n=993;
m=993;
road=[|1,2|
1,3|
2,4|
1,5|
4,6|
2,7|
4,8|
6,9|
2,10|
7,11|
2,12|
9,13|
2,14|
11,15|
10,16|
5,17|
4,18|
12,19|
13,20|
17,21|
4,22|
4,23|
10,24|
2,25|
14,26|
22,27|
17,28|
17,29|
23,30|
5,31|
12,32|
5,33|
24,34|
33,35|
12,36|
34,37|
7,38|
15,39|
29,40|
24,41|
27,42|
11,43|
25,44|
5,45|
42,46|
2,47|
39,48|
17,49|
47,50|
31,51|
39,52|
14,53|
15,54|
28,55|
10,56|
1,57|
29,58|
9,59|
50,60|
2,61|
5,62|
7,63|
33,64|
32,65|
20,66|
8,67|
48,68|
28,69|
38,70|
53,71|
56,72|
22,73|
19,74|
20,75|
9,76|
71,77|
72,78|
19,79|
15,80|
46,81|
3,82|
16,83|
51,84|
36,85|
2,86|
59,87|
59,88|
32,89|
1,90|
17,91|
72,92|
43,93|
13,94|
45,95|
15,96|
63,97|
83,98|
86,99|
5,100|
52,101|
85,102|
40,103|
28,104|
92,105|
24,106|
14,107|
57,108|
98,109|
91,110|
22,111|
89,112|
58,113|
70,114|
45,115|
11,116|
67,117|
97,118|
43,119|
38,120|
116,121|
72,122|
7,123|
95,124|
56,125|
103,126|
27,127|
77,128|
27,129|
101,130|
118,131|
58,132|
117,133|
79,134|
39,135|
78,136|
39,137|
35,138|
85,139|
9,140|
27,141|
89,142|
59,143|
49,144|
83,145|
2,146|
25,147|
48,148|
74,149|
60,150|
112,151|
85,152|
28,153|
80,154|
5,155|
153,156|
80,157|
78,158|
112,159|
99,160|
17,161|
61,162|
56,163|
5,164|
83,165|
141,166|
103,167|
103,168|
132,169|
157,170|
129,171|
76,172|
121,173|
88,174|
144,175|
170,176|
155,177|
120,178|
118,179|
109,180|
66,181|
5,182|
158,183|
67,184|
5,185|
80,186|
53,187|
163,188|
1,189|
132,190|
100,191|
12,192|
105,193|
170,194|
50,195|
63,196|
12,197|
83,198|
150,199|
56,200|
120,201|
62,202|
201,203|
3,204|
57,205|
118,206|
141,207|
201,208|
201,209|
203,210|
113,211|
211,212|
130,213|
34,214|
56,215|
204,216|
170,217|
119,218|
112,219|
160,220|
91,221|
54,222|
11,223|
66,224|
2,225|
93,226|
57,227|
53,228|
16,229|
89,230|
33,231|
100,232|
157,233|
182,234|
177,235|
159,236|
105,237|
163,238|
182,239|
162,240|
133,241|
241,242|
221,243|
106,244|
94,245|
162,246|
114,247|
211,248|
72,249|
167,250|
174,251|
201,252|
188,253|
187,254|
45,255|
15,256|
235,257|
28,258|
117,259|
173,260|
137,261|
250,262|
71,263|
23,264|
257,265|
236,266|
176,267|
199,268|
71,269|
171,270|
110,271|
46,272|
199,273|
64,274|
152,275|
53,276|
128,277|
255,278|
61,279|
269,280|
42,281|
137,282|
265,283|
110,284|
14,285|
75,286|
236,287|
65,288|
1,289|
208,290|
284,291|
27,292|
94,293|
236,294|
178,295|
237,296|
129,297|
68,298|
36,299|
162,300|
281,301|
36,302|
282,303|
176,304|
63,305|
54,306|
155,307|
202,308|
237,309|
35,310|
200,311|
97,312|
162,313|
69,314|
125,315|
4,316|
93,317|
133,318|
225,319|
38,320|
119,321|
214,322|
167,323|
113,324|
77,325|
304,326|
139,327|
104,328|
78,329|
223,330|
122,331|
285,332|
23,333|
314,334|
211,335|
252,336|
244,337|
75,338|
83,339|
74,340|
57,341|
262,342|
63,343|
66,344|
339,345|
116,346|
111,347|
34,348|
175,349|
33,350|
271,351|
350,352|
90,353|
55,354|
125,355|
88,356|
338,357|
170,358|
249,359|
137,360|
206,361|
207,362|
26,363|
246,364|
237,365|
194,366|
278,367|
111,368|
359,369|
125,370|
140,371|
93,372|
262,373|
127,374|
255,375|
91,376|
203,377|
121,378|
223,379|
137,380|
179,381|
172,382|
81,383|
118,384|
259,385|
142,386|
202,387|
209,388|
244,389|
372,390|
256,391|
380,392|
185,393|
107,394|
219,395|
43,396|
127,397|
276,398|
325,399|
285,400|
176,401|
144,402|
27,403|
114,404|
293,405|
161,406|
399,407|
380,408|
386,409|
406,410|
316,411|
181,412|
93,413|
264,414|
136,415|
398,416|
409,417|
333,418|
345,419|
263,420|
155,421|
207,422|
227,423|
158,424|
342,425|
81,426|
231,427|
325,428|
245,429|
281,430|
229,431|
288,432|
181,433|
244,434|
301,435|
102,436|
37,437|
41,438|
268,439|
352,440|
193,441|
382,442|
367,443|
413,444|
439,445|
132,446|
310,447|
310,448|
51,449|
427,450|
443,451|
298,452|
396,453|
261,454|
59,455|
410,456|
284,457|
299,458|
293,459|
339,460|
438,461|
459,462|
29,463|
99,464|
313,465|
76,466|
277,467|
458,468|
7,469|
54,470|
231,471|
421,472|
78,473|
209,474|
154,475|
217,476|
373,477|
110,478|
453,479|
313,480|
206,481|
384,482|
206,483|
46,484|
312,485|
468,486|
459,487|
146,488|
14,489|
443,490|
490,491|
381,492|
88,493|
330,494|
218,495|
481,496|
422,497|
494,498|
216,499|
117,500|
100,501|
314,502|
273,503|
97,504|
303,505|
402,506|
65,507|
262,508|
372,509|
369,510|
3,511|
501,512|
79,513|
251,514|
407,515|
386,516|
17,517|
210,518|
206,519|
54,520|
165,521|
429,522|
316,523|
314,524|
478,525|
293,526|
23,527|
263,528|
101,529|
341,530|
79,531|
440,532|
478,533|
330,534|
68,535|
187,536|
497,537|
278,538|
89,539|
503,540|
63,541|
447,542|
241,543|
307,544|
206,545|
291,546|
46,547|
88,548|
273,549|
156,550|
377,551|
439,552|
220,553|
199,554|
104,555|
477,556|
197,557|
189,558|
157,559|
107,560|
463,561|
388,562|
449,563|
56,564|
466,565|
80,566|
271,567|
209,568|
326,569|
403,570|
202,571|
49,572|
271,573|
569,574|
162,575|
271,576|
316,577|
440,578|
527,579|
264,580|
438,581|
211,582|
276,583|
303,584|
541,585|
311,586|
552,587|
570,588|
93,589|
484,590|
148,591|
162,592|
335,593|
16,594|
325,595|
101,596|
342,597|
133,598|
565,599|
384,600|
40,601|
452,602|
312,603|
339,604|
178,605|
289,606|
71,607|
285,608|
502,609|
273,610|
400,611|
74,612|
324,613|
137,614|
401,615|
176,616|
34,617|
510,618|
430,619|
509,620|
300,621|
389,622|
314,623|
540,624|
392,625|
114,626|
600,627|
231,628|
554,629|
8,630|
208,631|
321,632|
330,633|
374,634|
100,635|
359,636|
576,637|
307,638|
237,639|
352,640|
359,641|
535,642|
159,643|
173,644|
83,645|
276,646|
150,647|
104,648|
358,649|
188,650|
524,651|
176,652|
57,653|
271,654|
322,655|
649,656|
441,657|
477,658|
218,659|
127,660|
57,661|
659,662|
475,663|
327,664|
345,665|
451,666|
182,667|
658,668|
666,669|
475,670|
127,671|
471,672|
581,673|
189,674|
604,675|
494,676|
26,677|
270,678|
117,679|
596,680|
85,681|
121,682|
318,683|
588,684|
651,685|
682,686|
629,687|
377,688|
464,689|
6,690|
287,691|
489,692|
620,693|
376,694|
7,695|
497,696|
538,697|
428,698|
534,699|
565,700|
61,701|
617,702|
291,703|
168,704|
119,705|
565,706|
454,707|
401,708|
21,709|
220,710|
320,711|
531,712|
445,713|
150,714|
141,715|
170,716|
680,717|
359,718|
264,719|
379,720|
675,721|
700,722|
280,723|
587,724|
22,725|
621,726|
290,727|
693,728|
197,729|
655,730|
193,731|
399,732|
305,733|
674,734|
67,735|
247,736|
292,737|
200,738|
639,739|
555,740|
77,741|
52,742|
559,743|
741,744|
279,745|
552,746|
86,747|
528,748|
98,749|
741,750|
663,751|
254,752|
140,753|
698,754|
166,755|
238,756|
100,757|
413,758|
755,759|
337,760|
265,761|
732,762|
260,763|
554,764|
98,765|
86,766|
207,767|
542,768|
346,769|
327,770|
285,771|
606,772|
582,773|
659,774|
64,775|
684,776|
595,777|
404,778|
17,779|
203,780|
210,781|
668,782|
388,783|
192,784|
278,785|
483,786|
106,787|
313,788|
659,789|
649,790|
31,791|
234,792|
75,793|
141,794|
457,795|
84,796|
595,797|
575,798|
214,799|
428,800|
257,801|
126,802|
766,803|
400,804|
545,805|
250,806|
126,807|
65,808|
450,809|
581,810|
474,811|
291,812|
613,813|
348,814|
518,815|
637,816|
715,817|
740,818|
698,819|
702,820|
631,821|
610,822|
82,823|
56,824|
215,825|
750,826|
88,827|
14,828|
441,829|
812,830|
121,831|
768,832|
832,833|
629,834|
337,835|
130,836|
81,837|
67,838|
602,839|
577,840|
311,841|
89,842|
468,843|
28,844|
250,845|
841,846|
105,847|
654,848|
231,849|
126,850|
119,851|
179,852|
391,853|
304,854|
498,855|
456,856|
539,857|
547,858|
490,859|
822,860|
800,861|
251,862|
160,863|
678,864|
159,865|
641,866|
815,867|
581,868|
521,869|
854,870|
376,871|
485,872|
269,873|
455,874|
95,875|
565,876|
787,877|
672,878|
294,879|
492,880|
671,881|
763,882|
47,883|
392,884|
750,885|
300,886|
795,887|
585,888|
223,889|
785,890|
270,891|
191,892|
283,893|
769,894|
846,895|
664,896|
192,897|
815,898|
229,899|
211,900|
880,901|
373,902|
518,903|
826,904|
312,905|
473,906|
83,907|
517,908|
618,909|
274,910|
82,911|
892,912|
887,913|
207,914|
370,915|
287,916|
33,917|
367,918|
710,919|
401,920|
494,921|
34,922|
842,923|
884,924|
758,925|
488,926|
705,927|
242,928|
895,929|
342,930|
428,931|
717,932|
787,933|
139,934|
681,935|
7,936|
328,937|
682,938|
877,939|
45,940|
526,941|
826,942|
156,943|
773,944|
678,945|
307,946|
259,947|
152,948|
896,949|
601,950|
831,951|
572,952|
593,953|
209,954|
534,955|
797,956|
752,957|
569,958|
39,959|
47,960|
403,961|
491,962|
672,963|
414,964|
799,965|
251,966|
566,967|
827,968|
776,969|
99,970|
348,971|
626,972|
526,973|
826,974|
78,975|
199,976|
515,977|
426,978|
223,979|
115,980|
554,981|
100,982|
192,983|
158,984|
735,985|
563,986|
830,987|
456,988|
843,989|
580,990|
188,991|
714,992|
789,993|];
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701,94|
870,565|
536,364|
770,210|
308,312|
95,277|
338,988|
214,576|
283,272|
3,428|
239,554|
890,281|
400,709|
429,372|
362,335|
819,935|
196,865|
669,49|
58,788|
138,89|
602,745|
833,370|
505,247|
246,950|
984,317|
965,163|
194,513|
643,463|];