TopCoder Statistics - Problem Statement

Problem Statement

Smiles the Friendship Unicorn lives in the Friendship Kingdom. There are N people in the Friendship Kingdom, numbered from 0 to N-1. Some of them are friends with each other: you are given these pairs in the int[] A and the int[] B. For each valid i, the person numbered A[i] is friends with the person numbered B[i]. Friendship is two-way, so the person numbered B[i] is also friends with the person numbered A[i]. For every group containing between 1 and N-1 people (inclusive), at least one person in the group is friends with someone outside the group.

Smiles would like to know whether there exists a friendship chain. A friendship chain is a sequence of 5 distinct people A, B, C, D, and E such that:

A is friends with B.
B is friends with C.
C is friends with D.
D is friends with E.

(In the language of graph theory: a friendship chain is a simple path of length 4.)

If a friendship chain exists, output "Yay!". Otherwise, output ":(". (All quotes are for clarity only.)

Definition

Class:: SmilesTheFriendshipUnicorn
Method:: hasFriendshipChain
Parameters:: int, int[], int[]
Returns:: String
Method signature:: String hasFriendshipChain(int N, int[] A, int[] B)
(be sure your method is public)

Constraints

N will be between 5 and 2000, inclusive.
A will contain between 1 and 2000 elements, inclusive.
A and B will contain the same number of elements.
Each element of A and B will be between 0 and N-1, inclusive.
No one will be friends with themselves.
The same friendship will not be given twice in the input.
For every group containing between 1 and N-1 people (inclusive), at least one person in the group is friends with someone outside the group.

Examples

5

{0, 1, 2, 3}

{1, 2, 3, 4}

Returns: "Yay!"

A friendship chain is formed by: Person 0 Person 1 Person 2 Person 3 Person 4 in that order. (The reverse order 4-3-2-1-0 is also a valid friendship chain.)
5

{0, 1, 2, 3, 1}

{1, 2, 3, 0, 4}

Returns: "Yay!"

One example of a valid friendship chain is: Person 4 Person 1 Person 2 Person 3 Person 0
6

{0, 0, 0, 0, 0}

{1, 2, 3, 4, 5}

Returns: ":("
8

{1, 3, 4, 3, 4, 3, 0, 2}

{7, 7, 7, 4, 6, 5, 4, 7}

Returns: "Yay!"
7

{0, 1, 1, 5, 4, 5}

{5, 2, 3, 6, 1, 1}

Returns: ":("
42

{0, 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}

{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, 0}

Returns: "Yay!"
147

{61,121,36,88,76,53,107,87,71,126,109,11,88,123,75,63,136,31,115,115,36,122,94,8,122,41,44,67,20,118,94,88,4,69,120,0,44,7,88,108,145,93,93,55,13,4,18,59,85,129,13,117,42,102,120,2,97,56,142,48,1,125,138,24,0,131,22,32,50,55,6,19,16,86,48,64,32,46,53,35,81,32,3,129,17,131,61,124,96,129,135,29,129,98,88,26,118,68,124,7,17,89,6,24,46,103,89,122,76,88,137,39,39,61,112,11,111,111,92,26,32,0,39,3,69,4,23,89,17,75,124,34,89,90,54,141,121,3,94,80,20,10,39,30,23,75,125,78,19,51,94,12,69,39,71,12,27,40,58,27,75,46,108,127,43,5,28,45,135,58,142,5,134,96,15,50,87,70,135,51,110,60,31,118,85,116,2,4,34,104,19,123,88,37,15,112,95,129,97,142,2,37,7,1,11,74,82,76,82,117,8,0,45,100,101,122,4,122,17,142,133,89,144,86}

{51,21,98,54,20,73,61,77,72,119,134,3,118,47,22,124,0,23,44,131,96,79,33,108,103,76,146,140,122,47,31,83,113,102,33,1,108,116,134,45,70,15,110,78,91,75,111,122,130,23,74,8,82,141,2,1,136,57,10,134,101,145,100,113,71,116,130,138,75,85,71,123,103,37,127,67,99,73,109,96,39,20,34,37,83,77,42,136,108,27,17,13,2,56,101,59,114,70,5,77,10,144,132,106,63,136,4,25,0,17,34,91,35,50,89,14,128,1,125,65,78,49,73,111,65,66,9,7,51,5,130,19,34,134,38,10,80,55,16,77,56,84,74,146,143,24,127,123,128,76,136,52,99,119,99,60,28,104,41,139,0,132,112,22,8,91,19,10,38,76,67,6,27,15,8,95,44,46,106,63,140,101,85,70,57,128,95,121,116,9,39,76,133,41,105,67,100,52,45,43,92,72,27,70,76,57,61,15,76,120,62,88,76,102,125,102,69,9,146,12,66,35,121,51}

Returns: "Yay!"
108

{70,94,104,22,2,57,33,1,60,32,72,80,31,90,88,23,85,63,39,107,25,31,53,42,0,1,47,81,59,0,105,78,22,0,36,92,20,27,98,81,30,38,75,6,74,19,66,85,58,34,101,54,52,69,24,96,36,50,68,11,63,44,102,89,64,57,31,38,59,80,84,62,89,5,94,1,54,43,52,40,79,0,95,27,33,41,83,44,15,73,94,41,68,14,23,56,24,84,15,45,35,6,46,72,24,99,87}

{77,20,52,41,23,51,84,49,107,58,41,74,48,5,106,18,28,54,15,66,36,88,85,49,73,88,76,49,10,61,29,85,13,55,62,67,77,2,93,76,73,87,85,17,49,40,44,69,44,63,8,41,66,71,33,91,81,52,100,48,12,31,50,15,46,5,93,103,23,3,29,37,16,36,85,0,7,67,40,65,0,20,38,86,49,15,89,21,97,26,9,61,43,20,0,14,96,68,82,73,4,73,77,8,35,66,31}

Returns: "Yay!"
1911

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Returns: "Yay!"
342

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{196,17,315,26,203,269,234,92,242,69,304,1,185,226,219,180,231,328,228,324,78,21,1,178,273,133,305,102,221,65,302,273,162,281,130,270,246,70,296,206,3,277,7,166,333,64,302,120,252,248,162,183,158,320,46,326,304,185,274,213,185,84,31,172,226,285,250,228,70,58,271,317,262,206,339,182,17,95,134,47,109,17,115,214,298,128,189,153,244,52,103,209,69,321,93,137,103,16,35,71,106,206,78,105,160,105,87,118,38,9,243,330,10,0,127,262,120,20,224,332,217,24,287,119,323,247,126,114,114,56,37,110,100,74,276,137,193,196,339,86,141,179,291,49,67,267,191,275,266,287,106,31,2,191,209,303,109,303,269,132,340,268,324,34,292,249,75,162,206,266,108,192,193,51,317,100,116,219,289,225,273,117,63,36,90,226,218,199,95,28,177,190,339,48,100,17,115,233,110,289,121,121,33,3,161,339,93,150,263,92,0,19,158,94,73,282,245,77,127,277,174,320,99,170,175,39,42,151,314,18,146,232,215,118,93,1,124,194,121,71,71,98,207,256,41,223,312,52,189,331,39,307,93,62,176,132,214,142,179,44,179,22,28,288,39,327,115,135,36,138,7,202,266,103,215,298,53,66,37,76,146,149,163,103,317,5,318,305,60,287,204,267,205,310,300,101,184,100,257,83,253,3,140,341,179,118,42,284,280,279,331,321,316,225,7,236,321,326,226,230,320,123,264,304,263,144,291,135,258,188,288,29,287,202,315,288,175,217,125,82,227}

Returns: "Yay!"
408

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64,116,356,12,218,229,243,374,378,73,176,108,105,226,109,377,192,319,358,187,59,209,292,367,25,377,326,384,90,364,193,336,31,153,143,30,18,373,97,244,270,49,306,273,170,174,145,115,29,267,343,379,82,295,71,341,52,112,398,133,12,222,229,288,64,13,267,288,27,145,232,201,325,293,244,318,263,251,16,220,257,259,217,197,75,18,42,248,398,388,371,69,340,327,9,407,304,124,44,348,286,166,296,358,287,212,93,121,22,404,93,109,211,359,10,213,57,381,95,64,341,277,187,367}

{261,311,214,162,156,46,393,195,350,285,406,152,311,114,131,396,349,182,306,244,266,38,78,335,309,311,253,293,9,215,12,257,140,383,313,114,73,308,335,176,184,1,389,324,74,406,79,380,217,38,371,287,345,19,342,273,218,376,51,129,55,25,74,89,81,311,320,155,133,372,25,58,107,102,55,3,78,298,17,1,164,400,133,157,6,174,314,0,176,231,272,66,128,316,130,393,246,404,226,399,89,186,164,367,284,231,58,132,50,111,329,14,48,194,3,177,113,121,111,391,360,201,192,43,3,164,92,64,163,373,9,61,85,9,317,128,190,363,243,302,229,385,12,340,400,259,77,243,377,100,230,113,370,60,15,399,184,194,383,6,72,400,197,57,115,373,392,345,47,26,135,392,258,247,53,249,85,2,323,306,296,243,125,182,249,196,179,220,250,253,4,385,71,156,191,98,282,134,31,1,54,196,55,287,185,80,278,378,160,360,84,6,42,100,301,39,39,181,89,26,167,44,97,161,356,333,92,198,128,205,334,272,288,361,8,262,247,193,338,150,350,220,251,184,129,335,140,17,186,325,386,360,234,325,183,199,382,356,321,397,316,3,187,401,398,320,55,40,358,71,95,112,174,82,272,377,217,81,399,151,68,349,234,284,352,336,111,238,142,153,66,62,344,24,314,388,320,76,150,169,228,375,103,18,346,121,128,74,107,249,365,159,165,362,80,194,31,68,46,242,206,310,209,270,35,95,346,107,194,111,44,221,139,141,228,211,157,342,56,275,276,279,235,343,86,149,252,381,253,146,27,179,368,343,166,120,113,179,213,221,244,171,382,360,50,330,116,128,325,116,326,70,181,273,189,70,333,151,324,3,177,230,344,143,119,105,314,192,178,92,269,178,351,123,268,296,40,233,151,324,54,102,331,172,7,2,215,404,261,37,118,332,346,82,160,278,312,202,69,53,340,307,306,393,395,301,182,147,163,223,238,206,150,276,157,56,266,181,81,145,45,210,376,373,389,64,357,157,361,36,113,324,64,369,47,7,173,376,340,321,74,91,335,270,315,214,45,215,80,100,223,231,371,401,176,27,102,222,342,84,27,219,259,326,236,73,364,232,45,287,372,74,161,319,398,136,403,144,60,321,320,37,82,269,32,278,46,366,71,381,157,337,277,318,351,113,80,138,385,395,53,150,265,254,209,112,176,193,317,243,34,86,28,304,355,355,398,339,93,356,93,387,356,352,140,188,30,226,69,139,190,79,101,151,322,170,148,200,338,379,257,28,175,14,148,240,345,84,209,23,371,404,82,56,135,262,96,187,61,139,120,322,142,114,161,295,109,403,360,177,281,324,205,43,53,45,319,187,182,129,119,300,197,406,267,153,29,219,201,135,85,101,295,273,288,18,330,392,94,308,81,401,119,289,227,375,79,99,44,155,271,72,227,263,285,380,185,275,166,345,229,92,90,312,357,341,270,272,261,24,215,113,235,196,377,128,53,304,301,219,34,225,99,187,224,176,282,62,374,3,272,46,97,108,84,100,88,163,151,36,113,225,305,319,253,83,371,231,279,140,221,65,51,88,343,85,56,198,175,29,294,166,220,326,397,175,190,199,269,207,181,10,62,112,0,347,22,138,115,402,395,224,161,77,38,236,242,82,20,19,391,120,218,239,323,261,199,293,278,287,389,77,114,233,325,53,21,170,218,303,0,88,186,29,23,94,232,279,371,224,312,379,46,86,293,165,49,0,15,187,271,113,148,46,148,327,261,91,299,395,128,362,315,71,114,243,59,147,23,190,167,40,128,382,134,205,135,19,40,260,228,137,154,295,12,95,108,104,291,152,105,88,70,380,388,340,97,369,115,405,380,52,391,127,34,28,275,20,211,51,202,135,17,223,256,248,34,378,182,344,276,191,38,318,385,179,14,278,338,43,334,325,102,288,225,58,212,279,58,23,122,66,7,17,396,289,238,56,397,364,93,192,343,272,331,165,45,323,210,160,283,386,114,129,228,179,4,350,371,286,273,130,405,197,275,177,163,90,190,142,259,300,143,312,190,230,92,193,167,210,296,137,195,40,280,271,220,280,211,159,160,77,299,349,12,396,340,129,331,34,60,352,367,211,97,134,393,182,132,128,375,168,364,204,214,202,369,37,373,185,71,307,395,238,207,165,303,323,4,403,322,118,268,215,82,39,243,353,319,56,33,158,223,312,292,237,56,292,288,253,332,352,7,91,132,63,387,37,119,102,154,222,53,1,11,403,41,101,82,221,189,376,11,274,253,278,30,318,177,154,269,253,146,370,385,299,406,153,2,187,243,278,296,198,226,245,270,223,176,291,301,97,355,158,165,358,276,160,181,87,2,91,184,352,370,228,320,264,391,86,180,125,187,333,180,246,176,350,180,300,130,340,216,59,162,139,128,96,31,53,235,346,41,362,303,114,88,318,369,57,75,65,404,306,120,257,110,140,235,378,237,304,116,395,262,336,318,284,284,257,242,110,201,365,208,349,320,265,33,72,122,338,384,321,72,206,180,39,154,181,106,105,59,209,159,10,151,210,92,365,259,140,104,267,114,247,57,385,347,281,198,74,99,213,177,179,46,348,172,373,359,358,151,53,357,224,198,384,211,382,120,207,201,250,193,62,102,180,322,281,274,261,350,172,316,385,376,344,160,299,252,136,88,265,263,103,400,133,230,86,109,115,173,245,136,160,151,103,37,361,35,141,289,278,54,393,194,340,284,259,363,141,316,59,172,340,378,125,140,284,323,194,20,368,317,160,137,245,179,315,264,59,144,260,283,175,48,163,216,111,269,118,255,95,140,289,337,108,195,229,127,72,166,177,32,165,325,166,0,117,233,294,204,203,235,270,43,334,377,253,333,50,259,177,11,282,207,308,150,24,329,5,34,108,26,343,37,5,336,172,206,141,222,399,356,369,339,337,235,213,362,109,10,87,177,70,390,363,178,242,159,363,171,2,57,233,248,252,228,57,35,321,373,249,140,293,282,54,346,0,87,218,260,316,289,83,148,242,169,83,130,256,327,69,263,223,330,206,352,22,353,30,397,274,322,181,386,337,235,339,150,86,266,52,116,54,17,405,114,80,66,157,200,296,214,243,91,357,27,114,280,44,119,97,345,338,132,392,364,212,37,395,395,313,241,300,249,160,237,404,284,243,215,228,68,88,109,301,130,34,390,190,368,213,100,266,97,233,303,246,164,69,386,53,138,346,290,35,70,234,16,116,227,318,278,381,234,14,80,387,224,97,285,361,170,145,239,94,189,340,199,121,394,259,31,64,292,167,376,113,104,233,371}

Returns: "Yay!"
1712

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Returns: "Yay!"
2000

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Returns: ":("
2000

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Returns: "Yay!"
2000

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Returns: "Yay!"
63

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8,9,36,48,27,53,4,0,19,4,52,23,32,5,12,53,40,45,44,18,58,44,35,32,29,52,42,13,2,0,41,43,45,36,10,43,9,51,18,59,51,6,40,60,59,24,4,3,1,29,18,61,53,1,60,9,18,28,45,10,7,11,57,24,50,21,43,23,15,62,22,2,11,34,51,56,20,15,12,27,3,27,44,45,52,48,9,17,4,44,28,47,7,5,59,19,7,14,13,41,57,51,33,58,46,3,44,12,8,47,37,3,49,21,36,44,47,6,53,44,37,54,7,60,51,18,22,21,29,30,1,62,45,43,2,19,52,58,14,4,2,23,1,48,30,21,58,36,59,29,30,43,30,46,56,50,61,17,2,49,15,57,4,26,32,9,24,22,38,46,57,48,40,16,49,49,43,44,34,33,59,20,62,30,22,5,8,50,26,47,11,20}

Returns: "Yay!"
2000

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Returns: ":("
2000

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Returns: "Yay!"
2000

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Returns: ":("
2000

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Returns: "Yay!"
5

{0,0,2,4,0,0}

{3,1,3,1,4,2}

Returns: "Yay!"
2000

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Returns: ":("
2000

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Returns: "Yay!"
2000

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Returns: ":("
6

{0, 0, 0, 0, 0 }

{1, 2, 3, 4, 5 }

Returns: ":("
2000

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1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 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1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999 }

Returns: ":("
5

{1, 3, 3, 1, 1, 1 }

{3, 4, 2, 2, 4, 0 }

Returns: "Yay!"
2000

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Returns: ":("
5

{0, 0, 1, 1, 3 }

{1, 2, 2, 3, 4 }

Returns: "Yay!"
5

{0, 0, 1, 1, 1 }

{1, 2, 2, 3, 4 }

Returns: ":("
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

Returns: ":("
6

{0, 0, 0, 0, 0, 1 }

{1, 2, 3, 4, 5, 2 }

Returns: ":("
5

{0, 0, 0, 2, 2 }

{1, 2, 3, 3, 4 }

Returns: "Yay!"
5

{0, 1, 3, 4, 0, 3 }

{2, 2, 2, 2, 1, 4 }

Returns: "Yay!"
5

{0, 1, 2, 0, 0 }

{1, 2, 0, 3, 4 }

Returns: ":("
5

{0, 0, 0, 0, 1, 3 }

{1, 2, 3, 4, 2, 4 }

Returns: "Yay!"
5

{0, 0, 0, 0, 1 }

{1, 2, 3, 4, 2 }

Returns: ":("
6

{0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4 }

{1, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 5, 4, 5, 5 }

Returns: "Yay!"
5

{0, 0, 1, 2, 2 }

{1, 2, 2, 3, 4 }

Returns: ":("
5

{2, 2, 2, 2, 0, 3 }

{0, 1, 3, 4, 1, 4 }

Returns: "Yay!"
5

{1, 1, 2, 3, 4 }

{2, 0, 0, 1, 2 }

Returns: "Yay!"
5

{0, 1, 1, 2, 3 }

{1, 3, 2, 3, 4 }

Returns: "Yay!"
2000

{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, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 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}

Returns: ":("
5

{0, 1, 2, 2, 3 }

{2, 2, 3, 4, 4 }

Returns: ":("
5

{0, 4, 1, 1, 2 }

{1, 1, 2, 3, 3 }

Returns: ":("
5

{0, 1, 2, 1, 2 }

{1, 2, 3, 3, 4 }

Returns: "Yay!"
5

{0, 1, 1, 2, 2 }

{1, 2, 4, 3, 4 }

Returns: "Yay!"
5

{0, 1, 1, 0, 1, 3 }

{1, 4, 2, 2, 3, 4 }

Returns: "Yay!"
6

{0, 0, 0, 0, 1, 2, 2 }

{2, 3, 4, 5, 2, 4, 5 }

Returns: "Yay!"
2000

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1683, 1684, 1685, 1686, 1687, 1688, 1689, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 1 }

Returns: ":("
5

{0, 1, 2, 1, 1 }

{1, 2, 0, 3, 4 }

Returns: ":("
5

{2, 2, 2, 2, 0 }

{0, 1, 3, 4, 1 }

Returns: ":("
5

{0, 1, 2, 2, 1 }

{1, 2, 3, 4, 3 }

Returns: "Yay!"
5

{0, 0, 1, 0, 1 }

{1, 4, 4, 2, 3 }

Returns: "Yay!"
5

{0, 4, 0, 1, 2, 3 }

{2, 2, 1, 2, 3, 4 }

Returns: "Yay!"

Statistics

Problem Statement for "SmilesTheFriendshipUnicorn"

Problem Statement

Definition

Constraints

Examples