TopCoder Statistics - Problem Statement

Problem Statement

Given a set of points in the plane, its square count is the number of ways in which we can select four of those points in such a way that they form the corners of a square. The square may be rotated arbitrarily. Order of the four points does not matter. For example, the square count for the set { (1,2), (1,0), (0,1), (2,1) } is 1.

You are given a set S of points in the plane with integer coordinates. Return the number of points P with the following property: P is not in S, and if we add P to S, the square count will increase.

In order to keep the input size small, S is given as follows: You are given the ints N, SX, SY, and the int[]s Xprefix and Yprefix. Use the pseudocode given below to generate S.

X, Y = two empty arrays of length N each
L    = length(Xprefix)

for i = 0 .. L-1:
    X[i] = Xprefix[i]
    Y[i] = Yprefix[i]

for i = L .. N-1:
    X[i] = ( X[i-1] * 47 + 42 ) modulo SX
    Y[i] = ( Y[i-1] * 47 + 42 ) modulo SY

for i = 0 .. N-1:
    if (X[i], Y[i]) is not in S:
        add (X[i], Y[i]) to S

Definition

Class:: MoreSquares
Method:: countLocations
Parameters:: int, int, int, int[], int[]
Returns:: int
Method signature:: int countLocations(int N, int SX, int SY, int[] Xprefix, int[] Yprefix)
(be sure your method is public)

Notes

The reference solution would work fast enough for any input of the given size, it does not depend on any properties of the pseudorandom generator.
The new point P can lie anywhere in the plane.

Constraints

N will be between 1 and 3,000, inclusive.
SX and SY will each be between 1 and 10^6, inclusive.
Xprefix will have between 1 and min(100,N) elements, inclusive.
Yprefix will have the same number of elements as Xprefix.
Each element of Xprefix will be between 0 and SX-1, inclusive.
Each element of Yprefix will be between 0 and SY-1, inclusive.

Examples

3

100

100

{3, 0, 2}

{0, 1, 2}

Returns: 1

The set S contains the points (3,0), (0,1), and (2,2). By adding a fourth point at (1,-1) we can increase the square count from 0 to 1.
5

100

100

{47, 47, 47, 47, 47}

{47, 47, 47, 47, 47}

Returns: 0

The set S contains only one point: (47, 47). Adding a second point will always produce a two-element set with square count zero.
23

11

13

{7}

{0}

Returns: 5

The set S contains 20 points. In the order of insertion, these are: (7, 0), (8, 3), (0, 1), (9, 11), (3, 0), (7, 3), (8, 1), (0, 11), (9, 0), (3, 3), (7, 1), (8, 11), (0, 0), (9, 3), (3, 1), (7, 11), (8, 0), (0, 3), (9, 1), (3, 11). The last three points generated using the formula in the statement are (7, 0), (8, 3), and (0, 1) again. The five possible locations for the new point that increases the square count are (6, 2), (8, -1), (8, 2), (10, 2), and (11, 8).
500

127

131

{7}

{0}

Returns: 2384
6

100

100

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

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

Returns: 1

The only answer is the point (1, 1). Note that this point increases the square count by 2.
3000

1009

1013

{4}

{7}

Returns: 10937
3000

503

509

{4}

{7}

Returns: 39826
12

9

56

{8, 7, 5, 4, 8, 6, 6, 0, 6, 0, 1, 0}

{16, 50, 30, 46, 34, 0, 52, 20, 36, 27, 14, 15}

Returns: 0
17

66

46

{56, 30, 4, 47, 45, 43, 25, 30, 4, 16, 42, 12, 46, 49, 65, 32, 12}

{41, 14, 44, 21, 13, 30, 7, 26, 38, 22, 43, 18, 15, 35, 16, 22, 34}

Returns: 0
19

6

62

{2, 4, 3, 2, 5, 4, 1, 4, 0, 5, 1, 3, 3, 2, 4, 4, 1, 3, 0}

{10, 35, 40, 51, 48, 5, 4, 17, 32, 52, 39, 34, 30, 50, 51, 27, 23, 58, 48}

Returns: 1
2

78

34

{77, 66}

{30, 20}

Returns: 0
1

74

32

{27}

{22}

Returns: 0
14

89

24

{22, 60, 25, 16, 12, 17, 72, 44, 67, 50, 13, 34, 56, 0}

{20, 3, 13, 2, 11, 0, 8, 1, 4, 5, 23, 16, 15, 6}

Returns: 0
16

68

59

{1, 9, 22, 19, 43, 5, 30, 7, 48, 15, 2, 11, 38, 6, 39, 30}

{39, 57, 46, 34, 9, 35, 37, 48, 17, 39, 54, 36, 5, 36, 31, 21}

Returns: 0
18

7

15

{3, 3, 2, 2, 4, 6, 6, 3, 4, 1, 0, 4, 0, 3, 5, 6, 3, 6}

{0, 6, 12, 9, 8, 12, 1, 12, 12, 4, 12, 11, 7, 8, 1, 12, 3, 5}

Returns: 8
11

22

60

{0, 18, 3, 21, 14, 14, 8, 20, 17, 21, 0}

{35, 12, 52, 43, 18, 2, 49, 16, 34, 30, 24}

Returns: 0
3

93

14

{66, 90, 75}

{9, 7, 8}

Returns: 0
2995

3324

11548

{2590, 374, 420, 2098, 3314, 1249, 1659, 1362, 2207, 1475, 445, 381, 2549, 3047, 1745, 1476, 205, 1432, 2387, 231, 1605, 2596, 3305, 1097, 1041, 862, 1186, 856, 1904, 2708, 1226, 1823, 3177, 1804, 1300, 2762, 224, 636, 2376, 1964, 2, 112, 1731, 1873, 2130, 1793, 2515, 1055, 1204, 419, 1241, 507, 695, 1732, 1378, 2037, 1744, 960, 2061, 2335, 2102, 1077, 1282, 2272, 94, 2494, 2756, 1553, 2435, 2413, 2854, 2436, 2825, 2555, 1891, 2527, 2286, 735, 2795, 2874, 1544, 175, 743, 2510, 743, 2555, 319, 1986, 1683, 246, 919, 1891, 720, 2449}

{6519, 73, 10230, 2278, 1192, 9178, 6375, 12, 6297, 8180, 7456, 10318, 6114, 2006, 8376, 6561, 1672, 1409, 6886, 6749, 9019, 1708, 10113, 2864, 10897, 8168, 7795, 7196, 9770, 1535, 6479, 8593, 8284, 5364, 7087, 3221, 5183, 6506, 1222, 2171, 7989, 5456, 10648, 10638, 1717, 4136, 7953, 1518, 5851, 487, 6464, 10235, 1332, 9855, 3673, 8450, 10552, 3453, 8319, 4221, 5022, 8193, 9921, 1863, 9210, 1023, 4700, 2904, 7999, 11396, 3953, 6625, 10004, 7767, 115, 9651, 6546, 9978, 3854, 10245, 9082, 6129, 1748, 5535, 1053, 2573, 9664, 1734, 3915, 3001, 1310, 2321, 8437, 2754}

Returns: 588
2992

36

5

{25, 22, 7, 26, 18, 35, 14, 22, 5, 20, 6, 2, 12, 35, 8, 21, 5, 20, 27, 32, 34, 22, 33, 33, 27, 28, 27, 26, 31, 1, 12, 20, 3, 27, 6, 28, 7, 6, 21, 27, 3, 21, 11, 26, 30, 33, 30, 33, 7, 14, 12, 1, 34, 31, 20, 9, 10, 18, 4, 3, 19, 2, 0, 16, 22, 12, 35, 13, 23, 23, 8, 12, 28, 2, 19, 19}

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

Returns: 130
2986

6945

2

{4926, 5851, 2549, 426, 4998, 3618, 3796, 3332, 5968, 5900, 2724, 5894, 736, 2074, 3444, 3059, 804, 5802, 3091, 3092, 1445, 2422, 244, 249, 4711, 5539, 4725, 6652, 1567, 1032, 4596, 1825, 706, 62, 3464, 3503, 3410, 5792, 3465}

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

Returns: 0
2971

826

7180

{638, 781, 538, 275, 145}

{3828, 3214, 830, 6847, 6316}

Returns: 1884
2984

8

3441

{2, 0, 4, 5, 2, 0, 6, 7, 5, 2, 4, 4, 5, 6, 1, 3, 2, 3, 4, 3, 7, 5, 2, 5, 1, 2, 2, 3, 5, 3, 3, 0, 5, 6, 2, 7, 2, 3, 6, 0, 7, 5, 1, 4, 1, 2, 3, 4, 6, 1, 4, 5, 1, 6, 5, 3, 4, 4, 5, 0, 3, 4, 7, 5, 1, 2, 2, 4, 5, 4, 1, 4, 3, 0, 4, 3, 3, 7, 7, 1, 6, 0, 2, 1, 6}

{1232, 902, 1695, 3076, 777, 352, 877, 2630, 2598, 2721, 915, 2244, 365, 2275, 1717, 1265, 1291, 1531, 486, 373, 2834, 1287, 1862, 867, 3151, 481, 2675, 354, 2194, 2721, 1395, 3113, 2321, 2821, 1983, 3256, 896, 243, 1306, 1263, 3242, 2993, 3017, 2732, 3238, 1552, 1084, 3138, 2424, 243, 310, 1048, 1872, 2064, 902, 2100, 2093, 1987, 1160, 1304, 1787, 2114, 1019, 2498, 2786, 2877, 2631, 1345, 2336, 2597, 859, 2341, 3380, 726, 775, 980, 3086, 170, 120, 2846, 2490, 2087, 3328, 2480, 1067}

Returns: 0
2994

833300

107

{634048, 660543, 586373, 353079, 528862, 182256, 783626, 813803, 343702, 390805, 193781, 164830, 692858, 762425, 517400, 79202, 36896, 409867, 486767, 728235, 471918, 308567, 651789, 98506, 828695, 670481, 729970, 516232, 657877, 283617, 349998, 295984, 729073, 227533, 733298, 448251, 79143, 267838, 641623, 401136, 339278, 482039, 306114, 168897, 253812, 191245, 380285, 241413, 323999, 38031, 227115, 723901, 602556, 496673, 25851, 372823, 9678, 660968, 298201, 287144, 579746, 435995, 794456, 555316, 247535, 476163, 476318, 55475, 86732, 756051, 136451, 769693, 421944, 464770, 196285, 259919}

{5, 51, 86, 57, 68, 67, 12, 71, 3, 69, 57, 69, 62, 75, 20, 20, 100, 96, 30, 35, 85, 40, 24, 71, 86, 63, 65, 102, 95, 35, 58, 32, 43, 67, 14, 28, 97, 32, 100, 28, 4, 100, 17, 31, 88, 94, 91, 57, 94, 91, 99, 10, 41, 93, 70, 94, 82, 83, 27, 41, 80, 12, 101, 33, 66, 20, 35, 46, 17, 95, 21, 10, 23, 104, 7, 98}

Returns: 0
2965

38

554

{11, 5, 28, 17, 6, 19, 12, 37, 31, 9, 8, 15, 34, 15, 19, 16, 29, 1, 19, 12, 1, 27, 11, 17, 31, 12, 28, 0, 23, 15, 25, 32, 11, 11, 11, 3, 13, 20, 25, 19, 17, 5}

{310, 235, 44, 482, 313, 241, 302, 467, 183, 181, 310, 471, 296, 298, 53, 314, 38, 70, 409, 518, 435, 149, 387, 393, 229, 542, 423, 455, 552, 186, 258, 410, 328, 343, 127, 387, 445, 143, 91, 444, 255, 241}

Returns: 776
2900

268

1836

{155, 101, 129, 34, 25, 124, 89, 180, 177, 42, 255, 133, 143, 188, 104, 24, 133, 249, 119, 55, 156, 94, 203, 143, 103, 143, 82, 82, 163, 78, 142, 246, 50, 146, 133, 77, 200, 112, 113, 91, 44, 148, 264, 74, 238, 151, 16, 54, 113, 106, 54, 100, 255, 196, 154, 130, 6, 171, 184, 215, 49, 45, 168, 133, 118, 70, 125, 254, 102}

{1581, 69, 1517, 343, 48, 1166, 1781, 1782, 642, 466, 1405, 751, 1728, 469, 501, 1000, 758, 413, 1688, 1768, 869, 381, 949, 1219, 1259, 455, 72, 1576, 832, 954, 474, 867, 1568, 37, 865, 1266, 1049, 135, 1004, 396, 800, 384, 1483, 4, 490, 1008, 1064, 24, 1713, 1127, 605, 981, 643, 627, 1251, 1433, 1361, 1063, 1452, 1418, 1526, 1283, 1033, 769, 1279, 455, 1380, 110, 445}

Returns: 43
2927

61671

58977

{26354, 9171, 27433, 23411, 847, 45638, 34351, 22259, 35765, 48721, 7015, 50164, 39954, 23714, 54903, 33416, 56875, 25284, 17168, 10020, 58063, 3460, 14097, 3460, 36899, 17152, 45109, 16944, 11550, 24528, 57987, 40201, 24484, 15137, 37387, 37933, 36289, 53236, 56763, 60709, 8735, 15455, 6953, 58148, 8805, 23557, 56374, 3367, 9510, 48021, 60453, 11442, 25567, 50451, 54966, 50366, 45447, 43539, 17732, 34224, 4119, 40868, 47970, 34887, 10090, 61585, 58930, 15786, 21115, 29784}

{56121, 33974, 48351, 46473, 17214, 6173, 22980, 50026, 16813, 619, 41371, 36249, 18292, 34962, 17538, 30469, 34376, 40194, 30604, 57653, 9866, 23821, 8843, 43978, 56250, 13626, 1291, 6437, 3548, 25193, 32367, 13502, 43049, 44210, 34657, 44032, 37743, 10343, 41437, 45913, 24098, 3804, 36552, 48732, 11911, 57598, 36039, 15621, 31557, 50774, 31421, 27978, 3737, 46035, 32579, 45446, 46062, 57112, 45134, 50773, 57012, 15354, 33592, 37751, 21276, 33409, 14418, 25450, 48600, 29890}

Returns: 13
2917

42

106

{37}

{66}

Returns: 69
2994

121

50

{82, 55, 83, 60, 70, 55, 110, 87, 2, 21, 74, 54, 51, 4, 71, 6, 7, 77, 88, 13, 26, 61, 24, 102, 70, 114, 4, 101, 68, 114, 98, 15, 2, 42, 33, 61, 35, 12, 116, 96, 94, 84, 14, 45, 61, 1, 35, 73, 58, 112, 117, 57, 23, 15, 119, 33, 47, 59, 6, 62, 88, 4, 54, 82, 10, 88, 114}

{48, 44, 13, 23, 12, 14, 46, 37, 9, 13, 31, 32, 47, 6, 18, 49, 38, 40, 47, 43, 34, 48, 6, 31, 12, 2, 9, 47, 32, 48, 16, 9, 17, 23, 9, 21, 42, 34, 23, 8, 9, 27, 26, 36, 20, 43, 11, 38, 49, 24, 1, 6, 27, 47, 10, 43, 4, 6, 8, 6, 4, 13, 1, 11, 24, 6, 4}

Returns: 1016
2971

33911

10

{8578, 8623, 18266, 14689, 9088, 3370, 25417, 10404, 27468, 1913, 4759, 15996, 33021, 27961, 33315, 4148, 23209, 15911, 23376, 17457, 12341, 2898, 20026, 2919, 11616, 3876, 20399, 20169, 28635, 22298, 3086, 24089, 16491, 11996, 10717, 12485, 1580, 30517, 15072, 17013, 27366, 31469, 351}

{0, 5, 9, 6, 1, 1, 9, 5, 3, 4, 5, 1, 9, 2, 9, 7, 6, 9, 5, 3, 4, 4, 7, 3, 7, 2, 9, 6, 6, 3, 0, 5, 0, 3, 1, 1, 4, 3, 7, 7, 2, 9, 1}

Returns: 11
2989

1

553

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

{426, 122, 118, 233, 543, 183, 185, 113, 400, 331, 274, 7, 512, 547, 279, 181, 522, 8, 527, 314, 304, 419, 383, 338, 250, 288, 219, 344, 413, 380, 216, 140, 363, 526}

Returns: 0
2903

21238

223297

{2931, 2819, 2415, 18190, 13751, 16524, 5049, 6068, 5516, 14845, 2271, 6998, 12007, 12545, 6309, 16307, 2309, 20577, 18269, 16270, 6504, 1841, 656, 10588, 18420, 6377, 12471, 415, 4540, 18221, 12878, 12049, 7599, 3564, 8187, 6539, 12671, 8443, 19303, 15104, 12984, 13794, 15849, 1130, 5432, 5084, 6349, 11644, 19523, 17441, 11496}

{38671, 181766, 12363, 169308, 217527, 9537, 33398, 166129, 48223, 47074, 13216, 3117, 183409, 93662, 55279, 6097, 132706, 34936, 7986, 191614, 90043, 195694, 66305, 79152, 108630, 222236, 212766, 194799, 216493, 37536, 117366, 209167, 189727, 116304, 42262, 174011, 41907, 139040, 111779, 3445, 33681, 47593, 128994, 212923, 33212, 109327, 97045, 6571, 2244, 152568, 120272}

Returns: 1
2926

683

412

{625, 425, 188, 328, 103, 599, 376, 566, 674, 228, 215, 630, 468, 454, 191, 231, 668, 281, 24, 646, 98, 404, 49, 373, 581, 648, 62, 448, 39, 108, 261, 349, 674, 216, 376, 10, 354, 227, 216, 200, 189, 345, 240, 397, 61, 680, 118, 132, 624, 520, 635, 429, 334, 372, 459, 497, 472, 507, 607, 173, 37, 427, 607, 519, 558, 475, 330, 379, 443, 174, 532, 664, 567, 547, 234, 508, 421, 47, 359, 311, 639, 252, 480, 250, 208}

{47, 255, 339, 193, 297, 111, 254, 12, 164, 127, 99, 169, 373, 300, 264, 114, 8, 202, 362, 20, 261, 298, 171, 284, 277, 167, 176, 324, 261, 235, 404, 319, 17, 295, 304, 94, 386, 48, 105, 32, 128, 295, 136, 195, 300, 402, 342, 14, 411, 50, 266, 260, 393, 351, 186, 369, 213, 133, 398, 180, 136, 354, 74, 254, 398, 280, 342, 324, 65, 313, 410, 313, 275, 77, 158, 144, 23, 310, 222, 186, 279, 386, 315, 198, 360}

Returns: 5504
2979

492853

131290

{148481, 251710, 133417, 404455, 294703, 382852, 344362, 441143, 201826, 83342, 102646, 487210, 429181, 438905, 207366, 214925, 374334, 335117, 453618, 245746, 30175, 465741, 153698, 259659, 50559, 274227, 329455, 419833, 157540, 373097, 191891, 435433, 491357, 271233}

{64438, 22323, 18360, 8331, 33696, 69738, 82823, 106852, 23400, 56611, 75089, 52823, 89029, 26460, 56481, 126569, 48156, 18252, 129050, 13144, 53083, 16424, 94743, 9240, 115545, 17569, 16637, 126169, 55514, 41905, 17109, 44805, 17412, 50119}

Returns: 0
2927

45

7941

{2, 34, 10, 12, 35, 39, 3, 42, 21, 5, 17, 32, 29, 28, 26, 14, 31, 13, 16, 39, 32, 10, 42, 24, 19, 36, 39, 11, 37, 10, 19, 1, 2, 34, 34, 41, 12, 12, 37, 5, 41, 27, 35, 14, 35, 0, 32, 9, 15, 29, 27, 5}

{4220, 6224, 6316, 7481, 6367, 4310, 428, 6652, 5057, 4938, 6437, 1375, 5438, 6013, 3136, 2358, 2811, 2459, 6682, 3276, 4066, 726, 2434, 7679, 2330, 2532, 4037, 4906, 6683, 4629, 978, 6665, 6086, 2620, 6617, 7861, 4285, 2692, 2815, 3651, 1644, 331, 4993, 35, 202, 6015, 4041, 4168, 3801, 5424, 4537, 7384}

Returns: 140
2936

13667

18

{13263, 1669, 6023, 3478, 4570, 7951, 11977, 4720, 9839, 6021, 11799, 5170, 3434, 3080, 3512, 3065, 2674, 3411, 7870, 6082, 9766, 4977, 2580, 13633, 6557, 10938, 5239, 9628, 6275, 1886, 13363, 1935, 6894, 11794, 115, 397, 3272, 6370, 2797, 11058, 11531, 11057, 11057, 10756, 7913, 2013, 636, 3886, 10835, 331, 3425, 1279, 6981, 6737, 11321, 3256, 3623, 9498, 13483, 2251, 7756, 9187, 7362, 12759, 1268, 2615, 12926, 5079, 1289, 10876, 7087, 11146, 9564, 12814, 6580, 4721, 8565, 2922, 2367, 11195, 3582, 5796, 8488, 6072, 4187, 1266, 2285, 8955}

{2, 7, 9, 11, 14, 5, 16, 14, 13, 3, 5, 17, 1, 4, 15, 9, 13, 14, 16, 13, 16, 16, 13, 16, 7, 16, 8, 5, 13, 3, 3, 10, 12, 6, 7, 12, 1, 4, 2, 5, 11, 11, 13, 9, 1, 14, 13, 0, 17, 1, 0, 1, 3, 1, 3, 17, 3, 17, 7, 0, 17, 4, 9, 16, 15, 0, 2, 16, 17, 8, 15, 5, 6, 6, 10, 2, 15, 3, 0, 14, 14, 0, 1, 15, 14, 6, 3, 12}

Returns: 14
2941

14101

50

{12642, 10995, 7915, 9316, 4064, 4849, 7450, 5487, 13243, 6313, 8642, 5116, 13403, 7109, 10035, 12361, 5396, 7257, 50, 2452, 11998, 4046, 10053, 5872, 3638, 14009, 1944, 5015, 12945, 1322, 12394, 11380, 7921, 5344, 1628, 5326, 56, 6509, 3283, 12581, 8637, 4472, 8846, 4045, 2282, 12043, 13018, 10495, 528, 958, 5046, 2076, 9969, 8182}

{33, 19, 6, 31, 27, 12, 46, 26, 7, 23, 40, 25, 29, 11, 17, 49, 18, 2, 37, 37, 43, 18, 15, 2, 18, 21, 1, 31, 36, 24, 44, 42, 17, 41, 26, 38, 11, 42, 7, 37, 0, 24, 41, 34, 48, 35, 23, 46, 5, 35, 42, 44, 12, 36}

Returns: 92
2956

85809

218

{62705, 83745, 52267, 48778, 55302, 37773, 51713, 22059, 23699, 26982, 65255, 46809, 70916, 81129, 33572, 55126, 47012, 49811, 34529, 21994, 51714, 7088, 78028, 5820, 50669, 70635, 57773, 42575, 4737, 36119, 50271, 50901, 29654, 50797, 29573, 48516, 3236, 16362, 38461, 16244, 70178, 80850, 15059, 54136, 82161, 84786, 52004, 33753, 48408, 50048, 47684, 6832, 45022, 56030, 22089, 85508, 65685, 21340, 54796, 3594, 33080, 33861, 45363, 7690, 73971, 63673, 30842, 80743, 13289, 40886}

{171, 143, 193, 18, 109, 124, 141, 135, 97, 90, 130, 210, 49, 162, 147, 118, 52, 97, 123, 87, 63, 99, 71, 140, 183, 101, 97, 25, 94, 0, 180, 1, 59, 70, 11, 206, 29, 114, 85, 118, 186, 61, 110, 204, 213, 213, 145, 1, 71, 113, 99, 83, 40, 92, 82, 215, 95, 211, 193, 89, 59, 85, 186, 182, 66, 104, 8, 207, 185, 49}

Returns: 1
2936

146828

704782

{21219, 70934, 124065, 28812, 14470, 13593, 39397, 75118, 44901, 123417, 136792, 101035, 134275, 22159, 65467, 129939, 82536, 112423, 139246, 58561, 59285, 77101, 79021, 31011, 39829, 127231, 18422, 51579, 135242, 104698, 126522, 138674, 110967, 55377, 67768, 66143, 11872, 100350, 99194, 73940, 135187, 138719, 44697, 3834, 108377, 82074, 18918, 47176, 66387, 109318, 44991}

{160290, 134764, 463688, 198873, 220367, 587140, 403780, 453163, 282461, 130568, 296342, 309155, 682217, 486086, 523610, 64149, 29016, 212808, 4268, 457386, 19372, 108861, 563553, 438523, 687369, 178187, 464739, 303751, 480507, 333641, 434145, 480153, 465610, 118575, 637515, 513729, 577608, 230595, 273881, 62187, 2199, 603972, 419624, 60149, 678269, 701358, 536972, 29930, 699043, 526340, 101024}

Returns: 1
2997

17

505348

{10, 14, 11, 14, 11, 2, 13, 14, 8, 3, 10, 0, 15, 16, 16, 10, 14, 3, 6, 14, 2, 7, 6, 8, 5, 15, 14, 6, 14, 10, 8, 16}

{92630, 486523, 427695, 365185, 235055, 193119, 119517, 28981, 270446, 4660, 154744, 96138, 252871, 440258, 97210, 256499, 152413, 267662, 80739, 339234, 382338, 285352, 342902, 335463, 361909, 234277, 490206, 361160, 372397, 193006, 260573, 329103}

Returns: 0
2997

75

234

{13, 30, 40, 1, 6, 67, 64, 41, 12, 6, 6, 57, 43, 67, 63, 47, 16, 15, 30, 17, 6, 9, 30, 32, 16, 16, 30, 14, 46, 41, 50, 52, 51, 51, 25, 31, 51, 52, 33, 72, 17, 52, 22, 62, 29, 22, 56, 3, 17, 2, 4, 6, 24, 40, 22, 45, 51, 43, 26, 14, 54, 44, 20, 11, 40, 48, 13}

{211, 221, 181, 221, 194, 129, 187, 50, 26, 191, 78, 140, 69, 137, 42, 158, 88, 164, 76, 68, 176, 96, 1, 71, 3, 154, 76, 104, 37, 70, 211, 23, 84, 108, 115, 123, 135, 194, 84, 32, 173, 88, 25, 30, 46, 190, 178, 190, 87, 74, 100, 162, 18, 218, 188, 171, 158, 30, 153, 187, 7, 153, 121, 134, 122, 94, 139}

Returns: 7
2919

57

434370

{25, 50, 34, 13, 15, 0, 28, 13, 35, 5, 50, 56, 34, 20, 4, 37, 53, 0, 4, 14, 32, 6, 30, 24}

{409323, 291095, 330748, 68788, 319385, 180919, 370228, 159976, 5444, 272958, 171784, 223707, 250864, 79933, 394830, 13298, 318131, 60029, 149049, 411529, 387912, 137472, 281835, 276524}

Returns: 0
2909

3

603194

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

{250762, 178730, 361957, 63878, 120287, 164660, 13835, 83830, 278339, 597241, 486932, 249294, 504127, 317931, 542755, 457006}

Returns: 0
2986

25

429527

{13, 20, 8, 2, 18, 14, 11, 5, 24, 11, 1, 11, 20, 16, 6, 1, 0, 0, 7, 16, 9, 18, 21, 8, 21, 23, 24, 3, 21, 0, 6, 16, 14, 24, 20, 7, 7, 12, 13, 20, 11, 11, 16, 8, 14, 8, 9, 8, 18, 21, 5, 20, 9, 7, 17, 18, 16, 24, 1, 22, 8, 4, 24, 17, 16, 10, 1, 14, 23, 23, 2, 0, 18, 2, 9, 7, 21, 23, 21, 6, 7, 3, 22, 2, 10, 5, 16, 16, 21, 8, 5, 8, 13, 2, 12, 13, 23, 9}

{55980, 39593, 13172, 104893, 289860, 319386, 94641, 266535, 256021, 188011, 294761, 185167, 169876, 227205, 954, 134412, 32179, 177928, 318933, 17351, 21273, 54057, 215583, 158900, 262115, 214145, 207247, 412669, 203037, 133491, 354092, 289581, 384122, 147976, 427755, 325722, 81053, 154283, 119549, 126088, 391444, 206831, 363647, 189836, 241624, 242552, 236417, 424552, 242212, 167782, 301907, 414949, 104924, 168404, 9319, 417538, 164917, 23893, 412350, 263487, 144368, 47585, 50722, 387143, 402868, 311238, 201951, 293828, 247226, 248944, 263593, 285109, 133734, 196688, 235569, 185276, 346342, 288118, 289513, 38458, 328284, 192660, 209055, 141824, 50148, 294668, 394195, 285568, 325126, 233842, 70666, 309362, 246724, 81531, 364137, 340219, 407075, 291737}

Returns: 0
2945

3

65003

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

{62770, 62913, 36294, 1470, 22486, 29916, 60364, 29986, 13426, 29292, 2590, 27007, 28172, 58529, 1375, 17675, 15092, 22284, 20578, 10328, 39522}

Returns: 2
2962

120883

418799

{79502, 45596, 119242, 106685, 68515, 76861, 5849, 63268, 64773, 37113, 9582, 112838, 84086, 58372, 21234, 26604, 33963, 7487, 66347, 67498, 45533, 45664, 39901, 22937, 16036, 27415, 41079, 100906, 108959, 17995, 76661, 52595, 21231, 50216, 106011, 55972, 70842, 63659, 29282, 40243, 12779, 20874}

{166064, 58529, 233444, 137989, 80322, 364113, 138841, 134129, 317239, 377087, 394149, 53147, 225708, 168066, 96483, 39423, 121543, 65892, 83392, 383805, 120398, 16684, 274954, 393735, 2406, 173023, 301997, 403675, 29230, 67868, 45994, 143392, 16246, 331195, 28189, 191536, 3407, 381747, 302830, 140101, 153796, 1955}

Returns: 0
2922

23249

208

{10134, 3983, 3404, 2613, 14761, 384, 5768, 9599, 6122, 2768, 21962, 19144, 17875, 11065, 2660, 23088, 16105, 14502, 8089, 16080, 8537, 18076, 19093, 10509, 10053, 1366, 948, 12573, 10562, 6226, 18866, 5459, 5377, 18960, 4008, 13395, 15929, 5535, 3220, 2709, 3233, 17461, 19116, 21303, 14408, 11382, 716, 17172, 9203, 18732}

{140, 197, 131, 142, 46, 127, 3, 118, 17, 165, 62, 68, 28, 93, 87, 174, 73, 164, 200, 118, 135, 27, 127, 62, 8, 3, 159, 124, 111, 21, 6, 42, 107, 182, 143, 74, 184, 14, 71, 64, 15, 64, 31, 27, 134, 183, 164, 199, 70, 112}

Returns: 23
2922

178912

61

{135098, 12669, 133469, 93573, 101035, 13373, 30104, 144270, 98314, 79453, 148002}

{52, 51, 31, 43, 20, 40, 52, 5, 16, 23, 11}

Returns: 0
2978

6

350

{3, 0, 3, 5, 3, 3, 3, 4, 3, 3, 1, 4, 3, 5, 0, 5, 3, 5, 1, 0, 3, 3, 5, 2, 2, 2, 1, 5, 0, 2, 0, 2, 3, 5, 5, 0, 3, 0, 4, 3, 0, 0, 5, 5, 1, 1, 0, 1, 4, 3, 0, 2, 0, 1, 1, 5, 3, 1, 3, 1, 2, 0, 0, 1, 5, 4, 1, 1, 4, 1, 1, 4, 3, 1, 5}

{212, 100, 282, 118, 276, 65, 268, 114, 141, 67, 66, 103, 271, 184, 228, 322, 22, 51, 168, 145, 27, 35, 232, 180, 106, 227, 279, 105, 96, 340, 309, 316, 342, 259, 80, 261, 132, 268, 297, 62, 315, 168, 110, 146, 158, 304, 38, 14, 162, 194, 12, 68, 218, 338, 90, 45, 230, 189, 54, 260, 309, 316, 141, 122, 179, 9, 307, 339, 80, 168, 267, 264, 216, 298, 84}

Returns: 3
2903

69

41684

{11, 0, 6, 12, 59, 38, 15, 52, 67, 29, 4, 54, 12, 55, 19, 46, 56, 20, 59, 53, 26, 20, 51, 66, 27, 53, 54, 28, 48, 19, 7, 58, 24, 36, 66, 34, 16, 49, 9, 34, 15, 31, 37, 47, 27, 43, 30, 26, 6, 65, 27, 18, 33, 36, 28, 3, 42, 60, 33, 1, 46}

{32550, 35717, 35640, 16170, 18137, 7385, 37760, 31566, 33169, 40319, 11166, 8126, 30567, 3308, 14206, 38192, 34131, 21546, 33375, 2757, 21729, 24984, 31184, 5443, 28670, 17956, 36922, 4767, 22451, 11914, 27242, 6372, 38280, 34500, 41628, 5129, 28948, 9518, 25461, 41110, 38827, 35378, 23186, 41379, 27977, 1502, 31049, 28107, 11928, 12765, 27330, 23826, 15062, 4075, 36701, 2719, 4193, 26798, 38842, 12920, 17222}

Returns: 10
2949

3387

388

{1073, 3201, 1586, 408, 1993, 865, 1900, 1046, 969, 3166, 3291, 1496, 1879, 837, 233, 1551, 297, 2041, 1585, 866, 2541, 192, 2468, 2707, 3160, 1242, 468, 915, 108, 1750, 887, 899, 835, 2087, 2262, 872, 2815, 342, 334, 801, 326, 265, 1529, 2804, 3267, 1186, 1168, 1795, 2300, 2834, 650, 2247, 1568, 1909, 1475, 2884, 3319, 1811, 53, 1443, 1088, 2280, 1967, 2821, 266, 1402, 2010, 1071, 2563}

{387, 383, 337, 311, 134, 246, 364, 267, 363, 208, 338, 296, 147, 296, 26, 238, 177, 193, 325, 289, 339, 6, 210, 304, 289, 250, 34, 147, 381, 374, 374, 174, 270, 95, 349, 96, 153, 200, 379, 51, 56, 67, 178, 354, 171, 172, 347, 94, 96, 319, 1, 29, 55, 314, 50, 347, 233, 291, 6, 46, 17, 369, 35, 239, 106, 110, 136, 126, 236}

Returns: 106
2991

360

92

{100, 310, 346, 349, 338, 53, 129, 221, 200, 91, 100, 71, 286, 224, 50, 139, 316, 243, 269, 29, 57, 261, 59, 121, 287, 198, 289, 310, 274, 27, 80, 144, 294, 28, 315, 272, 173, 206, 89, 89, 179, 41, 157, 254, 294, 0, 50, 330, 343, 260}

{50, 4, 28, 76, 72, 53, 27, 34, 52, 57, 8, 6, 79, 82, 32, 54, 1, 42, 17, 82, 24, 10, 37, 78, 49, 57, 54, 41, 29, 63, 37, 29, 9, 44, 35, 85, 1, 66, 39, 48, 64, 81, 46, 21, 15, 76, 59, 65, 58, 71}

Returns: 206
2933

3250

393117

{1276, 969, 1618, 1301, 3201, 1667, 1622, 2304, 1001, 893, 228, 840, 1026, 1231, 969, 2783, 555, 1534, 1177, 2813, 2291, 2256, 1491, 1935, 3136, 759, 300, 3173, 156, 1231, 2793, 2098, 1198, 3072, 2348, 485, 2082, 991, 1034, 440, 2534, 306, 1181, 2046, 1560, 835, 620, 3188, 2700, 803, 602, 428, 12, 961, 2340, 2451, 3110, 2775, 1357, 949, 626, 1415, 450, 537, 2374, 2928, 1752, 2715}

{178695, 138235, 264170, 251842, 229467, 324406, 222316, 229879, 240549, 267607, 137179, 297799, 88085, 389378, 117217, 71731, 328695, 205499, 323491, 263546, 69414, 67705, 311254, 159377, 40086, 325962, 93987, 64261, 279275, 353821, 42638, 24675, 250492, 236965, 171148, 200990, 68474, 239817, 9362, 251741, 180564, 208532, 265641, 325379, 2801, 265441, 325858, 322399, 200354, 217654, 214704, 24158, 118330, 161530, 34797, 212379, 391933, 35997, 349368, 203756, 118874, 36384, 9405, 107879, 303467, 150852, 299689, 361167}

Returns: 0
2960

732443

10

{318029, 257287, 394078, 115207, 599147, 21407, 199358, 594862, 352038, 212832, 15106, 362515, 150183, 297347, 496957, 49880, 622687, 232034, 643310, 221881, 593721, 659993, 456545, 181690, 217239, 337157, 490970, 21290, 526596, 192274, 632962, 419889, 141484, 307966, 475822, 254075, 170599, 258781, 434969, 508007, 575599, 134293, 179584, 407371, 156555, 210469, 326014, 255701, 335207, 701746, 199757, 264585, 411716, 260038, 259105, 489061, 417042}

{2, 1, 2, 6, 6, 7, 6, 2, 7, 3, 8, 6, 6, 5, 7, 2, 2, 8, 3, 2, 3, 0, 6, 1, 3, 7, 8, 9, 5, 9, 1, 6, 2, 1, 6, 2, 8, 9, 9, 5, 6, 5, 6, 9, 8, 6, 2, 7, 1, 8, 3, 2, 7, 5, 1, 4, 5}

Returns: 0
2977

436227

24710

{35490, 93264, 410190, 48655, 10831, 236161, 16877, 387524, 150474, 397366, 85507, 204201, 264207, 66873, 296049, 415646, 406618, 349765, 290312, 195658, 315700, 176909, 177675, 75448, 165509, 332123, 324920, 181471, 410235, 13638, 409885}

{12373, 11351, 10970, 11273, 23691, 22049, 24200, 11104, 10772, 4187, 9074, 17298, 4355, 17220, 18741, 16598, 13534, 11021, 9008, 960, 10889, 22770, 5274, 3170, 1655, 5679, 9539, 10740, 2256, 1950, 13444}

Returns: 0
2972

73786

1227

{61549, 3805, 57954, 32118, 53862, 71345, 34769, 54117, 2562, 72635, 9197, 68981, 23314, 32290, 33421, 17853, 16152, 67075, 38147, 16563, 71648}

{744, 1086, 1195, 1180, 458, 821, 439, 477, 312, 898, 284, 551, 77, 1020, 378, 961, 1195, 1019, 1192, 567, 1127}

Returns: 9
3000

3

1861

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

{899, 1772, 693, 506, 1284, 1834, 1042, 157, 1413, 578, 3, 683, 490, 324, 10, 795, 861, 496, 36, 402, 290, 458}

Returns: 73
3000

565403

3

{73841, 346460, 434428, 235348, 127756, 39438, 149194, 75507, 272654, 136405, 300396, 398204, 446598, 341472, 435247, 160649, 547564, 545577, 375330, 16331, 383001, 23637, 364103, 467421, 291986, 340177, 479644, 217157, 359156, 142607, 440402, 149514, 448948, 467143, 524266, 287633, 53992, 105225, 9535, 524903, 389572, 38931, 327472, 212588, 129422, 503537, 495000, 539319, 191734, 380092, 206724, 379177, 270871, 167123, 72546, 23180, 270204, 437371, 469964, 70184, 46935, 302761, 18791, 20002, 544443, 322962, 2882, 30010, 123551}

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

Returns: 0
2987

204709

902

{21762, 66034, 144249, 195374, 137039, 76094, 97228, 30927, 38669, 101273, 132268, 24416, 145411, 176185, 169941, 136933, 43762, 43503, 79517, 163066, 78849, 49279, 82569, 143690, 161126, 165336, 95028, 163638, 87398, 150320, 70416, 104829, 176256, 84955, 174664, 104865, 160011, 88148, 113733, 59326, 8028, 83024, 164226, 184887, 103567, 203734, 132468, 169945, 74226, 197833, 164911, 61342, 167975, 96865, 92376, 801, 113627, 137152, 195754, 83382, 120628, 85163, 12115, 83381, 191608, 199754, 161994, 52717, 68246, 193249, 23364}

{889, 116, 103, 736, 248, 240, 397, 229, 109, 593, 614, 216, 843, 553, 163, 562, 24, 39, 413, 607, 211, 24, 730, 859, 229, 535, 865, 240, 301, 66, 881, 773, 195, 498, 602, 411, 644, 842, 219, 824, 578, 537, 408, 7, 778, 668, 534, 203, 520, 608, 605, 227, 112, 439, 481, 778, 316, 240, 873, 83, 590, 392, 408, 173, 177, 274, 363, 198, 404, 483, 49}

Returns: 0
2972

119

6

{88, 4, 78, 116, 61, 117, 57, 9, 85, 61, 107, 18, 102, 52, 24, 66, 113, 59, 37, 86, 39, 96, 65, 3, 35, 82, 66, 18, 70, 113, 33, 104, 98, 19, 0, 91, 86, 73, 76, 17, 79, 112, 113, 81, 68, 8, 72, 29, 94, 43, 94, 71, 100, 75, 80, 64, 19, 82, 39, 79, 72, 64}

{4, 4, 0, 3, 3, 4, 2, 2, 2, 0, 1, 2, 3, 4, 5, 4, 1, 5, 4, 3, 0, 0, 4, 0, 1, 3, 2, 1, 2, 0, 4, 2, 4, 4, 2, 3, 1, 2, 1, 5, 5, 0, 1, 2, 5, 0, 0, 2, 1, 0, 1, 3, 5, 5, 5, 4, 4, 2, 1, 0, 4, 2}

Returns: 18
2963

347983

3

{81071, 143238, 223833, 280509, 105524, 93365, 295268, 81039, 13233, 94240, 60104, 171271, 17306, 210252, 333179, 178300, 126112, 272892, 39939, 48837, 113779, 305908, 264936, 158840, 331732, 232213, 184163, 242875, 335344, 191762, 32305, 42179, 121446, 203418, 123250, 152027, 38824, 258645, 94949, 2780, 246565, 203105, 316893, 136061, 4945, 154495, 202746, 222435, 171042, 61919, 287459, 51311, 283272, 173638, 256424, 47505, 108920, 97888, 43922, 316590, 99265, 39349, 201685, 83723, 44271, 125222, 124065, 231535, 257350, 336156, 229187, 19140, 134208, 161222, 251111, 307450, 119150, 146203, 265783, 39489, 24941, 70905, 300569}

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

Returns: 0
2967

25

8851

{24, 6, 13, 14, 2, 14, 6, 21, 4, 9}

{7626, 6913, 5092, 5462, 5591, 707, 1572, 2977, 288, 2100}

Returns: 374
2967

1583

2901

{135, 10, 999, 1093, 598, 284, 793, 756, 468, 1079, 1086, 226, 343, 929, 395, 1013, 358, 1048, 1121, 180, 9, 1121, 1517, 414, 139, 1395, 225, 1482, 982, 1448, 555, 1167, 22, 442, 1448, 52, 1282, 532, 164}

{1082, 2136, 2408, 1631, 1679, 1330, 1204, 1565, 1098, 2519, 2374, 357, 426, 385, 1979, 437, 1470, 1465, 1780, 615, 2439, 1130, 2366, 2674, 2518, 1996, 1909, 2608, 2795, 2579, 2891, 1956, 1922, 989, 1242, 1962, 1594, 730, 2707}

Returns: 2125
2993

1933

54

{1177, 1153, 323, 1767, 1825, 971, 1053, 991, 684, 1820, 1836, 106, 886, 496, 1084, 865, 77, 1025, 1452, 1379, 250}

{23, 14, 20, 33, 39, 12, 4, 37, 18, 22, 53, 48, 12, 35, 35, 18, 6, 46, 7, 44, 27}

Returns: 176
2928

1065

14786

{870, 5, 814, 90, 770, 495, 165, 350, 745, 759, 381, 796, 713, 615, 721, 236, 787, 30, 659, 551, 153, 624, 59, 190, 380, 81, 996, 26, 836}

{12350, 7623, 4956, 12714, 6623, 12403, 6652, 2011, 3601, 2819, 8988, 2066, 1879, 633, 3373, 3740, 5772, 9824, 2862, 49, 13214, 9407, 7526, 6323, 5580, 13858, 3584, 12999, 341}

Returns: 106
2926

6697

81425

{1003, 441, 5491, 2857, 1700, 2128, 3919, 3156, 508, 310, 6017, 5579, 1666, 3784, 1901, 4078, 3650, 2122, 5593, 3512, 6173, 2221, 6526, 1575, 1082, 4484, 5101, 73, 2393, 4617, 3165, 2481, 3963, 4029, 5669, 6650, 1728, 6691, 4944, 2455, 5683, 813, 5297, 6359, 3350, 2946, 2094, 4660, 1974, 3277, 2775, 5493, 5103, 3794, 1370, 2138, 4248, 5956, 136, 892, 6659, 3863, 5052, 5979, 5583, 6488, 726, 484, 6020, 5347, 823, 5994, 3705, 5397, 2826, 2355, 1528, 4947, 156, 3721, 1614, 2283, 3227, 6046}

{7662, 3444, 7057, 11954, 76850, 23113, 11942, 19973, 9924, 68459, 19184, 37318, 5627, 55277, 37793, 35651, 170, 25838, 14479, 50109, 65600, 67817, 16698, 69692, 62487, 20690, 8602, 2038, 54852, 39677, 74756, 4098, 5916, 29845, 61242, 72209, 15230, 27811, 4917, 57174, 30779, 4582, 54875, 18904, 37609, 7264, 77839, 15173, 26887, 1914, 66728, 52019, 33906, 73830, 8276, 60175, 50618, 53257, 31305, 22433, 78859, 74614, 71268, 2587, 17394, 50033, 78975, 48533, 53146, 50672, 38540, 75003, 18075, 60350, 66998, 20182, 79343, 41521, 44244, 267, 52937, 40009, 23537, 9043}

Returns: 3
2997

442200

7912

{332454, 141469, 91967, 28430, 228125, 26248, 56789, 438641, 67513, 367245, 101097, 165536, 156129, 363674, 254118, 338948, 432262, 294370, 95466, 129639, 92014, 154282, 331208, 289258, 52461, 339097, 409261, 29054, 205424, 121708, 401448, 29595, 124628, 151132, 383081}

{287, 5004, 5786, 3208, 1467, 6746, 3236, 867, 5887, 7763, 3991, 2992, 1390, 1502, 4878, 358, 1250, 445, 7489, 2795, 3864, 2931, 3638, 782, 5328, 4279, 5111, 2481, 5318, 5798, 4870, 2939, 1101, 1848, 125}

Returns: 16
2955

39

4628

{12, 23, 33, 26, 23, 32, 24, 5, 28, 21, 11, 27, 24, 12, 1, 7, 17, 27, 10, 3, 21, 37, 38, 4, 24}

{208, 2807, 2408, 2767, 4051, 3874, 2251, 4275, 662, 2799, 1740, 2887, 60, 628, 450, 3671, 4288, 4416, 1864, 2909, 1189, 1825, 3133, 3821, 3024}

Returns: 0
2997

357

397

{63, 243, 322, 115, 37, 167, 316, 95, 136, 95, 191, 212, 38, 37, 150, 133, 0, 335, 329, 114, 246, 296, 257, 51, 319, 254, 122, 138, 329, 101, 40, 283, 47, 4, 115, 191, 174, 181, 302, 273, 295, 14, 215, 273, 296, 46, 285, 267, 173, 251, 308, 239, 138, 341, 24, 100, 26, 29, 92, 195, 208, 223, 336, 291, 79, 116, 133, 26, 38, 147, 2, 353, 247, 186, 279, 139, 200, 97, 312, 17, 316, 150, 220, 203, 54}

{3, 122, 344, 187, 14, 99, 141, 190, 355, 139, 142, 278, 31, 66, 47, 364, 301, 292, 51, 237, 369, 318, 379, 248, 252, 103, 107, 217, 304, 80, 173, 176, 95, 290, 94, 345, 59, 89, 66, 293, 103, 40, 342, 112, 108, 348, 166, 14, 248, 380, 64, 305, 258, 330, 8, 2, 244, 278, 338, 324, 270, 220, 196, 237, 37, 283, 379, 246, 78, 182, 208, 283, 94, 359, 334, 86, 128, 69, 60, 219, 267, 368, 154, 35, 377}

Returns: 265
2905

483

640

{223, 61, 138, 137, 254, 222, 321, 401, 300, 84, 108, 336, 24, 191, 234, 181, 259, 10, 96, 221, 343, 158, 3, 236, 331, 480, 270, 280, 447, 439, 84, 435, 257, 102, 79, 169, 418, 223, 355, 447, 238, 477, 36, 387, 340, 205, 63, 242, 452, 353, 407, 72, 9, 34, 384, 423, 281, 12, 297, 120, 431, 377, 98, 106, 348, 5, 164, 37, 190, 191, 206, 270, 205, 64, 391, 317, 26, 444, 227, 319, 62, 143, 177, 226, 276}

{431, 91, 448, 197, 529, 7, 269, 111, 364, 116, 614, 480, 558, 593, 16, 289, 298, 99, 73, 50, 65, 417, 550, 530, 105, 214, 538, 510, 456, 114, 477, 214, 438, 18, 616, 50, 624, 599, 77, 160, 529, 591, 331, 157, 352, 378, 212, 323, 232, 393, 323, 420, 570, 64, 530, 24, 523, 464, 99, 337, 41, 248, 628, 159, 556, 601, 529, 510, 396, 378, 49, 317, 333, 485, 590, 384, 625, 352, 232, 428, 27, 343, 241, 360, 500}

Returns: 138
2902

514

525

{54, 172, 442, 336, 479, 45, 131, 347, 490, 107, 295, 166, 226, 11, 39, 357, 81, 460, 421, 462, 162, 319, 406, 159, 429, 126, 140, 208, 110, 397, 62, 268, 125, 14, 395, 78, 191, 152, 293, 471, 142, 228, 90, 410, 398, 298, 218, 304, 178, 175, 71, 472, 181, 19, 499, 276, 136, 389}

{28, 4, 213, 341, 271, 5, 415, 1, 374, 285, 345, 259, 52, 70, 95, 79, 218, 506, 455, 106, 480, 461, 282, 510, 395, 281, 255, 35, 215, 92, 237, 159, 472, 24, 36, 417, 243, 15, 515, 394, 452, 92, 405, 383, 142, 211, 80, 276, 233, 3, 171, 133, 277, 457, 162, 348, 347, 71}

Returns: 30866
2963

464

589

{329, 359, 271, 281, 402, 342, 287, 120, 376}

{29, 1, 482, 45, 8, 506, 351, 294, 556}

Returns: 1978
2919

642

216

{282, 236, 479, 198, 308, 116, 450, 157, 170, 453, 120, 478, 255, 195, 638, 570, 359, 144, 549, 427, 70, 593, 563, 152, 411, 390, 186, 615, 630, 134, 148, 345, 428, 331, 28, 557, 213, 349, 245, 396, 215, 307, 516, 197, 256, 600, 476, 553, 90, 337, 352, 491, 268, 136, 72, 93, 611, 555, 520, 188, 269, 532, 44, 231, 340, 641, 610, 619, 376, 147, 361, 606, 471, 598, 446, 527, 67, 535, 350, 524, 437, 121, 420, 216, 1, 431, 204, 590, 82, 603, 195, 628, 563}

{18, 189, 145, 103, 84, 63, 55, 149, 20, 206, 0, 214, 7, 49, 66, 74, 35, 168, 61, 101, 136, 163, 107, 49, 40, 128, 120, 30, 109, 41, 192, 197, 159, 123, 168, 30, 211, 28, 119, 77, 15, 187, 205, 68, 163, 188, 197, 9, 2, 126, 28, 34, 28, 21, 34, 182, 75, 202, 200, 208, 3, 187, 89, 99, 109, 169, 157, 105, 92, 80, 137, 14, 135, 66, 127, 69, 120, 184, 127, 75, 35, 198, 109, 96, 51, 138, 12, 17, 7, 206, 74, 184, 71}

Returns: 2849
2906

555

688

{320, 433, 502, 369, 210, 194, 178, 283, 229, 66, 551, 91, 165, 243, 377, 377, 120, 493, 170, 99, 439, 36, 209, 47, 241, 429, 261, 103, 94, 36, 98, 552, 386, 519, 27, 545, 86, 531, 228, 416, 206, 404, 418, 378, 20, 444, 513, 532, 44, 104, 0, 162, 417, 438, 228, 413, 319, 235, 396, 508, 314, 276, 463, 265, 69, 305, 245}

{30, 571, 529, 466, 660, 673, 668, 45, 295, 684, 12, 205, 398, 459, 131, 150, 544, 152, 469, 302, 193, 332, 292, 675, 321, 389, 76, 200, 678, 88, 495, 504, 247, 202, 30, 383, 207, 277, 62, 397, 19, 528, 496, 124, 274, 151, 316, 194, 497, 429, 474, 60, 406, 417, 586, 585, 396, 544, 214, 616, 514, 591, 396, 155, 417, 386, 666}

Returns: 4
2988

211

517

{98, 85, 205, 176, 43, 55, 153, 189, 137, 28, 9}

{456, 22, 189, 263, 463, 1, 477, 343, 452, 21, 81}

Returns: 1
2966

224

628

{191, 179, 182, 144, 69, 153, 11, 59, 23, 223, 110, 60, 196, 183, 13, 157, 204, 161, 99, 142, 171, 188, 101, 156, 140, 106, 214, 89, 142, 222, 2, 64, 169, 118, 169, 192, 88, 26, 129, 28, 75, 211, 22, 25, 99, 180, 58, 54, 220, 19, 101, 92, 70, 101, 41, 112, 139, 16, 182, 41, 67, 109, 177, 218}

{432, 582, 237, 31, 101, 451, 302, 520, 205, 309, 241, 10, 180, 543, 314, 49, 307, 370, 180, 234, 377, 340, 383, 470, 93, 194, 579, 524, 291, 439, 52, 94, 314, 112, 59, 512, 225, 274, 158, 477, 306, 445, 62, 494, 6, 482, 528, 19, 31, 99, 618, 124, 398, 126, 159, 328, 187, 524, 321, 88, 363, 17, 356, 617}

Returns: 8
2919

541

646

{417, 311, 184, 227, 243, 77, 476, 295, 220, 155, 452, 509, 287, 104, 165, 402, 300, 196}

{627, 82, 62, 611, 471, 577, 367, 330, 508, 310, 1, 353, 308, 209, 142, 293, 98, 263}

Returns: 188
2966

681

526

{292, 165, 213, 235, 217, 2, 607, 475, 631, 403, 626, 197}

{525, 111, 389, 307, 261, 376, 60, 80, 401, 233, 110, 332}

Returns: 27381
2928

432

358

{340, 285, 156, 196, 65, 75, 294, 387, 352, 412, 193, 289, 194, 386, 263, 339, 208, 30, 27, 110, 313, 62, 337, 165, 184, 352, 280, 138, 324, 206, 118, 280, 362, 277, 14, 365, 29, 104, 291, 47, 159, 327, 263, 38, 219, 113, 116, 108, 65, 282, 204, 31, 175, 173, 322, 16, 234, 334, 201, 120, 167, 388, 59, 88}

{219, 156, 168, 87, 355, 256, 59, 231, 316, 292, 209, 176, 217, 284, 141, 267, 151, 67, 113, 234, 207, 276, 80, 279, 120, 356, 171, 280, 321, 292, 78, 163, 39, 287, 13, 116, 350, 179, 88, 346, 180, 353, 222, 306, 0, 155, 256, 267, 305, 96, 198, 120, 197, 78, 19, 280, 270, 324, 144, 260, 60, 269, 33, 286}

Returns: 9147
2932

320

648

{257, 40, 174, 142, 16, 129, 155, 300, 142, 254, 205, 261, 7, 236, 68, 248, 8, 127, 108, 243, 310, 186, 170, 178, 41, 119, 32, 48, 308, 74, 115, 295, 53, 243, 123, 246, 0, 114, 138, 6, 209, 297, 212, 192, 307, 196, 183, 31}

{149, 497, 566, 7, 115, 2, 397, 129, 182, 489, 302, 634, 267, 502, 61, 115, 126, 533, 239, 264, 554, 536, 174, 18, 336, 516, 292, 452, 357, 369, 19, 327, 400, 158, 188, 455, 524, 327, 116, 46, 527, 352, 40, 107, 70, 475, 474, 530}

Returns: 25
2970

515

284

{256, 435, 239, 128, 500, 368, 348, 60, 380, 493, 378, 355, 372, 166, 458, 461, 71, 54, 152, 188, 472}

{126, 83, 168, 96, 192, 204, 85, 40, 236, 51, 274, 265, 84, 56, 276, 112, 183, 87, 271, 245, 215}

Returns: 104
2980

269

290

{98, 10, 193, 211, 100, 201, 17, 44, 106, 110, 230, 169, 182, 64, 206, 178, 202, 87, 230, 133, 170, 57, 260, 190, 162, 142, 187, 254, 172, 133, 253, 22, 152, 128, 177, 156, 84, 254, 174, 48, 64, 22, 29, 95, 114, 131, 86, 100, 258, 135, 71, 206, 81, 161, 268, 63, 213, 33, 215, 184, 20, 90, 80, 0, 7, 105, 83, 14, 104, 254, 71, 182, 223, 195, 253, 39, 83, 152, 230, 262, 168, 215, 113, 139, 170, 0, 32, 71, 138, 30, 262, 225, 57, 226}

{46, 25, 286, 35, 207, 40, 158, 230, 4, 117, 43, 183, 210, 19, 152, 48, 60, 75, 82, 237, 20, 3, 237, 142, 254, 183, 276, 234, 25, 90, 28, 262, 129, 38, 0, 262, 265, 224, 42, 200, 121, 73, 166, 90, 160, 65, 195, 270, 141, 205, 10, 57, 23, 135, 285, 15, 183, 202, 115, 272, 152, 17, 47, 275, 169, 192, 96, 174, 258, 247, 171, 38, 100, 208, 165, 42, 280, 94, 152, 190, 266, 191, 145, 199, 258, 282, 275, 270, 213, 74, 193, 52, 108, 70}

Returns: 25669
2981

436

218

{391}

{139}

Returns: 0
2947

386

649

{253, 334, 48, 209, 205, 337, 148, 288, 115, 114, 82, 83, 232, 369, 300, 320, 41, 42, 75, 45, 98, 208, 145, 378, 317, 53, 319, 328, 176, 368, 160, 202, 64, 264, 92, 148, 287, 281, 357, 350, 71, 286, 264, 71, 262, 345, 38, 269, 80, 28, 36, 18, 74, 315, 149, 65, 49, 349, 10, 316, 133, 39, 110, 335, 69, 365, 200, 182, 35, 326, 102, 358, 18, 42, 300, 347, 282, 236, 259, 55, 261, 215, 271, 148, 109}

{283, 523, 621, 383, 493, 223, 243, 100, 351, 481, 418, 450, 49, 36, 510, 147, 221, 98, 524, 234, 416, 477, 620, 176, 512, 334, 643, 401, 198, 123, 611, 548, 627, 467, 270, 301, 386, 399, 25, 502, 209, 644, 365, 182, 328, 159, 576, 75, 357, 206, 595, 394, 43, 431, 585, 572, 117, 555, 317, 147, 311, 526, 265, 221, 516, 297, 41, 42, 306, 262, 454, 469, 502, 637, 365, 43, 116, 337, 395, 303, 130, 367, 595, 407, 32}

Returns: 33501
2945

669

416

{345, 580, 531, 58, 283, 400, 436, 523, 558, 499, 145, 578, 450, 471, 341, 121, 26, 308, 268, 534, 526, 302, 29, 389, 109, 8, 640, 622, 499, 437, 596, 435, 85, 13, 14, 241, 345, 150, 506, 615, 199, 438, 379, 581, 596, 467, 446, 363, 283, 148, 19, 236, 559, 375, 563, 473, 429, 486, 9, 575, 150, 172, 23, 276, 622, 254, 548, 286, 294, 495, 668, 49}

{329, 168, 287, 255, 154, 243, 351, 251, 411, 59, 176, 338, 63, 313, 327, 413, 320, 182, 389, 404, 346, 204, 205, 378, 232, 388, 21, 317, 298, 289, 303, 207, 64, 373, 259, 41, 370, 218, 295, 300, 369, 321, 32, 120, 276, 313, 247, 77, 121, 78, 243, 101, 389, 367, 322, 26, 96, 117, 333, 8, 89, 107, 415, 312, 245, 341, 131, 349, 373, 303, 392, 8}

Returns: 114
2953

600

590

{240, 274, 298, 502, 3, 286, 403, 232, 224, 160, 240, 18, 362, 138, 137, 240, 587, 412, 508, 286, 322, 390, 377, 137, 547, 398, 390, 18, 172, 343, 39, 141, 509, 280, 131, 499, 20, 347, 70, 336, 167, 107, 240, 232, 361, 336, 542, 158, 589, 38, 428, 203}

{310, 156, 267, 515, 210, 256, 239, 389, 525, 147, 233, 445, 208, 163, 189, 163, 548, 235, 551, 81, 290, 571, 99, 348, 100, 192, 503, 260, 533, 197, 115, 516, 355, 219, 4, 53, 378, 261, 78, 413, 7, 198, 150, 453, 469, 259, 443, 411, 579, 197, 469, 335}

Returns: 7
2923

463

282

{124, 43, 367, 55, 319, 349, 122, 340, 321, 327, 59, 256, 253}

{77, 113, 97, 83, 260, 228, 179, 34, 275, 127, 146, 97, 122}

Returns: 5
2910

455

418

{187, 202, 244, 23}

{344, 96, 296, 394}

Returns: 9
3

100

100

{3, 0, 2 }

{0, 1, 2 }

Returns: 1
8

100

100

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

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

Returns: 1
3000

999997

999997

{13 }

{19 }

Returns: 0
6

100

100

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

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

Returns: 2
3000

987654

871293

{1 }

{5 }

Returns: 0
3000

999991

999983

{7 }

{0 }

Returns: 0
5

100

100

{0, 0, 1, 2, 2 }

{0, 1, 0, 0, 1 }

Returns: 2
3000

999997

999997

{135679 }

{942375 }

Returns: 0
6

100000

100000

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

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

Returns: 1
3

1000000

1000000

{0, 0, 900000 }

{0, 900000, 0 }

Returns: 1
3000

1000000

1000000

{2, 3, 5, 7 }

{11, 13, 17, 21 }

Returns: 0
3000

100

199

{99 }

{198 }

Returns: 7902
100

100

100

{38, 18, 17, 16, 28, 10, 44, 2, 22, 18, 34, 18, 20, 31, 20, 27, 11, 39, 3, 36, 16, 27, 6, 13, 9, 44, 1, 35, 42, 38, 4, 32, 22, 1, 38, 36, 15, 0, 4, 29, 3, 10, 20, 4, 22, 10, 39, 21, 4, 19, 39, 29, 29, 9, 27, 1, 23, 39, 15, 17, 17, 43, 28, 3, 33, 35, 25, 29, 31, 31, 45, 1, 29, 34, 33, 33, 41, 5, 5, 25, 43, 32, 10, 9, 4, 31, 26, 19, 2, 13, 38, 23, 40, 34, 33, 15, 31, 3, 20, 15 }

{4, 23, 26, 3, 28, 17, 28, 20, 21, 36, 37, 38, 1, 17, 6, 37, 24, 7, 9, 31, 46, 13, 9, 28, 31, 43, 15, 21, 45, 41, 18, 15, 3, 25, 37, 34, 16, 22, 39, 14, 5, 4, 24, 16, 42, 27, 21, 14, 23, 42, 34, 8, 9, 34, 17, 9, 37, 22, 43, 37, 7, 10, 18, 11, 38, 41, 18, 34, 10, 32, 7, 38, 16, 0, 5, 8, 40, 23, 25, 38, 39, 21, 41, 20, 19, 2, 33, 34, 7, 14, 46, 11, 28, 45, 12, 29, 26, 41, 38, 3 }

Returns: 196
3000

999999

999998

{827082, 824610, 822713, 822091, 821786, 821478, 819354, 818812, 818015, 817377, 817210, 816820, 816315, 816231, 815408, 815311, 815241, 814972, 814748, 814543, 814476, 814399, 813947, 813434, 813364, 813221, 812813, 812470, 812378, 812218, 811933 }

{811772, 810961, 810363, 809498, 809398, 809238, 809002, 808748, 808531, 808275, 807848, 807318, 807044, 806697, 806677, 805628, 805552, 805406, 805127, 804474, 804258, 804211, 803988, 803877, 803342, 803310, 803286, 802742, 802129, 801522, 801372 }

Returns: 0

Statistics

Problem Statement for "MoreSquares"

Problem Statement

Definition

Notes

Constraints

Examples