****H!#77$$"%&y'!"#$"0'f,c,++I!#77$$"$z'!""$"0KyD#)*****H!#77$$"%&z'!"#$"0M2k*******H!#77$$"$!o!""$"0D+4,+++$!#77$$"%0o!"#$"0Z))G))*****H!#77$$"$"o!""$"0.*)*z)*****H!#77$$"%:o!"#$"0s[46+++$!#77$$"$#o!""$"0^#>k+++I!#77$$"%Do!"#$"0[E+*)*****H!#77$$"$$o!""$"0\+r)******H!#77$$"%No!"#$"0//(=******H!#77$$"$%o!""$"02_21+++$!#77$$"%Xo!"#$"0.n,)******H!#77$$"$&o!""$"0>(\#)******H!#77$$"%bo!"#$"0-d0,+++$!#77$$"$'o!""$"0vpR(******H!#77$$"%lo!"#$"0N^d,+++$!#77$$"$(o!""$"0K#e!*******H!#77$$"%vo!"#$"0\n>++++$!#77$$"$)o!""$"0M[3.+++$!#77$$"%&)o!"#$"0A(QT+++I!#77$$"$*o!""$"0OQE,+++$!#77$$"%&*o!"#$"0O<.-+++$!#77$$"$!p!""$"0vRa++++$!#77$$"%0p!"#$"0W!zB+++I!#77$$"$"p!""$"0A]#=+++I!#77$$"%:p!"#$"0a.M'******H!#77$$"$#p!""$"0tTM)******H!#77$$"%Dp!"#$"0@+2/+++$!#77$$"$$p!""$"0uIN*)*****H!#77$$"%Np!"#$"0cAT/+++$!#77$$"$%p!""$"0:?n/+++$!#77$$"%Xp!"#$"0R"z^,++I!#77$$"$&p!""$"0lpr0+++$!#77$$"%bp!"#$"0kq$e+++I!#77$$"$'p!""$"00Aw))*****H!#77$$"%lp!"#$"0yX(\******H!#77$$"$(p!""$"0bOt,+++$!#77$$"%vp!"#$"0`Mxy*****H!#77$$"$)p!""$"0/w@')*****H!#77$$"%&)p!"#$"0Fn?%******H!#77$$"$*p!""$"0OuT7+++$!#77$$"%&*p!"#$"09l/D+++$!#77$$"$+(!""$"0YcA"******H!#77$$"%0q!"#$"0Ou0,+++$!#77$$"$,(!""$"0uC_?+++$!#77$$"%:q!"#$"0$R?j+++I!#77$$"$-(!""$"08lt()*****H!#77$$"%Dq!"#$"0Ls!4)*****H!#77$$"$.(!""$"01*[o'*****H!#77$$"%Nq!"#$"/*>RH+++$!#67$$"$/(!""$"0@Rj!******H!#77$$"%Xq!"#$"0ms9y*****H!#77$$"$0(!""$"04]l()*****H!#77$$"%bq!"#$"0pk#=******H!#77$$"$1(!""$"0vf7/+++$!#77$$"%lq!"#$"0.Xl!******H!#77$$"$2(!""$"00Wz-+++$!#77$$"%vq!"#$"0#3:F+++I!#77$$"$3(!""$"0)oPn******H!#77$$"%&3(!"#$"0lu?,+++$!#77$$"$4(!""$"0D43$******H!#77$$"%&4(!"#$"/\qW+++I!#67$$"$5(!""$"0*zM(*******H!#77$$"%0r!"#$"0&)=8'******H!#77$$"$6(!""$"0$>>V******H!#77$$"%:r!"#$"0=>)G+++I!#77$$"$7(!""$"0JX^&******H!#77$$"%Dr!"#$"04Q8*******H!#77$$"$8(!""$"0/f%=******H!#77$$"%Nr!"#$"0u6![******H!#77$$"$9(!""$"0kT/#******H!#77$$"%Xr!"#$"07rB$******H!#77$$"$:(!""$"0ew7!)*****H!#77$$"%br!"#$".yDu*****H!#57$$"$;(!""$"0TV@.+++$!#77$$"%lr!"#$"01Ix3+++$!#77$$"$<(!""$"0<FL5+++$!#77$$"%vr!"#$"0XHk$******H!#77$$"$=(!""$"0bp5d*****H!#77$$"%&=(!"#$"0`Rc#)*****H!#77$$"$>(!""$"0b!36/++I!#77$$"%&>(!"#$"0R)eq%*****H!#77$$"$?(!""$"/GP<1++I!#67$$"%0s!"#$"07kA5+++$!#77$$"$@(!""$"0y&*[i+++$!#77$$"%:s!"#$"0xt')=+++$!#77$$"$A(!""$"/stc/++I!#67$$"%Ds!"#$"0sU8o+++$!#77$$"$B(!""$"0)*[=!******H!#77$$"%Ns!"#$"/u(>")*****H!#67$$"$C(!""$"0Zn!z+++I!#77$$"%Xs!"#$"0_%\p)*****H!#77$$"$D(!""$"0x#\A)*****H!#77$$"%bs!"#$"0=J*)4+++$!#77$$"$E(!""$"0:8I(******H!#77$$"%ls!"#$"07gw:+++$!#77$$"$F(!""$"0ne0k*****H!#77$$"%vs!"#$"0$4p5.++I!#77$$"$G(!""$"0*[gx)*****H!#77$$"%&G(!"#$"0mxZ,+++$!#77$$"$H(!""$"0hjd))*****H!#77$$"%&H(!"#$"0WHG%******H!#77$$"$I(!""$"0J1r/+++$!#77$$"%0t!"#$"0P4#))******H!#77$$"$J(!""$"/0V-+++I!#67$$"%:t!"#$"0v+2,+++$!#77$$"$K(!""$"04+x&******H!#77$$"%Dt!"#$"0j)R+,++I!#77$$"$L(!""$".UY*******H!#57$$"%Nt!"#$"/"3?"******H!#67$$"$M(!""$"0pt@"******H!#77$$"%Xt!"#$"0"Hgy+++I!#77$$"$N(!""$"0QH!e+++I!#77$$"%bt!"#$"0o&[F+++I!#77$$"$O(!""$"0O]I))*****H!#77$$"%lt!"#$"0'zhN-++I!#77$$"$P(!""$"0czZ")*****H!#77$$"%vt!"#$"0^Z\)******H!#77$$"$Q(!""$"0*H4?.++I!#77$$"%&Q(!"#$"0$*R$*z*****H!#77$$"$R(!""$".BG[*****H!#57$$"%&R(!"#$"0*Q5p,++I!#77$$"$S(!""$"0&G%H()*****H!#77$$"%0u!"#$"0a+x(******H!#77$$"$T(!""$"08gVE+++$!#77$$"%:u!"#$"/HVz'*****H!#67$$"$U(!""$"/eW,%*****H!#67$$"%Du!"#$"0*Qrw.++I!#77$$"$V(!""$"0)e`m******H!#77$$"%Nu!"#$"0;&>K(*****H!#77$$"$W(!""$"0\@wX*****H!#77$$"%Xu!"#$"0*=.O#*****H!#77$$"$X(!""$"0MV(f6++I!#77$$"%bu!"#$"0UPqj*****H!#77$$"$Y(!""$"0VG<L*****H!#77$$"%lu!"#$"0">ai3++I!#77$$"$Z(!""$"0rm#Q&*****H!#77$$"%vu!"#$"0))=g6+++$!#77$$"$[(!""$"0%>&oD+++$!#77$$"%&[(!"#$"0=4Lo*****H!#77$$"$\(!""$"0*QHz+++I!#77$$"%&\(!"#$"0"enW******H!#77$$"$](!""$"0bf">&*****H!#77$$"%0v!"#$"0%=Ul'*****H!#77$$"$^(!""$"0295r*****H!#77$$"%:v!"#$"0/#\o(*****H!#77$$"$_(!""$"0bz]4+++$!#77$$"%Dv!"#$"0;5"**)*****H!#77$$"$`(!""$"0PU5/+++$!#77$$"%Nv!"#$"/B)34+++$!#67$$"$a(!""$"/L"H++++$!#67$$"%Xv!"#$"0"=&)y+++I!#77$$"$b(!""$"0(\e>,++I!#77$$"%bv!"#$"/Tzp+++I!#67$$"$c(!""$"0//k,+++$!#77$$"%lv!"#$"0Y35;+++$!#77$$"$d(!""$"0C6W*******H!#77$$"%vv!"#$"0@Zv2+++$!#77$$"$e(!""$"/6Zx,++I!#67$$"%&e(!"#$"0ET"z%*****H!#77$$"$f(!""$"0K^\I*****H!#77$$"%&f(!"#$"09'3<,++I!#77$$"$g(!""$"0#3\\-++I!#77$$"%0w!"#$".\85,++$!#57$$"$h(!""$"0iu1N+++$!#77$$"%:w!"#$"0s!*p))*****H!#77$$"$i(!""$"00[\-+++$!#77$$"%Dw!"#$"0t_+c+++$!#77$$"$j(!""$"0Twj'4++I!#77$$"%Nw!"#$"0/H=k+++$!#77$$"$k(!""$"0_sgE*****H!#77$$"%Xw!"#$"0[H[&4++I!#77$$"$l(!""$"0@TGU)****H!#77$$"%bw!"#$"0`<:`*****H!#77$$"$m(!""$"0p[#p;++I!#77$$"%lw!"#$"/^VZ$)****H!#67$$"$n(!""$"0R>KW,++$!#77$$"%vw!"#$"07MaX*****H!#77$$"$o(!""$"/_%*G:++I!#67$$"%&o(!"#$"/EtZ7++I!#67$$"$p(!""$"0H'\p0++I!#77$$"%&p(!"#$"0%3!3N,++$!#77$$"$q(!""$"0&pJH&*****H!#77$$"%0x!"#$"0PB%o.++I!#77$$"$r(!""$"0N;j4*****H!#77$$"%:x!"#$"0QL-Q*****H!#77$$"$s(!""$"0ofw4+++$!#77$$"%Dx!"#$"0c374+++$!#77$$"$t(!""$"/w?G******H!#67$$"%Nx!"#$"0G$fX+++I!#77$$"$u(!""$"0,Ed))*****H!#77$$"%Xx!"#$"0:rA++++$!#77$$"$v(!""$"0kb$[******H!#77$$"%bx!"#$"0&R*y%******H!#77$$"$w(!""$"0)[O0******H!#77$$"%lx!"#$"0yYP,+++$!#77$$"$x(!""$"0$e5j******H!#77$$"%vx!"#$"0k#R%y*****H!#77$$"$y(!""$"0;1sw*****H!#77$$"%&y(!"#$"0nEZ()*****H!#77$$"$z(!""$"/(QH;+++$!#67$$"%&z(!"#$"0%y@%*******H!#77$$"$!y!""$"0*4])Q+++$!#77$$"%0y!"#$"/Z6['*****H!#67$$"$"y!""$"0h"*RB,++$!#77$$"%:y!"#$"0i8eN+++$!#77$$"$#y!""$"0V4rm,++$!#77$$"%Dy!"#$"0>@Dq,++$!#77$$"$$y!""$"0i]Q-+++$!#77$$"%Ny!"#$"0)QB\0++I!#77$$"$%y!""$"0`khu(****H!#77$$"%Xy!"#$"022VJ+++$!#77$$"$&y!""$"0H$Ht$)****H!#77$$"%by!"#$"/"[D"G++I!#67$$"$'y!""$"0"*)phE++I!#77$$"%ly!"#$"09@5I*****H!#77$$"$(y!""$"0,DG_'****H!#77$$"%vy!"#$"0`TET,++$!#77$$"$)y!""$"0Z5ZX-++$!#77$$"%&)y!"#$"0_:7n-++$!#77$$"$*y!""$"0.;`x,++$!#77$$"%&*y!"#$"0%)f*)\*****H!#77$$"$!z!""$"0'>x#>+++$!#77$$"%0z!"#$"0%Gi-E++I!#77$$"$"z!""$"0")G$4/++I!#77$$"%:z!"#$"0omX;*****H!#77$$"$#z!""$"0l'e'=)****H!#77$$"%Dz!"#$"/:qi*)****H!#67$$"$$z!""$"08v!=)*****H!#77$$"%Nz!"#$"0[n5q*****H!#77$$"$%z!""$"0*)f*)R+++$!#77$$"%Xz!"#$"0t'pc-++I!#77$$"$&z!""$"0c(*3o*****H!#77$$"%bz!"#$"0wTB++++$!#77$$"$'z!""$"0*e9"z*****H!#77$$"%lz!"#$"0R(yX/++I!#77$$"$(z!""$"0=iq")*****H!#77$$"%vz!"#$"0^V%Q,++I!#77$$"$)z!""$"0'RiP'*****H!#77$$"%&)z!"#$"0_%R;)*****H!#77$$"$*z!""$"0tzO'******H!#77$$"%&*z!"#$"0ZsSW*****H!#77$$"$+)!""$"01N^V+++$!#77$$"%0!)!"#$"0.!o&4+++$!#77$$"$,)!""$"0"e6?(*****H!#77$$"%:!)!"#$"0`=[#******H!#77$$"$-)!""$"02#ec/++I!#77$$"%D!)!"#$"0T61b)****H!#77$$"$.)!""$"0#*yV$y****H!#77$$"%N!)!"#$"0mV*e?++I!#77$$"$/)!""$"0#e$H@,++$!#77$$"%X!)!"#$"/h"eO-++$!#67$$"$0)!""$"/N'Ra+++$!#67$$"%b!)!"#$"0T(HEQ++I!#77$$"$1)!""$"0$f3?@++I!#77$$"%l!)!"#$"0XaC\.++$!#77$$"$2)!""$"0Ob%>M++I!#77$$"%v!)!"#$"0L(*f9/++$!#77$$"$3)!""$"00:%G.++I!#77$$"%&3)!"#$"0.XM(3++I!#77$$"$4)!""$"/$4$e9++I!#67$$"%&4)!"#$"06DN90++$!#77$$"$5)!""$"0:OD%******H!#77$$"%0")!"#$"0&)G<H-++$!#77$$"$6)!""$"/%4P$3++I!#67$$"%:")!"#$"0*f)=)\++I!#77$$"$7)!""$"01!GB#*****H!#77$$"%D")!"#$"0^Cyg.++$!#77$$"$8)!""$"0%GvfM++I!#77$$"%N")!"#$"0'*\^/)****H!#77$$"$9)!""$"0Z*Rd$*****H!#77$$"%X")!"#$"0P,H^-++$!#77$$"$:)!""$"0OaBN,++$!#77$$"%b")!"#$"0"\Tt-++I!#77$$"$;)!""$"0jT[()*****H!#77$$"%l")!"#$"0'*z/e*****H!#77$$"$<)!""$"0LW\x*****H!#77$$"%v")!"#$"/l,h(*****H!#67$$"$=)!""$"0GUmY*****H!#77$$"%&=)!"#$"0UFNT*****H!#77$$"$>)!""$"03(4%>+++$!#77$$"%&>)!"#$"0WqMZ+++$!#77$$"$?)!""$"/lNc.++I!#67$$"%0#)!"#$"/n>1.++I!#67$$"$@)!""$"0)3oV)*****H!#77$$"%:#)!"#$"0#o@1******H!#77$$"$A)!""$"0U/?y+++$!#77$$"%D#)!"#$"0&z$y;)****H!#77$$"$B)!""$"07!yq&)****H!#77$$"%N#)!"#$"0A()\L*****H!#77$$"$C)!""$"0Zh`$4++I!#77$$"%X#)!"#$"0%>z<.++I!#77$$"$D)!""$"0&z.P"*****H!#77$$"%b#)!"#$"0&>+]-++I!#77$$"$E)!""$"0W&=`J++I!#77$$"%l#)!"#$"0(z.g#*****H!#77$$"$F)!""$"0cp&4S****H!#77$$"%v#)!"#$"09\ab2++$!#77$$"$G)!""$"07()[E,++$!#77$$"%&G)!"#$"0G&o6_****H!#77$$"$H)!""$"0.lyh3++$!#77$$"%&H)!"#$"0e#)oY$****H!#77$$"$I)!""$"0_$3yv****H!#77$$"%0$)!"#$"0H&o,/****H!#77$$"$J)!""$"0$o`et++I!#77$$"%:$)!"#$"08LD"G++I!#77$$"$K)!""$"06Nbh+++$!#77$$"%D$)!"#$"/,'Qb(****H!#67$$"$L)!""$"0W&*yE1++$!#77$$"%N$)!"#$"01?Qe,++$!#77$$"$M)!""$"0p!)R"H****H!#77$$"%X$)!"#$"00i&4R****H!#77$$"$N)!""$"0iZQY,++$!#77$$"%b$)!"#$"0$)f"z:++I!#77$$"$O)!""$"/cvoV++I!#67$$"%l$)!"#$"0'zECm****H!#77$$"$P)!""$"0aLji+++$!#77$$"%v$)!"#$"0H))[h+++$!#77$$"$Q)!""$"0yegG)****H!#77$$"%&Q)!"#$"0;0X/+++$!#77$$"$R)!""$"0l]9],++$!#77$$"%&R)!"#$"/%*\">*****H!#67$$"$S)!""$"029Ay+++$!#77$$"%0%)!"#$"0"He13++I!#77$$"$T)!""$"0s!=y-++I!#77$$"%:%)!"#$"0^(z>******H!#77$$"$U)!""$"0$4pI+++I!#77$$"%D%)!"#$"0z:qp+++$!#77$$"$V)!""$"0x:qR)****H!#77$$"%N%)!"#$"0\cH$)*****H!#77$$"$W)!""$"/YhQD++I!#67$$"%X%)!"#$"0aCdL+++$!#77$$"$X)!""$"0Ev4#4++I!#77$$"%b%)!"#$"0D4>#R++I!#77$$"$Y)!""$"0/R3y$****H!#77$$"%l%)!"#$"0oMT7%****H!#77$$"$Z)!""$"07!z[P****H!#77$$"%v%)!"#$"0$p9$z,++$!#77$$"$[)!""$"04!>lA****H!#77$$"%&[)!"#$"0&4"Gn*)***H!#77$$"$\)!""$"0vE\)**)***H!#77$$"%&\)!"#$"0)z5al****H!#77$$"$])!""$"0;Z-/,++$!#77$$"%0&)!"#$"0>V;P/++$!#77$$"$^)!""$"0ilI34++$!#77$$"%:&)!"#$"0&ytIX++I!#77$$"$_)!""$"0(*[Ry#****H!#77$$"%D&)!"#$"0H)=*H&****H!#77$$"$`)!""$"0xq*oH++I!#77$$"%N&)!"#$"0B"==!)****H!#77$$"$a)!""$"0J#*GF&)***H!#77$$"%X&)!"#$"0`r[e.++$!#77$$"$b)!""$"/vlS$))***H!#67$$"%b&)!"#$"0raG"*4++$!#77$$"$c)!""$"0u\*>f++I!#77$$"%l&)!"#$"0yz$>F++I!#77$$"$d)!""$"0&)**30*****H!#77$$"%v&)!"#$"0%)R$[z****H!#77$$"$e)!""$"0GXJ'*)****H!#77$$"%&e)!"#$"0$G`SX****H!#77$$"$f)!""$".*3[S****H!#57$$"%&f)!"#$"0%48?$*****H!#77$$"$g)!""$"0UJ,0*****H!#77$$"%0')!"#$"0c&>f<++I!#77$$"$h)!""$"0$o&zw(****H!#77$$"%:')!"#$"0JxEs(****H!#77$$"$i)!""$"0"\^b'*****H!#77$$"%D')!"#$"0W(=(>*****H!#77$$"$j)!""$"0r#R2(*****H!#77$$"%N')!"#$"0'RI:*)****H!#77$$"$k)!""$"03W;b*****H!#77$$"%X')!"#$"0N&[c(*****H!#77$$"$l)!""$"0r<4q*****H!#77$$"%b')!"#$"0Xrtm*****H!#77$$"$m)!""$"0/(fBz****H!#77$$"%l')!"#$"00")pz0++$!#77$$"$n)!""$"/_:Sv****H!#67$$"%v')!"#$"0xTJi+++$!#77$$"$o)!""$"/)z!pt****H!#67$$"%&o)!"#$"04L0(Q****H!#77$$"$p)!""$"0pfH75++$!#77$$"%&p)!"#$"0J(**44,+I!#77$$"$q)!""$"0A^B]&****H!#77$$"%0()!"#$"00)fI2++I!#77$$"$r)!""$"0v&3gC)***H!#77$$"%:()!"#$"0#["fn&****H!#77$$"$s)!""$"0&pd'*3,+I!#77$$"%D()!"#$"0'R[<w(***H!#77$$"$t)!""$"0v:(**=)***H!#77$$"%N()!"#$"0$*40[$****H!#77$$"$u)!""$"09SY]<++$!#77$$"%X()!"#$"0j)4,\)***H!#77$$"$v)!""$"0c,2<%****H!#77$$"%b()!"#$"//3lW++I!#67$$"$w)!""$"0H,]X=++$!#77$$"%l()!"#$"0X)4Rd)***H!#77$$"$x)!""$"0Enzg$****H!#77$$"%v()!"#$"/G+m7++I!#67$$"$y)!""$"0z0[*)3++$!#77$$"%&y)!"#$"0VfPI0++$!#77$$"$z)!""$"0aNX`7++$!#77$$"%&z)!"#$"0cWge5++$!#77$$"$!))!""$"0<zk***)***H!#77$$"%0))!"#$"0n8%H?****H!#77$$"$"))!""$"/([-(p****H!#67$$"%:))!"#$"0htS'3++I!#77$$"$#))!""$"/fe(y+++$!#67$$"%D))!"#$"0(*z6-+++$!#77$$"$$))!""$"0^"e]5++I!#77$$"%N))!"#$"0$*f"=y****H!#77$$"$%))!""$"0'3saF++I!#77$$"%X))!"#$"0p&>&4)****H!#77$$"$&))!""$"0ZsTO*****H!#77$$"%b))!"#$"/^l,#)****H!#67$$"$'))!""$"0)[VJ7++I!#77$$"%l))!"#$"0:KYY+++$!#77$$"$())!""$"0t'>z))****H!#77$$"%v))!"#$"0/6D.*****H!#77$$"$)))!""$"0Ro^$f****H!#77$$"%&)))!"#$"0;#\JJ****H!#77$$"$*))!""$"0#zc-q****H!#77$$"%&*))!"#$"0a'*ob/++$!#77$$"$!*)!""$"0Xbx&Q++I!#77$$"%0*)!"#$"04Z0&4++I!#77$$"$"*)!""$"0(*3nI5++$!#77$$"%:*)!"#$"07K`;(****H!#77$$"$#*)!""$"0")f^bD++$!#77$$"%D*)!"#$"0LwG'4****H!#77$$"$$*)!""$"0E8nq,++$!#77$$"%N*)!"#$"/140x'***H!#67$$"$%*)!""$"0'><wj)***H!#77$$"%X*)!"#$"/*\^/#****H!#67$$"$&*)!""$"/hJG-++I!#67$$"%b*)!"#$"0JU#z)3++$!#77$$"$'*)!""$"0[\$)=u***H!#77$$"%l*)!"#$"0mJI(z(***H!#77$$"$(*)!""$"0-y)z'o***H!#77$$"%v*)!"#$"0m>aF3++$!#77$$"$)*)!""$"0k65>#****H!#77$$"%&)*)!"#$"0'[O"R4++$!#77$$"$**)!""$"0=c2&)y***H!#77$$"%&**)!"#$"0cjP@6++$!#77$$"$+*!""$"/'3;q*)***H!#67$$"%0!*!"#$"02)Q$>.++$!#77$$"$,*!""$"0*y"3u&****H!#77$$"%:!*!"#$"0uFvD'****H!#77$$"$-*!""$"/3%yE$****H!#67$$"%D!*!"#$"0HW\T4++$!#77$$"$.*!""$"0#=FV0****H!#77$$"%N!*!"#$"0_XHr)****H!#77$$"$/*!""$"0h$)***G++I!#77$$"%X!*!"#$"0#*\,[+++$!#77$$"$0*!""$"/W&ot'****H!#67$$"%b!*!"#$"0&3de()****H!#77$$"$1*!""$"0sC]#e****H!#77$$"%l!*!"#$"0x:Hx(****H!#77$$"$2*!""$"0TCp%>++I!#77$$"%v!*!"#$"0sHu'y****H!#77$$"$3*!""$"/fi&G(****H!#67$$"%&3*!"#$"0))G;8'****H!#77$$"$4*!""$"0/W/*p****H!#77$$"%&4*!"#$"0Je'3V****H!#77$$"$5*!""$"028RR1++$!#77$$"%0"*!"#$"0@"3B<****H!#77$$"$6*!""$"023=R+++$!#77$$"%:"*!"#$"0,2iZ-++$!#77$$"$7*!""$"0KJ8i$****H!#77$$"%D"*!"#$"/$y!p+,+I!#67$$"$8*!""$"0))H"*[$****H!#77$$"%N"*!"#$"0#=4j$G++$!#77$$"$9*!""$"0HWU_)****H!#77$$"%X"*!"#$"0zR*>?,+I!#77$$"$:*!""$"0$Q#*)yU++$!#77$$"%b"*!"#$"0(>I\a)***H!#77$$"$;*!""$"03wRE1++$!#77$$"%l"*!"#$"0Bo5:x***H!#77$$"$<*!""$"0:cS1U++$!#77$$"%v"*!"#$"0/!\7A&***H!#77$$"$=*!""$"0\2U;i***H!#77$$"%&=*!"#$"01EC/M++$!#77$$"$>*!""$"0y3Mc#****H!#77$$"%&>*!"#$"0D0^y*)***H!#77$$"$?*!""$"0a;;z()***H!#77$$"%0#*!"#$"0Qw4J>++$!#77$$"$@*!""$"0z,I3k***H!#77$$"%:#*!"#$"0@+[Cw***H!#77$$"$A*!""$"0>#e8<++I!#77$$"%D#*!"#$"0Zby*\-+I!#77$$"$B*!""$"0i7g!y-+I!#77$$"%N#*!"#$"07B"4#z***H!#77$$"$C*!""$"0n**o_&****H!#77$$"%X#*!"#$"0%y/!3*)***H!#77$$"$D*!""$"0/DBv#****H!#77$$"%b#*!"#$"0)*3#>d****H!#77$$"$E*!""$"0#[zHS****H!#77$$"%l#*!"#$"0*RJa<++I!#77$$"$F*!""$"0RHR&>++I!#77$$"%v#*!"#$"0Ac**z$****H!#77$$"$G*!""$"0pIn?+++$!#77$$"%&G*!"#$"0KhR!f++I!#77$$"$H*!""$"/X)yd)****H!#67$$"%&H*!"#$"0d'3As****H!#77$$"$I*!""$"0B$Gnt****H!#77$$"%0$*!"#$"0/2YZ/++$!#77$$"$J*!""$"0[o'>%*****H!#77$$"%:$*!"#$"0Yjz`()***H!#77$$"$K*!""$"0$*fYP#****H!#77$$"%D$*!"#$"0Hct\D++$!#77$$"$L*!""$"0@vT0"****H!#77$$"%N$*!"#$"0v0Jo()***H!#77$$"$M*!""$"0uHFr#****H!#77$$"%X$*!"#$"0cP#Q9****H!#77$$"$N*!""$"0Gs_^,++$!#77$$"%b$*!"#$"0')oj%y++I!#77$$"$O*!""$"0mRv4g***H!#77$$"%l$*!"#$".ZdPD++$!#57$$"$P*!""$"/YO%pH++$!#67$$"%v$*!"#$"09`6%3&***H!#77$$"$Q*!""$"/AF`j(***H!#67$$"%&Q*!"#$"0Y(oIl(***H!#77$$"$R*!""$"0Z*=v#4++$!#77$$"%&R*!"#$"0WY,]%)***H!#77$$"$S*!""$"0<yOcH***H!#77$$"%0%*!"#$"0JISt$)***H!#77$$"$T*!""$"0$)o(=q,+I!#77$$"%:%*!"#$"0x"Qt;)***H!#77$$"$U*!""$"/UV+i(***H!#67$$"%D%*!"#$"0Q5G0\***H!#77$$"$V*!""$"0e#zo%=++$!#77$$"%N%*!"#$"09wJ^I++$!#77$$"$W*!""$"0_#oW6-+I!#77$$"%X%*!"#$"0@f"e")****H!#77$$"$X*!""$"0yZ+d(****H!#77$$"%b%*!"#$"0<%G#[0++$!#77$$"$Y*!""$"0bp!R2****H!#77$$"%l%*!"#$"/**="*>)***H!#67$$"$Z*!""$"0'ps]O++I!#77$$"%v%*!"#$"0t$fMf++I!#77$$"$[*!""$"02ANa5++$!#77$$"%&[*!"#$"0B4lf*)***H!#77$$"$\*!""$"0PXC?'****H!#77$$"%&\*!"#$"01I<b+++$!#77$$"$]*!""$"0YOPP.++$!#77$$"%0&*!"#$"0sz.M*****H!#77$$"$^*!""$"02*))*e2++$!#77$$"%:&*!"#$"0e7e!o++I!#77$$"$_*!""$"0Z)pOO****H!#77$$"%D&*!"#$"0<,3d.++$!#77$$"$`*!""$"0[))>c>++$!#77$$"%N&*!"#$"0Kb*GH-+I!#77$$"$a*!""$"0'\Wgd(***H!#77$$"%X&*!"#$"0MzYhF++$!#77$$"$b*!""$"0#y&fv$****H!#77$$"%b&*!"#$"0ikl]8++$!#77$$"$c*!""$"0`")fwo++$!#77$$"%l&*!"#$"/*QvYc++$!#67$$"$d*!""$"0["e`G&***H!#77$$"%v&*!"#$"0ybCx*)***H!#77$$"$e*!""$"0.d"\G%***H!#77$$"%&e*!"#$"0;AC#H!***H!#77$$"$f*!""$"0&*\%eG!***H!#77$$"%&f*!"#$"0-_q?9++$!#77$$"$g*!""$"06b+$[2+I!#77$$"%0'*!"#$"0C5;w*3+I!#77$$"$h*!""$"00)HJC!***H!#77$$"%:'*!"#$"0co9G")***H!#77$$"$i*!""$"0iJ173***H!#77$$"%D'*!"#$"0YzL+!))**H!#77$$"$j*!""$"00ol'R$***H!#77$$"%N'*!"#$"0_zjQ@***H!#77$$"$k*!""$"0mIp3"****H!#77$$"%X'*!"#$"/"=aT()***H!#67$$"$l*!""$"/j#o)f)***H!#67$$"%b'*!"#$"0%[gAJ1+I!#77$$"$m*!""$"0@Q+4V***H!#77$$"%l'*!"#$"0y.Pc"****H!#77$$"$n*!""$"0w"H_,,+I!#77$$"%v'*!"#$"0JcEoC++$!#77$$"$o*!""$"0Lj!z$=++$!#77$$"%&o*!"#$"0'>W;Y(***H!#77$$"$p*!""$"0E![#Hx***H!#77$$"%&p*!"#$"0&[!Q#)y***H!#77$$"$q*!""$"0"*e^U"****H!#77$$"%0(*!"#$"06dsI6++$!#77$$"$r*!""$"0y[1-+++$!#77$$"%:(*!"#$"0))))y%3,+I!#77$$"$s*!""$"0))z*y)4++$!#77$$"%D(*!"#$"0>J`H*****H!#77$$"$t*!""$"03DdL()***H!#77$$"%N(*!"#$"0F#y?L)***H!#77$$"$u*!""$"0&z9\*y***H!#77$$"%X(*!"#$"0Utm?))***H!#77$$"$v*!""$"0.&ex,)***H!#77$$"%b(*!"#$"0[='3C1+I!#77$$"$w*!""$"0f(=W8****H!#77$$"%l(*!"#$"0R%Gj-%***H!#77$$"$x*!""$"0$e>%)R$***H!#77$$"%v(*!"#$"0WL5Qb***H!#77$$"$y*!""$"0%G!HQ*****H!#77$$"%&y*!"#$"0dI+"z4+I!#77$$"$z*!""$"0)o9e?4+I!#77$$"%&z*!"#$"02:#ol6+I!#77$$"$!)*!""$"0Tl+O!*)**H!#77$$"%0)*!"#$"0t8dX%3+I!#77$$"$")*!""$"0'R**yy3+I!#77$$"%:)*!"#$"0#RK"e')***H!#77$$"$#)*!""$"01:X*>'***H!#77$$"%D)*!"#$"0VZR1N++$!#77$$"$$)*!""$"0"*H'Hx2+I!#77$$"%N)*!"#$"/O'4ED)**H!#67$$"$%)*!""$"0>-s8=++$!#77$$"%X)*!"#$"0$*H`=0,+$!#77$$"$&)*!""$"0;\Tef***H!#77$$"%b)*!"#$"0Euu)o.+I!#77$$"$')*!""$"0Vjt2"****H!#77$$"%l)*!"#$"/l(pQ<,+$!#67$$"$()*!""$"0>n#\o****H!#77$$"%v)*!"#$"06=VYc++$!#77$$"$))*!""$"0-hy12***H!#77$$"%&))*!"#$"0,bna;++$!#77$$"$*)*!""$"0Y%ywc,+I!#77$$"%&*)*!"#$"0)y(RVq***H!#77$$"$!**!""$"03M7bG++$!#77$$"%0**!"#$"0:V1MD++$!#77$$"$"**!""$"0#\VO"4++$!#77$$"%:**!"#$"0\!ew8,+I!#77$$"$#**!""$"0j\#)3%****H!#77$$"%D**!"#$"0Z$>5q,+I!#77$$"$$**!""$"0-T5]0++$!#77$$"%N**!"#$"0%QIQs****H!#77$$"$%**!""$"0xT_a1++$!#77$$"%X**!"#$"0$G4CO++I!#77$$"$&**!""$"0p6;T7++$!#77$$"%b**!"#$"/))3Ac****H!#67$$"$'**!""$"/8qye++I!#67$$"%l**!"#$"/J')*)3++I!#67$$"$(**!""$"0^?A=P++$!#77$$"%v**!"#$"08iHP/++$!#77$$"$)**!""$"0(f2SP,+I!#77$$"%&)**!"#$"02@PD<***H!#77$$"$***!""$"0nZ"H/*)**H!#77$$"%&***!"#$"0)y\2k3+I!#7-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q%time6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q,temperature6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#""$-%*AXESSTYLEG6#%$BOXG-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+]!""-%.BOUNDS_HEIGHTG6#$"%+]!""-%)CHILDRENG6"Ig==</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L14543" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" family="P052" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L14577" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">From the plot, it can be clearly seen that in this NVT simulation, the temperature remains perfectly constant up to a certain point, beyond which there is a sharp increase in the fluctuations. This is so because PIMD simulations are very difficult to converge without efficient thermostatting. A simple velocity rescaling scheme was used here (written in the form of a more general Berendsen thermostat), but for larger number of steps, more efficient methods are required. Furthermore, ideally one should propagate the beads such that the motion of the centroid is also accounted for. A Box-Muller sampling algorithm can also be used for initialising the velocities of the beads from the Boltzmann distribution. As a final remark, it can be stated that though this simple code can generate a constant temperature run up to a certain limit, to get an accurate canonical distribution and constant temperature throughout the entire simulation, advanced methods must be resorted to.</Font></Text-field><Text-field style="Text" size="10" family="P052" layout="Normal"></Text-field>
</Input>
</Group>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" size="10" family="P052" layout="Heading 2"><Font size="14" family="P052">Discussions</Font></Text-field></Title>
<Group labelreference="L14616" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">This worksheet broadly consists of two parts - PIQM and PIMD. In the first part, the basics of the path integral formalism was introduced, including the density matrix and the action integral. In particular, the eigenvalues and eigenstates of the harmonic oscillator were derived. Electronic structure calculations were carried out on a model system and were used for fitting parameters of a harmonic oscillator type function. These fitted parameters were finally used for plotting the HO wavefunctions and the path integral kernel.
The second part of this worksheet is much more specific in the sense that it deals with a widely used numerical method of implementing path integrals - PIMD. Following a brief introduction to how PIMD is carried out, the concept of quantum-classical isomorphism and finally an illustrative example of a PIMD simulation on a toy system are presented. The short PIMD simulation proves that for better convergence, advanced techniques must be used.</Font></Text-field>
</Input>
</Group>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" size="10" family="P052" layout="Heading 2"><Font size="14" family="P052">References</Font></Text-field></Title>
<Group labelreference="L14617" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" size="10" family="P052" layout="Normal"><Font size="10" family="P052">1) Mark Tuckerman, Statistical Mechanics: Theory and Molecular Simulation, Oxford University Press, 2010
2) Richard P. Feynman, Albert R. Hibbs, Daniel F. Styer, Quantum Mechanics and Path Integrals, New York: Dover Books on Physics; Dover Publications, 2010
3) T. E. Markland; M. Ceriotti, Nature Reviews Chemistry 2018, 2(0109)
4) M. Ceriotti; W. Fang; P. G. Kusalik; R. H. McKenzie; A. Michaelides; M. A. Morales; T. E. <Font encoding="UTF-8">Markland, Chemical Reviews 2016, 116(13), 7529\342\200\2237550
</Font>5) http://www.sklogwiki.org/SklogWiki/index.php/Path_integral_formulation
6) Daniel F. Styer, Miranda S. Balkin, Kathryn M. Becker, Matthew R. Burns, Christopher E. Dudley, Scott T. Forth, Jeremy S. Gaumer, Mark A. Kramer, David C. Oertel, Leonard H. Park, Marie T. Rinkoski, Clait T. Smith, Timothy D. Wotherspoon, Am. J. Phys., 2002, 70 (3)</Font></Text-field>
</Input>
</Group>
</Section>
<Group labelreference="L14621" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" family="P052" layout="Normal"></Text-field>
</Input>
</Group>
</Section>
</Worksheet>