blob: 9aa4ffe58d5a8cea5ada1420ac134e3ecb921ba8 (
plain) (
blame)
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
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
|
rows:18 cols:32
^...........#...........................#...#..........................#..########.....................#...............................#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................@.......#...#..........................#..########.....................#...............................#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................@......#..########.....................#...............................#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~......#..########..............@......#...............................#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~......#..########..............~......#........................@......#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~......#..########..............~......#........................~@.....#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~......#..########..............~@.....#........................~~.....#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~......#..########..............~~@....#........................~~.....#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~......#..########..............~~~....#........................~~@....#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~......#..########..............~~~....#........................~~~@...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~......#..########..............~~~@...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~.......#...#...................~..@...#..########..............~~~~...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~..@....#...#...................~..~...#..########..............~~~~...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...........#...................~..~@...#...#...................~..~...#..########..............~~~~...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...@.......#...................~..~~...#...#...................~..~...#..########..............~~~~...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~@......#...................~..~~...#...#...................~..~...#..########..............~~~~...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~@..#...#...................~..~...#..########..............~~~~...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~.@.#..########..............~~~~...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~@~.#..########..............~~~~...#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~@..#........................~~~~...#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~@..#..............................#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................@.#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~@#............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~@............................#.........#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#.@.......#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#@~.......#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................@~~.......#....##############...#.........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#@........#.........................#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#......................@..#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................@~..#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...@~........#.....................~~..#.....#.....#...............................#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#.....#.....#...............@...............#....................#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#.....#.....#...............~...............#...............@....#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#.....#.....#...............~...............#...............~@...#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#.....#.....#...............~...............#...............~~@..#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#.....#.....#...............~...............#...............~~~@.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#.....#.....#...............~..@............#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#.....#.....#...............~..~@...........#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#.....#.....#...............~..~~@..........#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#@....#.....#...............~..~~~..........#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~@...#.....#...............~..~~~..........#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~@..#.....#...............~..~~~..........#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.@........#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~@.......#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~@......#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~@.....#...............~~~~.#..........#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#....@.....#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#...@~.....#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#...~~.....#................#...#...@#.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..@~~.....#................#...#...##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..@##.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~@#.....#....................#..........#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#..@.......#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.@~.......#...#########...................#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########..........@........#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........@~........#...............................#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................@.........#......$..................................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~.........#......$..............@...................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~.........#......$..............~@..................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~@........#......$..............~~..................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~@.......#......$..............~~..................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.......#......$..............~~@.................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.......#......$..............~~~@................................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.......#......$..............~~~~@...............................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.@.....#......$..............~~~~~...............................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~@....#......$..............~~~~~...............................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~....#......$..............~~~~~@..............................#...............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~....#......$..............~~~~~~..............................#@..............................#..................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~....#......$..............~~~~~~..............................#~..............................#@.................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~....#......$..............~~~~~~..............................#~..............................#~@................
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~....#......$..............~~~~~~..............................#~..............................#~~@...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~....#......$..............~~~~~~..............................#~.@............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~....#......$..............~~~~~~..............................#~@~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~....#......$..............~~~~~~@.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~@...#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~........#.....................~~~.~~~@..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~.......#...#########.........~~.....@..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~....@..#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##.....#....................#.~~....~@.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##...@.#....................#.~~....~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.....#................#...#..~##..@~.#....................#.~~....~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~..@..#................#...#..~##..~~.#....................#.~~....~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.....#...............~~~~.#..~~~.@~..#................#...#..~##..~~.#....................#.~~....~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~.@...#...............~~~~.#..~~~.~~..#................#...#..~##..~~.#....................#.~~....~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~@~...#...............~~~~.#..~~~.~~..#................#...#..~##..~~.#....................#.~~....~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~@~~..#................#...#..~##..~~.#....................#.~~....~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##@.~~.#....................#.~~....~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~..@.~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~.@~.~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~@~~.~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~@#~.~~.#....................#.~~~~~.~~.#...#########.........~~.....~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~~~~.~~.#...#########.........~~.@...~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~~~~.~~.#...#########.........~~@~...~..#.....................~~~.~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~~~~.~~.#...#########.........~~-~...~..#.....................~~~@~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~~~~.~~.#...#########.........~~-~@..~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~~~~.~~.#...#########.........~~-~~@.~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~~~~.~~.#...#########.........~~-~~~@~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~.~~.#....................#.~~~~~@~~.#...#########.........~~-~~~~~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~##~@~~.#....................#.~~~~~~~~.#...#########.........~~-~~~~~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~#@~-~~.#....................#.~~-~~-~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#.....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~~~~..#................#...#..~#@~-~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#.....................~~..#~~~..#@....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#@....................~~..#~~~..#~....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........@~....................~~..#~~~..#~....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~@...................~~..#~~~..#~....#...............~..~~~.~~~~~~...#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~...................~~..#~~~..#~@...#...............~..~~~.~~~~~~...#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~...................~~..#~~~..#~~@..#...............~..~~~.~~~~~~...#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~...................~~..#~~~..#~~~..#...............~..~~~.~~~~~~@..#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~...................~~..#~~~..#~~~..#...............~..~~~.~~~~~~~@.#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~...................~~..#~~~..#~~~..#...............~..~~~.~~~~~~~~@#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~...................~~..#~~~..#~~~..#...............~..~~~.~~~~~~~~~@...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~...................~~..#~~~..#~~~.@#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~..@................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#....##############...#~........#~~.@~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#...@##############...#~........#~~.~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#...~@#############...#~........#~~.~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#..@~##############...#~........#~~.~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#............................#~~.......#..~~##############...#~........#~~@~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#.........@..................#~~.......#..~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#........@~..................#~~.......#..~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#........~~..................#~~.......#.@~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#........~~..................#~~.......#@~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#............................~~#.......@~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#........................~~~~~..#......@.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#......@.................~~~~~..#......~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#.....@~.................~~~~~..#......~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#....@~~.................~~~~~..#......~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..##@#####..............~~~~~..#....~~~.................~~~~~..#......~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#....~~~.................~~~~~..#....@.~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#....~~~.................~~~~~..#...@~.~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#...@~~~.................~~~~~..#...~~.~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#..@~~~~.................~~~~~..#...~~.~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#.@~~~~~.................~~~~~..#...~~.~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#@~~~~~~.................~~~~~..#...~~.~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..@~~~~~~~.................~~~~~..#...~~.~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#@..~~.~.....................~~#.......~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.@.....~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~@....~~~..................#~~.......#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~...@...#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~..@~...#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.@~~...#~~~~##############...#~........#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.~~~...#~~~~##############...#~..@.....#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.~~~...#~~~~##############...#~.@~.....#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.~~~...#~~~~##############...#~@~~.....#~~-~~................~~..#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.~~~...#~~~~##############...#~~~~.....#~~-~~................~~@.#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.~~~...#~~~~##############...#~~~~.....#~~-~~................~~~@#~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.~~~...#~~~~##############...#~~~~.....#~~-~~................~~~~@~~~..#~~~.~#...............~..~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.~~~...#~~~~##############...#~~~~.....#~~-~~................~~~-#~~~..#~~~.~#...............~.@~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~.~~~...#~~~~##############...#~~~~.....#~~-~~................~~~-#~~~..#~~~.~#...............~@~~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~@~~~...#~~~~##############...#~-~~.....#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~@.~~....~~~..................#~~~~~~...#~~~~##############...#~-~~.....#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~-~~~...#~~~~##############...#~--~.....#~~-~~................~~--@~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~-~~~...#~~~~##############...#~--~@....#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~-~~~...#~~~~##############...#~--~~@...#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~-~~~...#~~~~##############...#~--~~~@..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~-~~~@..#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~....~~~..................#~~-~~~~@.#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~.@..~~~..................#~~-~~~~~.#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~..~~.~.....................~~#.~~@~..~~~..................#~~-~~~~~.#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~.@~~.~.....................~~#.~~~~..~~~..................#~~-~~~~~.#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~@~~~.~.....................~~#.~~~~..~~~..................#~~-~~~~~.#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~.~.....................~~#.~~-~@.~~~..................#~~-~~~~~.#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~.~.....................~~#.~~-~~@~~~..................#~~-~~~~~.#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~.~.....................~~#.~~-~~~~~~..................#~~-~~~~~.@~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~@~.....................~~#.~~-~~~~~~..................#~~-~~~~~.#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#.~~-~~-~~~..................#~~-~~~~~@#~~~~##############...#~--~~~~..#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#.~~-~~-~~~..................#~~-~~~~~~#~~~~##############...#~--~~~~.@#~~-~~................~~--#~~~..#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#.~~-~~-~~~..................#~~-~~~~~~#~~~~##############...#~--~~~~.~#~~-~~................~~--#~~~.@#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#.~~-~~-~~~..................#~~-~~~~~~#~~~~##############...#~--~~~~.~#~~-~~................~~--#~~~@~#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#.~~-~~-~~~..................#~~-~~~~~~#~~~~##############...#~--~~~~@~#~~-~~................~~--#~~~~~#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#.~~-~~-~~~..................#~~-~~~~~~#~~~~##############...#~--~~~~-~#~~-~~................~~--#~~~-~@~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#.~~-~~-~~~..................#~~-~~~~~~#~~~~##############...#~--~~~~-~@~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#.~~-~~-~~~..................#~~-~~~~~~@~~~~##############...#~--~~~~--#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~#@~~----~~~..................#~~-~~~---#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..@~--~~-~.....................~~#~~~----~~~..................#~~-~~~---#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..#~--~~-~.....................~~@~~~----~~~..................#~~-~~~---#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.#..########..............~~~~~..#~~~~~~~.................~~~~~..@~--~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#@.########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..@...#...................~..~~~.#~.########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~......#...................~..~~~..#...#...................~..~~~.@~.########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#...#...................~..~~~.#~@########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~......#...................~..~~~..#@..#...................~..~~~.#~~########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~...@..#...................~..~~~..#~..#...................~..~~~.#~~########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~..@~..#...................~..~~~..#~..#...................~..~~~.#~~########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~.@~~..#...................~..~~~..#~..#...................~..~~~.#~~########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~@~~~..#...................~..~~~..#~..#...................~..~~~.#~~########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~~~~~..#...................~..~~~@.#~..#...................~..~~~.#~~########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~@#~~########..............~~~~~..#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~~#~~########..............~~~~~.@#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~~#~~########..............~~~~~.~@~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~~#~~########..............~~~~~@~#~~~~~~~.................~~~~~..#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~~#~~########..............~~~~~~~#~~~~~~~.................~~~~~@.#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~~#~~########..............~~~~~~~#~~~~~~~.................~~~~~~@#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~~#~~########..............~~~~~~~#~~~~~~~.................~~~~~~~@---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~~#~~########..............~~~~~~~#~~~~~~~.................~~~~~~~#---~~-~.....................~~@-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~~~~~..#...................~..~~~~.#~..#...................~..~~~~@~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~~~~~..#...................~..~~~~@#~..#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~~~~~..#...................~..~~~~~#~..#...................~..~~~-@~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~~~~~..#...................~..~~~~~@~..#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~--~~..#...................~..~~~--@~..#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~---~@.#...................~..~~~--#~..#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~---~~.#...................~..~~~--#~@.#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~---~~.#...................~..~~~--#~~.#...................~..~~~-#~~@#######..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~---~~.#...................~..~~~--#~~@#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~---~~.#...................~..~~~--#~~~@...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~---~~.#...................~..~~~--#~~~#...................~..~~~-#~~#@######..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~---~~@#...................~..~~~--#~~~#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~---~~~@...................~..~~~--#~~~#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--@~--#...................~..~~~-#~~########..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--#---#...................~..~~~-#~~@#######..............~~~~~--#~~~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--#---#...................~..~~~-#--@#######..............~~~~~--#--~~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--#---#...................~..~~~-#--#@######..............~~~~~--#---~~~~.................~~~~~--#---~~-~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--#---#...................~..~~~-#--###@####..............~~~~~--#-----~~.................~~~~~--#------~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~@................~~~~~--#------~.....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~@....................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~@...................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~@..................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~@.................~~#-------~~~..................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.................~~#-------~~~.@................#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.................~~#-------~~~.~................#~~-------#~~~~@#############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.................~~#-------~~~.~@...............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.................~~#-------~~~.~~@..............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.@...............~~#-------~~~.~~~..............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.~@..............~~#-------~~~.~~~..............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.~~..............~~#-------~~~.~~~@.............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.~~..............~~#-------~~~.~~~~@............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.~~@.............~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~................~~~~~--#------~~~~~.~~~@............~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......@........~~~~~--#------~~~~~.~~~~............~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~@.......~~~~~--#------~~~~~.~~~~............~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~@......~~~~~--#------~~~~~.~~~~............~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~@.....~~~~~--#------~~~~~.~~~~............~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~..@.........~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~.@~.........~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~@~~.........~~#-------~~~.~~~~~............#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~.........~~#-------~~~.~~~~~.@..........#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~.........~~#-------~~~.~~~~~.~..........#~~-------#~~~~######@#######...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~.........~~#-------~~~.~~~~~@~..........#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~.........~~#-------~~~.~~~~~~~..........#~~-------#~~~~#####@########...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~.........~~#-------~~~.~~~~~-~@.........#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~.........~~#-------~~~.~~~~~-~~.........#~~-------#~~~~#######@######...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~.........~~#-------~~~.~~~~~-~~@........#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~.........~~#-------~~~.~~~~~-~~~@.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~.....~~~~~--#------~~~~~.~~~~~~~@........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~@....~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..............~~~~~--#------~~.......~~~~~@...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########..........@...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#...................~..~~~-#--########.........@~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#..............@....~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...................~..~~~--#---#.............@~....~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............@.....~..~~~--#---#.............~~....~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~@....~..~~~--#---#.............~~....~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~@...~..~~~--#---#.............~~....~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~@..~..~~~--#---#.............~~....~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~@.~..~~~--#---#.............~~....~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~.~..~~~--#---#.............~~..@.~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~.~..~~~--#---#.............~~..~@~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~@~..~~~--#---#.............~~..~~~..~~~-#--########.........~~...~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~..@~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~.@~~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~@~~~~~~~--#------~~.......~~~~~~...~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~@..~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~@.~~~~~--#------~~~~~.~~~~~~~~........~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~..@.....~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~..~@....~~#-------~~~.~~~~~-~~~~.......#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~..~~....~~#-------~~~.~~~~~-~~~~...@...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~..~~....~~#-------~~~.~~~~~-~~~~..@~...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~..~~....~~#-------~~~.~~~~~-~~~~..~~...#~~-------#~~~~############@#...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~..~~....~~#-------~~~.~~~~~-~~~~.@~~...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~.@~~....~~#-------~~~.~~~~~-~~~~.~~~...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~@~~~....~~#-------~~~.~~~~~-~~~~.~~~...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~~~~~....~~#-------~~~.~~~~~-~~~~@~~~...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~~~~~....~~#-------~~~.~~~~~-~~~~~~~~...#~~-------#~~~~##########@###...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~--~~....~~#-------~~~.~~~~~-~~~~-~~~...#~~-------#~~~~###########@##...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~.~~~~~--#------~~~~~.~~~~~~~~--~~....~~#-------~~~.~~~~~-~~~~---~...#~~-------#~~~~#############@...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~..~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~~~@~~~~~--#------~~~~~.~~~~~~~~--~~....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~.@~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.............~~~~~-~..~~~--#---#.............~~@~~~~..~~~-#--########.........~~~~~~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#............@~-----~..~~~--#---#.............~~----~..~~~-#--########.........~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...........@~~-----~..~~~--#---#.............~~----~..~~~-#--########.........~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#..........@~~~-----~..~~~--#---#.............~~----~..~~~-#--########.........~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........@~~~~-----~..~~~--#---#.............~~----~..~~~-#--########.........~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........@...~~----~..~~~-#--########.........~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~...~~----~..~~~-#--########....@....~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~...~~----~..~~~-#--########....~@...~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~...~~----~..~~~-#--########....~~@..~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~...~~----~..~~~-#--########....~~~@.~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~...~~----~..~~~-#--########....~~~~@~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~..@~~----~..~~~-#--########....~~~~-~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~.@~~~----~..~~~-#--########....~~~~-~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~@~~~~----~..~~~-#--########....~~~~-~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########...@~----~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########..@~~----~~---~~~~~--#------~~.......~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########..~~~----~~---~~~~~--#------~~....@..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########..~~~----~~---~~~~~--#------~~...@~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########.@~~~----~~---~~~~~--#------~~...~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########@~~~~----~~---~~~~~--#------~~...~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~..@~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~.@~~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--#######@~~~~~----~~---~~~~~--#------~~.~~~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~@~~~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.........~~~~~-----~..~~~--#---#.........~---~~----~..~~~-#--######@#~~~~~----~~---~~~~~--#------~~~~~~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#.....@...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.........~~~~~-----~..~~~--#---#....@~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#....@....~~~~~-----~..~~~--#---#....~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#...@~....~~~~~-----~..~~~--#---#....~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#..@~~....~~~~~-----~..~~~--#---#....~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.@~~~....~~~~~-----~..~~~--#---#....~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.~~~~....~~~~~-----~..~~~--#---#.@..~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.~~~~....~~~~~-----~..~~~--#---#.~..~~...~---~~----~..~~~-#--####@###~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.~~~~....~~~~~-----~..~~~--#---#.~@.~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.~~~~....~~~~~-----~..~~~--#---#.~~@~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.~~~~....~~~~~-----~..~~~--#---#.~~~~~...~---~~----~..~~~-#--######@#~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.~~~~....~~~~~-----~..~~~--#---#.~~-~~...~---~~----~..~~~-#--#####@##~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#.~~~~....~~~~~-----~..~~~--#---#@~--~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.~~~~....~~~~~-----~..~~~--#---#~~--~~...~---~~----~..~~~-#--###@####~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#.~~~~....~~~~~-----~..~~~--#---@~~--~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#@~~~~....~~~~~-----~..~~~--#---#~~--~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------@~~~~~....~~~~~-----~..~~~--#---#~~--~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#----~@...~~~~~-----~..~~~--#---#----~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#----~~@..~~~~~-----~..~~~--#---#----~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#----~~~@.~~~~~-----~..~~~--#---#----~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#----~~~~@~~~~~-----~..~~~--#---#----~~...~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#----~~~~~~~~~~-----~..~~~--#---#----~~..@~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#----~~~~~~~~~~-----~..~~~--#---#----~~.@~~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#----~~~~~~~~~~-----~..~~~--#---#----~~@~~~---~~----~..~~~-#--########~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#---------~~~~~-----~..~~~--#---#----~~---~---~~----~..~~~-#--#######@~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#---------~~~~~-----~..~~~--#---#---------~---~~----~..~~~-#--#######@~~~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~.~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#---------~~~~~-----~..~~~--#---#---------~---~~----~..~~~-#--########--~~~----~~---~~~~~--#------~~---~~..~~~~~~---~~~~~--#------~~~~~@~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#---------~~~~~-----~..~~~--#---#---------~---~~----~..~~~-#--########--~~~----~~---~~~~~--#------~~----~@.~~~~~~---~~~~~--#------~~~~~-~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#---------~~~~~-----~..~~~--#---#---------~---~~----~..~~~-#--########--~~~----~~---~~~~~--#------~~----~~@~~~~~~---~~~~~--#------~~~~~-~~~~~~~~----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------~~-------~~~~-----~~~~~--#------~~~~~-~~~~~~~-----....~~#-------~~~.~~~~~-~~~~----...#~~-------#~~~~#########@####...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------~~-------~~~~-----~~~~~--#------~~~~~-~~~~~~~-----....~~#-------~~~.~~~~~-~~~-----...#~~-------#~~~~########@#####...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------~~----------------~~~~~--#------~~~~~-~~----------....~~#-------~~~.~~~~~---------...#~~-------#~~~~####@#########...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------~~----------------~~~~~--#------~~~~~-~~----------....~~#-------~~~.~~~~----------...#~~-------#~~~~###@##########...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------~~----------------~~~~~--#------~~~~~-------------....~~#-------~~~.~~~-----------...#~~-------#~~~~##@###########...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------~~----------------~~~~~--#------~~~~~-------------....~~#-------~~~.~~------------...#~~-------#~~~~#@############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------~~----------------~~~~~--#------~~~~~-------------....~~#-------~~~@~-------------...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--#####@##--------------~~~~~--#------~~----------------~~~~~--#------~-----------------....~~#-------~~~---------------...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--####@###--------------~~~~~--#------~-----------------~~~~~--#------~-----------------....~~#-------~~~---------------...#~~-------#~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#--------~~---------------...#~~-------@~~~~##############...#~--------#~~-~~................~~--#~~~--#~~~.~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~-~~................~~--#~~~--#~~~@~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----@#############...#~--------#~~--~................~~--#~~~--#~~~-~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~@...............~~--#~~~--#~~~-~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~@..............~~--#~~~--#~~~-~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~@.............~~--#~~~--#~~~-~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~@............~~--#~~~--#~~~-~#...............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~............~~--#~~~--#~~~-~#..@............~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~............~~--#~~~--#~~~-~#..~@...........~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~............~~--#~~~--#~~~-~#..~~@..........~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~............~~--#~~~--#~~~-~#..~~~@.........~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..@.........~~--#~~~--#~~~-~#..~~~~.........~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----#######@######...#~--------#~~--~~~~~..~.........~~--#~~~--#~~~-~#..~~~~.........~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~@........~~--#~~~--#~~~-~#..~~~~.........~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----########@#####...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~.........~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~@........~--~~~.~~~~~~~~~#...............~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~~........~--~~~.~~~~~~~~~#......@........~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~~........~--~~~.~~~~~~~~~#.....@~........~~~~.#..~~~-~~..#................#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~~........~--~~~.~~~~~~~~~#.....~~........~~~~.#..~~~-~~..#.....@..........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~~........~--~~~.~~~~~~~~~#.....~~........~~~~.#..~~~-~~..#.....~@.........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~~........~--~~~.~~~~~~~~~#.....~~........~~~~.#..~~~-~~..#.....~~@........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~~........~--~~~.~~~~~~~~~#.....~~@.......~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~........~~--#~~~--#~~~-~#..~~~~~@.......~--~~~.~~~~~~~~~#.....~~~.......~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~@.......~~--#~~~--#~~~-~#..~~~~~~.......~--~~~.~~~~~~~~~#.....~~~.......~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----#########@####...#~--------#~~--~~~~~..~~~.......~~--#~~~--#~~~-~#..~~~~~~.......~--~~~.~~~~~~~~~#.....~~~.......~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~@......~~--#~~~--#~~~-~#..~~~~~~.......~--~~~.~~~~~~~~~#.....~~~.......~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~@.....~~--#~~~--#~~~-~#..~~~~~~.......~--~~~.~~~~~~~~~#.....~~~.......~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.@.....~--~~~.~~~~~~~~~#.....~~~.......~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~@....~--~~~.~~~~~~~~~#.....~~~.......~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~..@....~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.@~....~~~~.#..~~~-~~..#.....~~~........#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.~~....~~~~.#..~~~-~~..#.....~~~.@......#...#..~##--~~.#....................#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.~~....~~~~.#..~~~-~~..#.....~~~.~......#...#..~##--~~.#.........@..........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.~~....~~~~.#..~~~-~~..#.....~~~.~......#...#..~##--~~.#.........~..........#.~~----~~.#...######@##.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.~~....~~~~.#..~~~-~~..#.....~~~.~......#...#..~##--~~.#.........~@.........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.~~....~~~~.#..~~~-~~..#.....~~~.~......#...#..~##--~~.#.........~~.........#.~~----~~.#...#######@#.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.~~....~~~~.#..~~~-~~..#.....~~~.~......#...#..~##--~~.#.........~~@........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.~~....~~~~.#..~~~-~~..#.....~~~.~.@....#...#..~##--~~.#.........~~~........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~....~--~~~.~~~~~~~~~#.....~~~.~~@...~~~~.#..~~~-~~..#.....~~~.~.~....#...#..~##--~~.#.........~~~........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.....~~--#~~~--#~~~-~#..~~~~~~.~~@...~--~~~.~~~~~~~~~#.....~~~.~~~...~~~~.#..~~~-~~..#.....~~~.~.~....#...#..~##--~~.#.........~~~........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~.@...~~--#~~~--#~~~-~#..~~~~~~.~~~...~--~~~.~~~~~~~~~#.....~~~.~~~...~~~~.#..~~~-~~..#.....~~~.~.~....#...#..~##--~~.#.........~~~........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~@~...~~--#~~~--#~~~-~#..~~~~~~.~~~...~--~~~.~~~~~~~~~#.....~~~.~~~...~~~~.#..~~~-~~..#.....~~~.~.~....#...#..~##--~~.#.........~~~........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----############@#...#~--------#~~--~~~~~..~~~~~~~...~~--#~~~--#~~~-~#..~~~~~~.~~~...~--~~~.~~~~~~~~~#.....~~~.~~~...~~~~.#..~~~-~~..#.....~~~.~.~....#...#..~##--~~.#.........~~~........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----#############@...#~--------#~~--~~~~~..~~~~~-~...~~--#~~~--#~~~-~#..~~~~~~.~~~...~--~~~.~~~~~~~~~#.....~~~.~~~...~~~~.#..~~~-~~..#.....~~~.~.~....#...#..~##--~~.#.........~~~........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#.....~~~.~@~....#...#..~##--~~.#.........~~~........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#.....~~~.~--....#...#..~##--~~.#.........~~~........#.~~----~~.#...########@.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#.....~~~.~--....#...#..~##--~~.#........@~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#.....~~~.~--....#...#..~##--~~.#.......@~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#.....~~~.~--....#...#..~##--~~.#......@~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#.....~~~.~--....#...#..~##--~~.#......~~~~--........#.~~----~~.#...###@#####.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#.....~~~.~--....#...#..~##--~~.#.....@~~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#.....~~~.~--....#...#..~##--~~.#....@~~~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.....~~~.~~-...~~~~.#..~~~-~~..#....@~~~.~--....#...#..~##--~~.#....~~~~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#....@~~~.~~-...~~~~.#..~~~-~~..#....~~~~.~--....#...#..~##--~~.#....~~~~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...@~~~~.~~-...~~~~.#..~~~-~~..#....~~~~.~--....#...#..~##--~~.#....~~~~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#...@~~~~.~--....#...#..~##--~~.#....~~~~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..@~~~~~.~--....#...#..~##--~~.#....~~~~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..~~~~~~.~--....#...#..~##--~~.#..@.~~~~~~--........#.~~----~~.#...#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..~~~~~~.~--....#...#..~##--~~.#..~.~~~~~~--........#.~~----~~.#..@#########.........~~-----~..#.....................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..~~~~~~.~--....#...#..~##--~~.#..~.~~~~~~--........#.~~----~~.#..~#########.........~~-----~..#..@..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..~~~~~~.~--....#...#..~##--~~.#..~.~~~~~~--........#.~~----~~.#..~#########.........~~-----~..#.@~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..~~~~~~.~--....#...#..~##--~~.#..~.~~~~~~--........#.~~----~~.#.@~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..~~~~~~.~--....#...#..~##--~~.#.@~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..~~~~~~.~--....#...#..~##--~~.#@~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#..~~~~~~.~--....#...#..~##--~~.@~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#@.~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#...~~~~~.~~-...~~~~.#..~~~-~~..#~@~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#.@.~~~~~.~~-...~~~~.#..~~~-~~..#~~~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#..~~~~~~.~~-...~--~~~.~~~~~~~~~#@~.~~~~~.~~-...~~~~.#..~~~-~~..#~~~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#@.~~~~~~.~~-...~--~~~.~~~~~~~~~#~~.~~~~~.~~-...~~~~.#..~~~-~~..#~~~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~@~.~~~~~~.~~-...~--~~~.~~~~~~~~~#~~.~~~~~.~~-...~~~~.#..~~~-~~..#~~~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#~@~~~~~~.~~-...~--~~~.~~~~~~~~~#~~.~~~~~.~~-...~~~~.#..~~~-~~..#~~~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~@~~.~~~~~.~~-...~~~~.#..~~~-~~..#~~~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#-~@~~~~~.~~-...~~~~.#..~~~-~~..#~~~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
!^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..@~-~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#.~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#@~~#########.........~~-----~..#.~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#@~~..................~~~-~~~~..#......$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#@.....$..............~~~~~~~.............................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~.....$..............~~~~~~~....@........................#~~~............................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~.....$..............~~~~~~~....~........................#~~~...@........................#~~~...............
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~.....$..............~~~~~~~....~........................#~~~...~........................#~~~...@...........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~.....$..............~~~~~~~....~........................#~~~...~........................#~~~...~@..........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~.....$..............~~~~~~~....~........................#~~~...~........................#~~~...~~@.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~.....$..............~~~~~~~....~........................#~~~...~.@......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~.....$..............~~~~~~~....~.@......................#~~~...~.~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~.@...$..............~~~~~~~....~.~......................#~~~...~.~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~@~...$..............~~~~~~~....~.~......................#~~~...~.~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~~~...$..............~~~~~~~....~@~......................#~~~...~.~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~~~...$..............~~~~~~~....~~~......................#~~~...~@~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~..................~~~-~~~~..#~-~@..$..............~~~~~~~....~-~......................#~~~...~-~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~@.................~~~-~~~~..#~-~~..$..............~~~~~~~....~-~......................#~~~...~-~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~~@................~~~-~~~~..#~-~~..$..............~~~~~~~....~-~......................#~~~...~-~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~~~................~~~-~~~~..#~-~~@.$..............~~~~~~~....~-~......................#~~~...~-~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~~~................~~~-~~~~..#~-~~~@$..............~~~~~~~....~-~......................#~~~...~-~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~~~@...............~~~-~~~~..#~-~~~~$..............~~~~~~~....~-~......................#~~~...~-~......................#~~~...~~~.........
^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~~~~@..............~~~-~~~~..#~-~~~~$..............~~~~~~~....~-~......................#~~~...~-~......................#~~~...~~~.........
|^...~~------#-------------------~..~~~--#---#-------------------~..~~~-#--########--------------~~~~~--#------------------------~~~~~--#------------------------....~~#-------------------------...#~~-------#----##############...#~--------#~~--~~~~~..~~~~~--...~~--#~~~--#~~~-~#--~~~~~~.~~-...~--~~~.~~~~~~~~~#---~~~~~.~~-...~~~~.#..~~~-~~..#--~~~~~~.~--....#...#..~##--~~.#~~~.~~~~~~--........#.~~----~~.#~~~#########.........~~-----~..#~~~~~~~..............~~~-~~~~..#~-~~~~$..............~~~~~~~....~-~......................#~~~...~-~......................#~~~...~~~.........
|