n=992;
m=992;
road=[|1,2|
1,3|
3,4|
4,5|
2,6|
5,7|
5,8|
1,9|
2,10|
4,11|
2,12|
12,13|
3,14|
12,15|
10,16|
13,17|
11,18|
4,19|
2,20|
10,21|
15,22|
17,23|
2,24|
20,25|
24,26|
10,27|
16,28|
25,29|
23,30|
13,31|
1,32|
20,33|
28,34|
7,35|
8,36|
18,37|
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21,39|
37,40|
6,41|
33,42|
5,43|
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40,47|
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19,50|
25,51|
49,52|
1,53|
43,54|
51,55|
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49,58|
2,59|
21,60|
57,61|
53,62|
36,63|
2,64|
22,65|
48,66|
46,67|
11,68|
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61,70|
11,71|
39,72|
69,73|
64,74|
74,75|
61,76|
67,77|
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5,79|
56,80|
44,81|
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28,83|
29,84|
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78,86|
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80,88|
17,89|
59,90|
21,91|
88,92|
46,93|
84,94|
91,95|
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39,99|
41,100|
3,101|
68,102|
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60,106|
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98,108|
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61,110|
37,111|
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114,121|
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100,123|
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104,130|
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156,157|
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38,161|
128,162|
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160,168|
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93,172|
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106,174|
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90,181|
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126,190|
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157,200|
194,201|
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192,203|
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112,207|
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71,209|
84,210|
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113,217|
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216,220|
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219,222|
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235,239|
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139,243|
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289,291|
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188,300|
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137,307|
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86,309|
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270,327|
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367,387|
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316,389|
270,390|
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265,497|
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232,504|
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398,506|
110,507|
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349,509|
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432,511|
341,512|
304,513|
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475,515|
280,516|
41,517|
215,518|
180,519|
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128,522|
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482,541|
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396,557|
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385,596|
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342,598|
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122,600|
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33,604|
366,605|
575,606|
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601,615|
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506,710|
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653,719|
547,720|
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617,729|
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686,731|
571,732|
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313,758|
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379,656|
782,975|
435,156|
168,186|
75,661|
683,114|
368,981|
542,894|
617,137|
65,889|
802,805|
885,478|
261,761|
425,257|
870,8|
669,246|
898,59|
731,94|
802,477|
430,27|
918,758|
89,619|
754,773|
91,842|
184,255|
286,837|
908,910|
627,454|
930,251|
182,192|
932,293|
690,260|
70,866|
943,187|
920,257|
185,882|
146,499|
607,237|
544,899|
787,326|
394,102|
586,41|
59,199|
693,620|
378,628|
905,513|
51,715|
816,60|
383,408|
588,222|
329,326|
482,538|
266,567|
931,213|
43,599|
550,780|
645,664|
615,265|
491,835|
554,790|
202,310|
563,471|
987,73|
766,120|
618,249|
816,646|
972,785|
427,431|
739,765|
730,300|
402,274|
945,357|
869,71|
627,787|
18,165|
348,167|
928,727|
92,118|
507,889|
253,432|
780,969|
418,525|
392,511|
877,334|
221,781|
271,41|
404,248|
929,138|
197,27|
397,706|
122,723|
412,959|
306,122|
293,225|
520,212|
107,236|
798,131|
122,261|
414,182|
723,114|
672,93|
915,583|
225,628|
665,548|
2,1|
732,468|
100,847|
585,437|
730,23|
455,781|
790,274|
941,755|
803,464|
21,618|
435,579|
122,793|
363,977|
248,675|
900,61|
248,598|
632,234|
461,564|
527,828|
980,216|
830,893|
884,559|
968,682|
300,219|
634,887|
957,28|
481,208|
254,160|
107,843|
315,108|
451,416|
930,452|
717,749|
764,162|
151,829|
280,594|
475,334|
809,463|
784,466|
189,14|
118,935|
765,233|
604,362|
317,702|
133,73|
93,611|
850,644|
299,84|
197,282|
452,12|
365,335|
770,411|
285,803|
101,363|
111,376|
458,414|
644,717|
948,451|
104,900|
900,523|
838,985|
977,291|
79,897|
290,30|
832,207|
309,930|
600,622|
972,308|
226,875|
669,553|
930,80|
383,841|
507,946|
936,668|
72,5|
756,158|
206,439|
8,434|
926,392|
58,513|
611,123|
232,548|
705,460|
203,463|
115,240|
748,553|
220,929|
959,853|
588,599|
992,9|
288,358|
787,602|
346,572|
196,688|
428,497|
627,734|
152,615|
79,909|
459,87|
516,843|
727,672|
963,974|
411,625|
623,436|
39,19|
920,54|
644,66|
270,270|
884,628|
977,368|
985,554|
130,82|
157,970|
144,110|
140,849|
581,698|
871,215|
303,427|
431,270|
960,511|
930,981|
717,284|
789,541|
355,662|
790,1|
711,5|
11,190|
738,939|
928,401|
693,976|
906,929|
93,744|
291,820|
377,601|
731,725|
795,492|
539,565|
46,974|
797,780|
928,88|
487,545|
264,661|
487,710|
35,900|
145,974|
797,828|
801,67|
453,91|
341,577|
973,79|
246,262|
200,946|
538,784|
446,550|
709,756|
766,154|
851,695|
699,571|
611,984|
228,55|
346,981|
265,955|
447,43|
19,36|
359,702|
640,472|
804,552|
671,373|
496,41|
102,495|
190,984|
84,234|
477,377|
587,265|
791,653|
207,946|
435,901|
786,441|
727,17|
294,121|
35,502|
607,762|
682,328|
385,190|
911,57|
493,179|
228,863|
668,647|
120,897|
20,859|
888,719|
883,332|
945,828|
3,500|
661,747|
466,59|
156,837|
335,973|
407,496|
157,420|
488,235|
901,907|
869,965|
92,461|
412,209|
432,315|
567,307|
539,127|
581,457|
253,155|
30,225|
537,811|
537,129|
452,380|
465,655|
199,974|
371,886|
498,753|
331,964|
68,373|
532,665|
555,790|
694,983|
893,759|
56,846|
580,282|
915,503|
415,782|
943,43|
177,15|
180,821|
774,652|
89,855|
14,251|
267,578|
370,911|
513,901|
778,941|
339,115|
178,59|
801,185|
774,921|
93,502|
985,119|
54,554|
802,147|
311,712|
807,672|
152,736|
866,405|
140,751|
578,578|
280,691|
892,914|
847,634|
273,965|
729,248|
429,10|
426,11|
394,218|
687,433|
320,420|
218,358|
30,358|
952,968|
948,476|
983,843|
942,388|
421,520|
513,158|
881,535|
322,568|
821,493|
9,319|
503,64|
619,923|
373,864|
336,611|
63,486|
331,775|
660,395|
265,466|
289,469|
566,145|
725,145|
793,916|
415,678|
459,705|
800,732|
876,937|
183,959|
733,767|
879,630|
561,582|
791,348|
575,667|
438,515|
943,546|
697,276|
839,887|
285,321|
574,456|
917,227|
803,894|
442,303|
161,295|
408,628|
629,20|
32,792|
171,294|
299,459|
751,839|
377,249|
260,277|
705,45|
167,884|
357,398|
624,976|
699,521|
291,812|
307,444|
219,137|
492,957|
647,922|
692,731|
190,406|
379,535|
771,925|
497,797|
224,887|
646,710|
694,422|
635,771|
831,915|
961,983|
162,550|
608,507|
193,829|
952,258|
141,801|
989,488|
893,7|
863,919|
566,922|
503,451|
306,675|
118,47|
940,686|
888,246|
164,234|
959,40|
669,481|
135,559|
249,735|
736,433|
559,488|
419,282|
767,316|
199,960|
773,580|
574,142|
674,411|
877,255|
597,784|
156,807|
810,215|
933,838|
878,169|
397,708|
850,902|
520,961|
35,384|
956,859|
751,791|
290,311|
412,734|
37,648|
182,374|
563,586|
892,299|
748,522|
838,278|
420,934|
831,635|
593,393|
35,415|
800,129|
318,25|
920,220|
747,962|
15,367|
18,579|
562,676|
543,709|
763,520|
906,901|
838,643|
452,66|
460,355|
300,214|
230,453|
346,34|
151,842|
34,358|
690,234|
781,844|
925,494|
167,775|
77,514|
955,583|
381,353|
12,308|
420,146|
832,502|
728,954|
339,660|
646,70|
146,573|
940,143|
385,94|
247,969|
342,767|
905,853|
840,12|
150,922|
390,87|
735,787|
192,508|
75,703|
57,148|
848,698|
46,217|
152,555|
114,255|
428,489|
434,154|
890,763|
356,886|
626,211|
149,396|
959,161|
526,980|
650,22|
59,165|
942,227|
473,639|
489,532|
462,580|
595,455|
92,25|
98,255|
140,40|
511,858|
315,849|
370,463|
66,643|
742,763|
776,257|
773,147|
165,715|
931,597|
559,696|
782,910|
541,68|
643,968|
755,542|
751,793|
161,308|
228,257|
211,810|
764,184|
87,32|
517,19|
467,974|
153,679|
267,856|
42,151|
610,901|
462,698|
598,187|
893,713|
895,13|
368,681|
469,965|
287,181|
203,347|
142,412|
529,403|
969,280|
906,959|
968,709|
50,902|
835,827|
314,113|
600,147|
854,168|
269,96|
224,882|
50,319|
633,419|
92,875|
786,954|
150,19|
101,288|
144,729|
651,320|
492,219|
311,130|
256,864|
108,789|
572,38|
579,675|
641,221|
500,514|
95,231|
851,583|
718,125|
928,606|
777,835|
528,555|
99,831|
67,800|
756,558|
197,105|
357,71|
360,974|
182,684|
388,733|
952,681|
77,913|
989,280|
917,567|
492,563|
946,617|
797,677|
215,27|
547,417|
869,928|
158,449|
423,488|
337,184|
594,855|
431,628|
940,645|
500,313|
849,30|
830,60|
44,113|
523,602|
773,397|
773,407|
527,489|
220,618|
518,611|
400,54|
160,276|
45,388|
400,164|
414,144|
770,261|
417,663|
237,512|
956,676|
332,83|
796,205|
432,514|
490,524|
6,582|
828,690|
980,435|
810,41|
24,398|
441,346|
554,85|
50,613|
702,138|
915,940|
1,729|
154,856|
156,467|
825,982|
125,888|
99,189|
789,138|
693,516|
784,62|
633,334|
654,13|
295,92|
456,521|
544,587|
679,41|
652,923|
27,357|
435,848|
815,711|
256,348|
623,863|
827,738|
919,718|
740,145|
699,861|
409,627|
988,946|
584,836|
528,208|
810,966|
605,389|
894,77|
789,969|
837,825|
955,574|
214,879|
947,476|
613,81|
136,870|
84,363|
30,464|
660,420|
280,283|
485,956|
167,547|
663,967|
328,220|
609,917|
117,145|
594,376|
712,161|
322,56|
313,465|
53,672|
742,94|
243,733|
210,52|
972,7|
544,397|
32,913|
694,687|
420,308|
161,4|
103,601|
308,929|
143,112|
979,539|
227,189|
628,347|
74,108|
954,471|
636,107|
9,324|
149,780|
805,113|
584,73|
273,146|
580,645|
516,298|
725,230|
458,349|
75,255|
789,155|
269,343|
173,925|
731,960|
884,750|
562,798|
674,753|
259,19|
236,754|
965,183|
830,278|
513,542|
642,581|
922,616|
651,363|
632,775|
262,495|
829,784|
585,528|
641,363|
149,119|
598,901|
296,103|
850,211|
351,244|
108,694|
389,417|
376,276|
991,954|
505,228|
402,92|
943,629|
184,10|
313,55|
631,420|
339,220|
747,978|
105,679|
12,487|
470,27|
678,147|
717,859|
29,453|
307,544|
828,720|
182,646|
581,126|
741,900|
860,688|
336,495|
302,205|
642,481|
138,114|
365,1|
137,481|
46,767|
543,423|
664,892|
984,145|
944,586|
543,336|
14,652|
122,77|
345,875|
348,324|
397,955|
494,374|
32,63|
85,723|
802,365|
218,484|
336,657|
610,335|
188,649|
982,437|
233,608|
553,644|
461,238|
460,142|
78,397|
430,698|
74,632|
710,576|
909,783|
281,208|
53,705|
403,813|
592,848|
671,350|
913,792|
181,895|
640,436|
367,484|
162,656|
900,746|
137,804|
912,754|
818,402|
409,601|
986,154|
196,502|
711,296|
344,565|
878,511|
821,387|
218,692|
529,234|
876,849|
966,865|
430,55|
754,19|
540,315|
328,469|
645,288|
473,849|
743,436|
932,497|
280,536|
787,10|
515,268|
447,553|
47,786|
436,437|
46,900|
227,500|
609,789|
809,921|
581,378|
217,312|
758,884|
518,172|
138,781|
816,324|
130,388|
344,519|
884,908|
209,48|
906,753|
259,505|
75,108|
903,82|
964,365|
743,159|
882,784|
373,542|
983,277|
889,944|
609,85|
491,890|
110,253|
360,602|
920,974|
484,239|
526,614|
110,908|
482,18|
698,377|
689,563|
127,582|
203,702|
494,250|
981,548|
571,385|
941,504|
73,197|
990,461|
964,471|
224,820|
882,946|
864,247|
342,873|
88,934|
825,795|
638,629|
393,688|
371,366|
31,788|
34,372|
957,477|
517,258|
92,1|
946,751|
572,612|
964,945|
84,939|
470,860|
327,87|
736,111|
817,363|
857,984|
48,831|
483,309|
60,628|
464,765|
141,975|
194,212|
628,313|
31,321|
262,816|
295,797|
5,176|
695,233|
820,353|
763,816|
940,249|
132,472|
257,382|
394,28|
830,945|
59,260|
322,459|
222,895|
933,366|
147,887|
985,77|
667,229|
580,48|];