TopCoder Statistics - Problem Statement

Problem Statement

You want to make a new wooden fence.

You have some scrap wood. You would like to use some of it as the planks in the fence.

All planks in the fence need to have exactly the same length.

If you have two shorter pieces of wood that together have the correct length, you can nail them together and use them as a single plank.

You cannot combine more than two pieces of wood into a plank (the fence wouldn't be sturdy enough) and you cannot shorten the pieces you have (you only have a hammer and nails, but no saw).

You are given the int[] wood. The elements of wood are the lengths of the pieces of wood you own.

You want to make the longest fence possible. I.e., you want to maximize the number of planks. You can choose the height of your fence (i.e., the length of all planks that form it) and you can also choose how to combine the pieces of wood in your collection. Return the maximum number of planks in your fence.

Definition

Class:: ANewFence
Method:: build
Parameters:: int[]
Returns:: int
Method signature:: int build(int[] wood)
(be sure your method is public)

Constraints

wood will contain between 1 and 200 elements, inclusive.
Each element of wood will be between 1 and 10^9, inclusive.

Examples

{10, 10, 10, 10, 4, 10, 7, 10}

Returns: 6

The optimal fence height is 10. We have six pieces of wood that can be used as planks. The pieces with lengths 4 and 7 will remain unused.
{10, 10, 10, 10, 4, 10, 6, 10}

Returns: 7

As in the previous example, the optimal fence height is 10. However, now we can combine the two shorter pieces of wood into the seventh plank for the fence: 4+6 = 10.
{10, 10, 10, 10, 3, 10, 3, 4, 10}

Returns: 6

Remember that we cannot make planks for the fence from more than two pieces of wood. In particular, here we cannot use the pieces with lengths 3, 3, 4 to form a plank for the fence.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Returns: 5

The optimal fence height is either 10 or 11. In both cases we can assemble five planks.
{10, 110, 100, 100, 10}

Returns: 3

We can use everything we have to make three planks of length 110 each.
{10, 24, 47, 193, 558}

Returns: 1
{3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 5, 5, 5}

Returns: 6
{3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 5, 5, 5, 5}

Returns: 7
{5, 5, 10}

Returns: 2

You can either have two planks of length 5, or combine the two shorter pieces and have two planks of length 10. Both solutions are optimal.
{2268, 1859, 2338, 1407, 1055, 2099, 1584, 1608, 2522, 168, 3257, 1715, 2698, 97, 420, 3, 1081, 3246, 1973, 2965, 2240, 38, 3758, 3342, 3682, 1293, 2325, 1752, 943, 974, 2144, 2106, 1471, 1812, 992, 137, 2298, 1533, 2936, 2817, 1448, 2462, 1401, 2285, 2356, 3121, 803, 978, 3231, 3444, 2987, 3748, 145, 515, 1368, 402, 1487, 2369, 1572, 2083, 2213, 3330, 1036, 398, 2658, 3572, 3610, 930, 3798, 2864, 3464, 1372, 896, 1930, 3049, 452, 3167, 1707, 2477, 1447, 2765, 3574, 1173, 3601, 3166, 3318, 979, 3315, 2275, 3777, 1072, 1463, 2182, 2316, 165, 1983, 1279, 2305, 3194, 1620, 1066, 2991, 2128, 3276, 905, 2484, 467, 2570, 3447, 849, 1556, 1989, 1037, 2473, 3792, 2286, 612, 1819, 63, 698, 2241, 2569, 3295, 3119, 340, 306, 1089, 2095, 3329, 2550, 2240, 1952, 3205, 3285, 1785, 1498, 3763, 3110, 136, 2490, 1086, 3684, 2640, 2493, 2118}

Returns: 8
{746029, 19358250, 8154384, 7092224, 11608638, 14483349, 23212579, 6174553, 5928311, 15763636, 6666476, 4290817, 3302351, 4585545, 24508812, 26343698, 19113318, 11544572, 17696646, 13165439, 3626736, 8954510, 14895506, 15164, 21898474, 4106251, 13893886, 2253668, 12389927, 695302, 8866685, 1399395, 4712332, 6079366, 24801598, 17168396, 16474665, 6749422, 26275928, 25933324, 27235780, 16599204, 17725964, 15219990, 18911464, 19036671, 335120, 23321507, 2477841, 5876129, 5052198, 18234965, 11352895, 21324678, 1566514, 20872477, 7868557, 23898908, 2054711, 12708042, 4132161, 745379, 2972545, 10157877, 1808317, 18382987, 10323542, 8023468, 20557179, 24629494, 17947841, 5073591, 18452531, 19453463, 25582828, 9165749, 20769768, 19154035, 2707949, 18889773, 16483749, 11499632, 18673771, 1750954, 3845179, 13874015, 14013868, 11869635, 10160695, 18935467, 25492139, 16416679, 20054168, 4685947, 2131924, 17041468, 3928097, 15477474, 21909456, 26402545, 15225874, 599879, 14582184, 27168150, 18922345, 17519612, 25615932, 2221019, 26226685, 26481992, 9651229, 26298115, 23647703, 16448459, 16857563, 3829518, 25331987, 8224853, 11817503, 26717766, 11110197, 5600827, 15520975, 758131, 19720714, 3294570, 22512891, 15417260, 15452772, 9287428, 21408798, 18284497, 23018901, 23329702, 23124880, 798059, 18797151, 6351364, 22803588, 9631958, 1371913, 25897464, 8833594, 18194992, 16196156, 12874950, 2297339, 24240466, 26373659, 3658598, 17477267, 23792145, 19796993, 20096324, 16016153, 18023988, 24975659, 26534392, 12145450, 19409949, 10458817, 13827641, 25836521, 22911183, 6874291, 24574023, 21223775, 3068403, 3445391, 17193016, 27149675, 10234013, 13592214, 11165428, 18085559, 12083706, 3650690, 3126617, 20885132, 24963662, 14298439, 12097356, 1685943, 11736710, 19556651, 1895029}

Returns: 2
{55211, 75950, 54843, 121898, 173362, 78516, 116719, 115462, 83219, 176815, 14358, 40705, 152119, 125751, 162, 7216, 110820, 119906, 136374, 114788, 160972, 67561, 77061, 26872, 79450, 32467, 44499, 110910, 88253, 130425, 111673, 61475, 131952, 149493, 134542, 68971, 82049, 145436, 6047, 159617, 176442, 99437, 155874, 154483, 182658, 155935, 180841, 163581, 121065, 161738, 146359, 47055, 178922, 183999, 98833, 11219, 47615, 160691, 47570, 163547, 20430, 127128, 107747, 15800, 58831, 121038, 46114, 156746, 104306, 1171, 163695, 36462, 194838, 19081, 146851, 102004, 198, 100761, 130896, 194474, 119308, 165093, 97833, 191529, 32109, 134021, 104985, 26767, 22555, 110177, 107991, 144312, 27332, 161819, 45831, 174357, 130697, 124729, 115147, 156325, 24570, 103679, 137500, 132550, 85826, 113398, 196328, 51549, 82939, 104102, 19554, 34738, 186839, 127827, 87310, 170378, 170211, 27484, 66191, 127261, 24304, 93627, 7795, 103429, 163763, 21319, 157694, 58783, 135214, 168839, 55256, 133117, 67550, 186979, 80367, 131090, 158742, 29816, 147366, 16371, 75211, 188649, 46470, 127998, 182340, 63259, 106003, 160072, 124273, 1856}

Returns: 3
{2622776, 2325243, 1569090, 447595, 1417046, 269661, 658821, 2474139, 444133, 1002375, 768512, 335427, 594395, 2159980, 705272, 3014790, 693779, 323943, 388768, 528273, 2470909, 1651654, 1460929, 510845, 1739239, 1236795, 2303737, 2686606, 920837, 2848308, 1455074, 377908, 2690328, 1317663, 427463, 150099, 846505, 2344978, 568210, 1384991, 381235, 1339363, 3000599, 2782479, 1799219, 2123239, 2289928, 2401571, 2852369, 1477037, 2186592, 2178860, 1784676, 2675344, 1841812, 1828888, 2836157, 1732725, 3052498, 2057978, 95107, 817110, 1369165, 205823, 2515191, 1797370, 424094, 1841693, 2444450, 520231, 403884, 1403687, 1833563, 247516, 1399659, 786325, 2805492, 1714524, 1966306, 2172454, 1992245, 2905646, 2166017, 501311, 962339, 833023, 2631304, 110647, 2264594, 2070204, 1364041, 595624, 2832804, 687111, 1212468, 304469, 196974, 2536009, 1252842, 185451, 2692456, 2589502, 2807353, 26434, 1074505, 1445638, 806250, 2329983, 902023, 1549272, 1554765, 560401, 848917, 1876529, 2584512, 144865, 1265041, 2527634, 2808181, 1256552, 1769058, 464711, 1772632, 1754528, 1457537, 2087840, 1077198, 190401, 3036907, 2369562, 3027203, 2891750, 2058539, 963537, 1134865, 1700916, 245262, 100669, 1648846, 800023, 1750306, 1538626, 2181884, 372099, 1447669, 3030662, 2619887, 2632317, 1421882, 1850572, 284287, 274538, 1984593, 1119065, 269932, 680575, 858686, 953915, 1770409, 1982401, 828177, 1244508, 24910, 478934, 2535513, 2367331, 49759, 1053216, 2237251, 893382, 2232644, 1563092, 1975561, 898665, 1394285}

Returns: 2
{667, 1661, 1648, 1102, 706, 1834, 16, 224, 43, 637, 1622, 100, 1248, 448, 1686, 1682, 1730, 1074, 1771, 1254, 7, 72, 1786, 1136, 1205, 101, 786, 1829, 1563, 951, 392, 184, 568, 1383, 1303, 1817, 810, 1045, 713, 78, 1816, 134, 623, 1232, 1463, 638, 107, 1250, 905, 950, 834, 1493, 1476, 682, 1474, 185, 519, 1747, 1827, 862, 765, 202, 1451, 773, 774, 362, 606, 62, 63, 1178, 1385, 1182, 1664, 1816, 392, 259, 1150, 457, 177, 16, 867, 876, 853, 1449, 867, 1185, 1503, 262, 316, 1584, 1478, 1516, 1519, 1746, 770, 1104, 1314, 1857, 943, 538, 1312, 1690, 1314, 303, 154, 82, 1209, 495, 1666, 1498, 1204, 263, 145, 1860, 36, 281, 252, 1062, 1598, 261, 1254, 1750, 599, 1168, 1235, 1804, 857, 1122, 1527, 1000, 1255, 1749, 1190, 1784, 49, 343, 1602, 1649, 1225, 1110, 1185, 1687, 1298, 1484, 299, 474, 1738, 241, 311, 1835, 1860}

Returns: 12
{481831638, 433208515, 349179942, 263094725, 247295541, 442434100, 458451030, 324818534, 166008221, 219966633, 404714065, 497108868, 514205569, 241435672, 325111302, 98505939, 6868358, 229752266, 434108905, 423086717, 501597339, 468257502, 261646843, 262871318, 393014492, 219063960, 184405779, 201294411, 298352614, 162075686, 429345162, 481756520, 164980225, 211781051, 446778616, 444402717, 202115899, 19089406, 334867296, 409636065, 282579800, 144270326, 76043868, 250915746, 210657936, 54407803, 448739629, 473518261, 413980157, 354070770, 57791112, 318264413, 18225247, 197444899, 503509997, 342794071, 440622224, 478295466, 182643778, 356398555, 363852488, 306939248, 403398866, 79184473, 588398, 139792312, 188571748, 85895726, 333287032, 461303227, 21354180, 427828416, 432268727, 221361493, 258195814, 385042175, 173666798, 79198177, 142628572, 506310913, 137522190, 177578345, 219444166, 352837544, 59881072, 110326959, 484465616, 520098100, 514846492, 359158575, 501826449, 94812377, 333632669, 472025371, 123756854, 494900638, 151481651, 356629467, 131907385, 247314823, 373379665, 411257393, 283339140, 183034448, 496050628, 83790888, 508450444, 283434317, 193782368, 59871248, 481428112, 78641885, 494522755, 95411158, 303126280, 496662919, 122139250, 289856119, 453641649, 306776297, 420624666, 283191765, 446409613, 416547806, 172010016, 342987765, 424993378, 343156803, 290889991, 110566427, 424556574, 341918689, 133773590, 509176783, 21904841, 196220148}

Returns: 1
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Returns: 5
{2482631, 248995, 318436, 1073994, 1917742, 2114206, 923827, 2151343, 2143550, 2035676, 1188636, 1335944, 1830487, 2165391, 1043536, 2558289, 2853601, 2946102, 2694250, 1378245, 2392424, 2659332, 879672, 2397345, 744359, 794419, 1003596, 3161063, 174096, 123233, 2914593, 2550574, 2137266, 2540486, 1092774, 3086623, 2554593, 1236049, 832809, 1439910, 2482734, 2536195, 2642173, 2345494, 1412319, 2115450, 729026, 3134507, 1374810, 1563221, 775127, 659321, 2771435, 3049703, 2069602, 316810, 147588, 1639471, 1947069, 2912943, 1887673, 1234271, 2607160, 394028, 2681928, 2919881, 2064930, 2631512, 1134472, 1399994, 1183939, 2916296, 910134, 2933193, 1793005, 316575, 1071356, 2566495, 1604548, 1357116, 1928160, 1224457, 675592, 1015250, 764981, 1521142, 965653, 1296000, 152128, 908464, 2895608, 2410228, 1986694, 103407, 1491295, 38715, 2643876, 1192808, 1148578, 2318985, 1743983, 3177825, 2221265, 990143, 1904655, 1905275, 221901, 346931, 3024206, 545806, 3078774, 1687779, 1859082, 785144, 1039680, 192547, 1684961, 2821518, 1896481, 2232102, 2197274, 418240, 2339957, 111131, 2283884, 1880516, 2266880, 2036296, 2470140, 676328, 664930, 3176909, 999848, 1155997, 2816350, 1335910, 812281, 2337317, 2832241}

Returns: 2
{30855253, 17138416, 22616379, 35238946, 7820051, 14821355, 51079308, 17061389, 15166206, 2193560, 9254097, 16410719, 46235878, 49453818, 47823998, 30058082, 49383320, 47931566, 5688898, 21751155, 48879149, 36750673, 49537130, 43369946, 43999752, 14499602, 21710724, 42061740, 6313789, 17464804, 34797224, 10541133, 18655567, 24215850, 9363239, 50230990, 11047978, 5283747, 12365337, 3744300, 51888231, 34168463, 12049833, 40524297, 43409281, 37277949, 41065531, 41194484, 6890273, 19199566, 2816586, 21512701, 12446722, 5800009, 30174656, 18508287, 6619335, 20028269, 13110150, 39773371, 50603077, 50593435, 33214514, 41876151, 48453429, 9663366, 51776868, 9144158, 16327280, 47761823, 36132522, 16137901, 40840537, 20970352, 17236604, 45168943, 49617182, 30491950, 1764340, 20740863, 12649775, 50013959, 1706847, 28908713, 11695718, 18032861, 46916109, 32676251, 12663160, 30099550, 862573, 24799092, 42684449, 16600095, 26939626, 34041044, 12016917, 11836355, 12013101, 40467591, 3367924, 14437596, 21149659, 40934942, 27017461, 43985357, 20125045, 49177448, 17960535, 41995867, 6230125, 20318490, 15440191, 2917641, 37624966, 31626114, 20538149, 15833725, 19849857, 30633703, 12021111, 11865594, 37193422, 20317957, 30880327, 19404822, 19557852, 41064871, 49746999, 3475036, 20580488, 2545849, 44244303, 4602120, 40972315, 40220814, 26822641, 38072960, 33967005, 28520367, 9822394, 25396114, 25808378, 44163255, 36429136, 15045362, 35572503, 37596771, 27753495, 46421260, 29861152, 36223170, 12240731, 16945319, 26885546, 21496424, 22493363, 8364548, 25373036, 29219797, 9432471, 6024866, 49298977}

Returns: 2
{464, 33690, 71045, 3328, 44180, 51986, 69656, 39699, 93451, 25955, 33240, 8870, 88954, 6636, 31839, 22888, 80005, 46214, 45386, 10958, 89708, 65429, 34197, 36780, 78320, 48236, 26788, 6285, 34138, 63865, 30511, 87100, 14335, 69226, 40064, 24194, 52008, 36855, 77560, 93432, 26427, 69213, 36735, 21030, 21162, 41957, 20085, 36468, 63188, 12939, 37447, 90980, 34263, 19793, 51255, 88403, 28751, 29073, 23346, 11303, 38020, 67743, 19104, 60966, 38693, 4139, 13971, 89089, 72734, 28951, 27175, 13934, 25814, 65457, 50235, 39641, 93927, 33469, 1596, 43964, 47236, 55047, 12674, 11527, 43200, 34087, 69903, 30375, 76157, 94291, 90452, 18054, 32237, 88269, 65179, 72203, 91497, 82856, 26299, 4472, 21983, 3107, 74627, 41123, 29825, 89925, 48076, 30025, 32071, 64047, 48561, 26448, 55663, 24437, 60766, 78061, 80598, 29160, 4661, 53307, 61097, 30387, 55514, 2384, 55413, 81031, 67195, 8643, 64305, 25345, 51229, 24579, 94961, 270, 31403, 64520, 68131, 1539, 72159, 38743, 62831, 41189, 40161, 80095, 91744, 87153, 68035, 92988, 90755, 82160, 66171, 49222, 81881, 29155, 88367}

Returns: 4
{32194, 38530, 28904, 32663, 26210, 35639, 26355, 9172, 27434, 23412, 848, 45639, 34352, 22260, 35766, 7016, 39955, 23715, 33417, 25285, 17169, 10021, 3461, 14098, 3461, 36900, 17153, 45110, 16945, 11551, 24529, 40202, 24485, 15138, 37388, 37934, 36290, 8736, 15456, 6954, 8806, 23558, 3368, 9511, 11443, 25568, 45448, 43540, 17733, 34225, 4120, 40869, 34888, 10091, 15787, 21116, 29785, 33975, 46474, 17215, 6174, 22981, 16814, 620, 41372, 36250, 18293, 34963, 17539, 30470, 34377, 40195, 30605, 9867, 23822, 8844, 43979, 13627, 1292, 6438, 3549, 25194, 32368, 13503, 43050, 44211, 34658, 44033, 37744, 10344, 41438, 45914, 24099, 3805, 36553, 11912, 36040, 15622, 31558, 31422, 27979, 3738, 46036, 32580, 45447, 46063}

Returns: 3
{66820, 28838, 50902, 97202, 59782, 17790, 83886, 22257, 22520, 25967, 105432, 43585, 246, 77596, 68595, 96457, 26214, 71884, 58698, 21441, 38221, 68383, 84156, 56951, 85811, 61912, 72665, 57155, 89990, 2814, 21864, 76349, 56128, 52281, 4231, 73078, 6477, 7942, 79417, 90420, 13350, 27204, 63190, 24680, 104692, 72288, 4202, 103478, 69946, 100882, 15750, 2166, 43486, 33920, 62863, 36471, 12919, 99311, 96826, 86406, 15336, 47029, 63348, 1187, 36498, 74901, 60309, 58460, 24332, 16158, 33912, 48322, 61060, 7066, 64488, 90737, 4296, 55819, 84087, 10737, 90303, 99648, 91637, 27531, 48589, 25713, 30208, 94902, 76724, 18771, 26993, 64942, 67377, 97610, 13981, 38090, 100989, 79420, 83593, 96872, 89836, 70831, 99584, 13034, 103983, 64227, 25450, 4954, 19689, 96502, 66350, 99106, 33881, 19420, 36766, 48893, 19250, 43609, 104203, 87084, 69708, 48537, 16657, 18794, 56132, 53312, 74816, 106074, 41631, 88893, 23568, 79287, 107031, 101867, 49165, 2484, 13712, 55638, 97677, 21863, 89456, 8522, 13212, 17020, 13535, 103907, 10020, 105272, 28569, 3757, 23713, 107689, 50688, 12650, 8397, 106740, 73193, 63115, 98103, 2288, 16083, 22655, 43747, 87803, 96239, 17158, 92021, 17248, 36534, 29379, 18177, 6742, 50836, 20810, 54938, 105843, 72583, 3827, 9519, 31994, 88700, 91177, 66044, 55923, 66631, 82301, 78501, 8298}

Returns: 3
{748033, 558654, 394925, 92742, 640860, 93414, 371744, 124056, 1097767, 652795, 645418, 916324, 1504474, 713537, 98784, 770871, 1361869, 1261030, 527743, 1336328, 383904, 1091082, 1316257, 342949, 399538, 1298573, 50570, 1116760, 976571, 482315, 544441, 875715, 1007010, 11236, 1374282, 109525, 715428, 1294513, 853515, 194613, 159054, 1303029, 717034, 437712, 544632, 717264, 1453779, 253140, 1305486, 318766, 1249037, 945053, 794016, 1219220, 704573, 424081, 540599, 575363, 1410093, 959677, 524218, 1011246, 372006, 1204269, 858363, 814640, 415841, 73821, 678584, 93256, 493360, 141379, 244279, 574162, 502176, 1011083, 925300, 293202, 1298764, 201325, 1470339, 17344, 1230266, 698612, 594857, 1196023, 83982, 555363, 784963, 781431, 765592, 331406, 184419, 539128, 188391, 1011856, 1124475, 1061134, 979138, 1399028, 714571, 1269589, 811805, 341611, 618719, 253059, 933910, 887442, 1225565, 1417337, 555561, 522585, 1512553, 505430, 96689, 328937, 69824, 639560, 1356405, 879701, 1037410, 519110, 444538, 118282, 1454244, 571388, 1216175, 1219611, 445985, 1080652, 80576, 674438, 574567, 279535, 872913, 251392, 242202, 478733, 1112139, 376027, 1461590, 1523040, 1280280, 380665, 1264319, 233426, 820873, 679125, 562658, 14684, 1445538, 1451158, 1049396, 1121985, 572504, 1510579, 370860, 1070042, 17933, 1321135, 1080335, 1233768, 644552, 1203656, 623916, 1407907, 859213, 1207725, 1224236, 785564, 693370, 512479, 590595, 448742, 1427666, 1447412, 706479, 845963, 1465547, 779962, 1436578, 1550450, 443779, 286749, 744206, 1077760, 60792, 973628, 310669, 1144930, 737801, 829757, 187599, 180474, 154589, 1164189, 880115, 1057562, 323196}

Returns: 2
{14846, 2272, 6999, 12008, 12546, 6310, 16308, 2310, 20578, 18270, 16271, 6505, 1842, 657, 10589, 18421, 6378, 12472, 416, 4541, 18222, 12879, 12050, 7600, 3565, 8188, 6540, 12672, 8444, 19304, 15105, 12985, 13795, 15850, 1131, 5433, 5085, 6350, 11645, 19524, 17442, 11497, 4834, 1546, 21164, 1193, 4175, 20767, 6028, 5885, 1653, 390, 11708, 6910, 763, 16589, 4368, 999, 11256, 8289, 9895, 13579, 4693, 14671, 14539, 5283, 21752, 5239, 17381, 13973, 431, 4211, 5950, 16125, 4152, 13666, 12131, 822, 281, 19072, 15035, 6679, 9919, 5500, 9148, 16922, 10027, 21528, 20015, 13612, 6027, 10525, 3316, 19173, 12064, 18137, 21582, 7301, 6903, 20191, 14992, 14546, 6134, 7394, 21397, 9009, 788, 20689, 3138, 12945, 1572, 11939, 18609, 20744, 2011, 14352, 1277, 3484, 8381, 11187, 21591, 6913, 12043, 331, 11349, 7265, 6923, 6417, 6076, 11064, 7689, 12720, 1964, 21763, 3801, 4234, 19989, 16656, 20321, 13735, 10695, 11915, 14702, 15926, 15125, 16254, 19428, 5544, 1192, 13665, 19427, 16635, 17886, 15226, 10569, 12144, 14195, 5586, 17036, 21259, 18151, 17517, 7514, 16269, 13478, 1522, 11517, 9972, 20457, 8066, 15379, 8016, 6687, 3012, 16339, 21711, 12359, 19027, 7115, 16315, 774, 10507, 8146, 6345, 10830}

Returns: 5
{4672700, 105978141, 190155253, 10896414, 136956086, 156461373, 89747406, 149070602, 145611117, 87818261, 92763587, 169991952, 137141452, 123347771, 167571757, 9386392, 155142984, 159840226, 49566721, 25368904, 55566089, 16960102, 67224762, 154823358, 71438052, 102657696, 157447230, 179559925, 7486939, 26319842, 139871454, 136354346, 184394852, 97596126, 193897547, 112053992, 70034538, 94834449, 71824385, 185677053, 39236519, 133448295, 146815906, 179690707, 169946392, 34191834, 164284390, 164297092, 144589605, 40886126, 83070365, 75911553, 12416889, 162657905, 116793853, 97812920, 146533114, 165618382, 104086440, 189167547, 167437322, 153076650, 169404086, 180762096, 118123187, 148004948, 167700396, 193622117, 224056, 69716429, 76022628, 128875807, 68309654, 150888002, 176313765, 103335247, 42671528, 52555010, 106171813, 110041742, 191659327, 171580009, 125822184, 15449912, 78693568, 132945767, 25886227, 140404284, 168681468, 80660759, 191025845, 98248492, 138871633, 148637520, 65985014, 22859605, 155024323, 18801631, 8531216, 34505555, 71412146, 187956603, 84811606, 109416909, 23962314, 57970643, 166708173, 151598622, 76891729, 54090916, 91165973, 27096006, 144801445, 57836758, 129607532, 49312132, 18690070, 132147984, 13459908, 54357948, 16818770, 97017825, 9462301, 118318160, 17991297, 193715100, 186500481, 150458715, 17037218, 129197449, 193956284, 56846644, 42911481, 17520196, 45881140, 17830849, 51322238, 56636319, 49415345, 154530097, 176969860, 57791049, 106086407, 148510091, 126020730, 108193254, 10258836, 144838167, 45545717, 52420432, 150555441, 163691015, 14326934, 179898928, 91391660, 24865370, 72646572, 135878463, 124067234, 119173332, 109147664, 60430870, 130383019, 56015643, 69613487, 167051259, 137190463, 45779496, 176770675, 104038067, 81358132, 154695256, 167419006, 46580681, 193490896, 155536315, 43015658, 82633996, 8340657, 11327441, 144659029, 145016826, 172833822, 190324458, 51192841, 53137699, 158028232, 22152924, 172455075, 117141296, 149610151, 59144450, 148638272}

Returns: 1
{16428847, 31455636, 29340867, 5952232, 34573953, 35314100, 3509713, 41434838, 40457003, 11266061, 25691693, 19319032, 23032394, 20145939, 26843529, 33310441, 5951213, 19939705, 19091950, 20747166, 33077329, 40190970, 37926011, 8019361, 21465674, 35105981, 22057118, 23062886, 29913553, 13470727, 2717343, 40910118, 290404, 1662221, 33104567, 34144956, 31144235, 37174979, 19395715, 28603189, 22429457, 42614500, 8730017, 43340529, 4604370, 6836820, 24673456, 14249464, 18722534, 32570493, 19335348, 40301307, 24662995, 21177272, 14067662, 12618350, 14386033, 12556210, 10954161, 13974606, 32237325, 24913858, 40002695, 20387404, 10571249, 26860734, 21462156, 39436883, 25702992, 7725412, 7926662, 28240142, 471732, 1628902, 13402787, 26095408, 11458945, 32412875, 8248884, 2608996, 15918557, 1356831, 14030096, 5242184, 28594275, 27595591, 13339611, 14843627, 38905098, 9224024, 31770782, 37630260, 30155839, 5197124, 10711329, 20806694, 5280489, 29029142, 39176029, 26951926}

Returns: 1
{9697387, 14673995, 23741146, 34767763, 24871578, 17152613, 5189279, 9362659, 36682678, 44826330, 5484319, 16740275, 40407254, 20534153, 24638924, 30759124, 42431298, 11014200, 43341113, 34028762, 29642916, 40687976, 29280843, 6595159, 10752992, 36998451, 2675995, 9820266, 31969347, 39892387, 20778207, 41048943, 27349463, 31049899, 34011213, 27506398, 44318755, 35051708, 34015333, 27792115, 33657660, 15441978, 34063169, 18086616, 11778393, 28589320, 40496224, 7511465, 7888939, 21098465, 25292031, 12674756, 14998945, 26748720, 2795422, 9984408, 4411109, 40883281, 12085097, 24774421, 23692863, 43686312, 28891510, 18883232, 40403014, 3981808, 30405467, 29165359, 1545143, 37095711, 2442137, 1056932, 3422709, 40680293, 7914671, 2727137, 6980477, 36626528, 7509392, 36006029, 16355343, 963097, 36405775, 9624308, 20243142, 33948096, 32152446, 188689, 5528881, 33606750, 40178196, 36537055, 41561882, 38493173, 17818475, 31840803, 12483055, 14452210, 14659349, 22352685, 5679258, 45049801, 39973421, 39118566, 33427745, 7430204, 1362513, 31299871, 29852641, 1876945, 2822527, 33519715, 30833563, 13893161, 7864841, 38913696, 26924542, 21729759, 28487192, 24205133, 10681149, 19716003, 27799041, 45037166, 32422690, 38158773, 16646744, 19864170, 30516509, 22474998, 25860366, 35397922, 20956314, 29121364, 41107182, 22106094}

Returns: 1
{253, 629, 368, 228, 122, 314, 83, 496, 335, 102, 333, 4, 407, 206, 540, 280, 553, 253, 143, 656, 34, 60, 316, 130, 624, 512, 535, 307, 102, 509, 442, 200, 429, 116, 373, 642, 401, 475, 190, 285, 293, 35, 604, 595, 295, 249, 34, 299, 349, 25, 503, 584, 394, 284, 659, 431, 618, 181, 114, 607, 6, 396, 665, 550, 571, 383, 93, 570, 206, 581, 451, 522, 553, 542, 159, 249, 618, 361, 559, 490, 655, 409, 382, 433, 296, 405, 173, 186, 211, 510, 366, 555, 634, 263, 431, 368, 390, 270, 172, 405, 56, 610, 46, 396, 552, 452, 333, 38, 283, 393, 398, 232, 397, 232, 380, 26, 128, 301, 127, 549, 632, 118, 423, 642, 663, 407, 264, 379, 392, 373, 54, 352, 438, 173, 514, 167, 429, 29, 259, 265, 355, 61, 578, 498, 241, 631, 104, 320, 574, 74, 439, 499, 565, 541, 390, 362}

Returns: 23
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Returns: 3
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Returns: 2
{927, 690, 1082, 1020, 756, 268, 249, 490, 279, 105, 154, 481, 518, 268, 271, 493, 234, 749, 664, 812, 844, 828, 825, 414, 499, 822, 847, 538, 287, 844, 359, 998, 476, 357, 902, 51, 284, 44, 73, 107, 387, 642, 363, 735, 818, 699, 430, 230, 878, 708, 325, 183, 642, 780, 210, 1037, 402, 215, 631, 559, 1101, 337, 707, 610, 549, 772, 11, 569, 28, 614, 836, 300, 562, 190, 676, 868, 922, 990, 1088, 676, 261, 709, 207, 241, 374, 699, 599, 803, 150, 246, 63, 975, 1075, 980, 755, 1118, 316, 349, 802, 673, 380, 825, 1093, 420, 505, 6, 926, 420, 183, 1120, 665, 135}

Returns: 12
{236, 522, 104, 496, 388, 569, 135, 354, 313, 11, 534, 336, 437, 490, 157, 26, 118, 292, 269, 551, 541, 73, 54, 388, 78, 127, 55, 553, 104, 318, 117, 457, 491, 329, 216, 466, 343, 245, 175, 354, 63, 118, 161, 14, 82, 272, 584, 476, 244, 493, 311, 531, 447, 156, 293, 327, 441, 265, 70, 478, 369, 182, 372, 55, 372, 521, 221, 59, 22, 7, 239, 519, 313, 280, 108, 22, 208, 542, 468, 242, 243, 396, 431, 367, 359, 541, 287, 460, 261, 317, 260, 183, 307, 238, 555, 531, 47, 282, 156, 561, 524, 330, 42, 458, 86, 10, 577, 68, 297, 248, 212, 239, 117, 88, 345, 184, 525, 531, 282, 168, 274, 429, 88, 404, 431, 302, 110, 78, 26, 205, 567, 185, 521, 501, 368, 576, 362, 332, 444, 2, 263, 63, 348, 34, 42, 106, 422, 311, 512, 419, 405, 397, 261, 566, 290, 159, 302, 234, 247, 404, 371, 472, 474, 462, 474, 328, 205, 329, 19, 323, 47, 515, 282, 93}

Returns: 24
{150440361, 126579878, 127459469, 134960105, 145976050, 68472218, 100704307, 120611543, 94861425, 177327522, 147516503, 148231144, 19690984, 168081750, 98642065, 107036335, 230999002, 230810179, 72613976, 25676190, 150870267, 201827923, 146211259, 166464750, 119727540, 36181055, 158393695, 126323171, 41744129, 186438388, 174192302, 208422836, 149369469, 94520899, 13457494, 78597837, 132190572, 233867200, 132037124, 43210200, 203580759, 155895572, 36012684, 126200569, 195546197, 204387709, 9572408, 65086495, 142629248, 199520269, 105369055, 160933395, 205485684, 76293669, 72742778, 11823943, 120165391, 13861177, 75004179, 224231409, 27560350, 211167528, 145760850, 42867098, 180596513, 164860356, 148663788, 6024310, 92106262, 122537368, 122822978, 54994897, 119980223, 10609439, 110621218, 115395588, 5634932, 72400142, 61820193, 91275616, 84290690, 42306362, 161882718, 131133209, 141378352, 113352594, 155762851, 181880664, 80207526, 86245181, 162820983, 93381761, 218491613, 140320584, 157411606, 11978811, 129574239, 132657005, 76008493, 19625091, 231093763, 172209418, 119546229, 43487317, 54485825, 69557930, 15334199, 135880079, 138237802, 93253292, 93520378, 81717569}

Returns: 2
{2568, 1125, 4792, 3288, 1327, 3139, 3499, 4428, 3979, 1831, 2516, 799, 1305, 2595, 915, 3648, 2157, 1256, 5690, 2170, 2096, 4957, 831, 3527, 2627, 1508, 616, 1900, 1030, 1304, 1882, 261, 4297, 38, 2704, 4719, 457, 1061, 719, 2241, 254, 5175, 441, 2993, 54, 4732, 2190, 2404, 31, 1422, 3763, 1717, 1966, 2587, 3151, 2534, 996, 852, 654, 3691, 97, 1443, 2400, 1531, 693, 5491, 4787, 4469, 2767, 666, 5773, 4027, 3626, 2023, 4021, 2135, 4520, 4774, 2628, 2514, 342, 238, 3144, 2641, 1557, 4717, 1365, 1345, 4741, 1003, 3349, 3983, 1384, 806, 678, 809, 4366, 4780, 5326, 3603, 2846, 180, 4294, 2301, 4684, 4499, 4222, 4571, 1497, 4088, 123, 3778, 559, 5301, 2003, 2207, 921, 2996, 2793, 5576, 2363, 5261}

Returns: 6
{8359896, 4087435, 561949, 229772, 8142347, 7337746, 1392809, 441688, 2797576, 7024741, 9419371, 4864140, 956222, 4693917, 4204785, 996913, 4258474, 2069912, 1770309, 8823168, 4587670, 7381904, 2938648, 9426242, 3061821, 2717041, 7778369, 1377229, 8646299, 810857, 8542064, 5988720, 6466278, 855908, 1926712, 9233294, 6292125, 5085055, 9472157, 8140561, 5360338, 1342138, 4292585, 6158631, 2897443, 1502997, 5277300, 4523949, 3086315, 9765056, 7449076, 507785, 6847358, 6787341, 7134432, 8207333, 8983046, 6892520, 8366448, 3562035, 8543638, 7310396, 567179, 7125415, 3567757, 19292, 6450587, 7553786, 4965710, 4662171, 5941508, 2836613, 1223121, 4826065, 1664737, 4876806, 7055571, 1017540, 8132305, 2045496, 8686410, 7026184, 609711, 409287, 2639658, 3573038, 1950029, 2754312, 9159870, 6700758, 1822398, 5685885, 282048, 3979975, 3227706, 7875403, 2746151, 8038709, 3106664, 4309906, 907638, 662670, 3101423, 9181048, 2781868, 2663552, 8677500, 3335289, 2777429, 8469989, 7909039, 2428486, 6955930, 3298845, 9260119, 3892783, 9047425, 2161341, 8799731, 3758863, 4626953, 2222620, 2185214, 3398798, 8901897, 6032526, 7496008, 723382, 1694740, 5533400, 4765060, 899421, 1154673, 7626893, 5929806, 3502702, 7452854, 9164035, 3450735, 3147563, 10127918, 8500017, 2625840, 8559529, 4334947, 8796080, 9740342, 2035605, 5516199, 3630995, 4809225, 5179131, 9992372, 1275890, 488132, 5330528, 6367800, 402551, 2248391, 7155048, 2968564, 1481357, 7559655, 6205344, 1785672, 8548620, 10145976, 4630968, 4003927, 5895404, 317964, 10084440, 2629004, 5508381, 8753727, 8653136, 7095283, 9777240, 2757133, 497167, 3227202, 766850, 8154013, 2282596, 7883259, 1515567, 118359, 9931139, 848730, 1700320, 7757871, 5092098, 2006093, 6843628, 8803749, 9531966, 3869764, 647880, 7091117, 1602970}

Returns: 2
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Returns: 6
{15572862, 8573196, 7941590, 12261601, 15396734, 6858612, 1915695, 12711741, 2436141, 16725946, 12990482, 7099085, 20822131, 1576013, 20224625, 22178400, 10180019, 3838951, 7499897, 888665, 14340323, 7271297, 7372196, 6847059, 17101052, 18533394, 7145867, 23067879, 2804904, 2742216, 6563092, 2673797, 2178661, 12525658, 22976222, 9716140, 9571369, 14710640, 18849509, 23220528, 5325697, 18410950, 12851718, 15641417, 12083966, 23633620, 14836021, 439058, 11824703, 8916764, 18683093, 16117020, 23110813, 2182842, 11490854, 16471894, 8780984, 21002741, 22136838, 20446331, 8842922, 16127058, 23870069, 17518343, 23817724, 13656239, 22162145, 19425644, 9682464, 19444267, 1749052, 15638750, 11656857, 12654055, 21363134, 18988198, 22217788, 455910, 13787874, 19938217, 18971602, 16413878, 2245562, 9685613, 11464314, 17703680, 6276527, 22934784, 6336020, 10051088, 13147018, 3369597, 3723334, 4391973, 11685977, 23208621, 11227891, 11274302, 22797155, 6188991, 6330447, 20942466, 100999, 1965384, 3607992, 20611594, 3334240, 22781641, 15321309, 19121699, 400774, 3062548}

Returns: 1
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Returns: 6
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Returns: 2
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Returns: 1
{525, 549, 549, 420, 549, 470, 549, 70, 595, 545, 549, 586, 355, 539, 519, 549, 33, 102, 183, 353, 423, 282, 234, 481, 30, 517, 549, 453, 140, 568, 549, 421, 348, 299, 131, 549, 549, 343, 127, 126, 183, 284, 549, 549, 433, 176, 348, 549, 549, 272, 549, 549, 549, 341, 579, 247, 549, 52, 423, 540, 299, 408, 341, 549, 549, 61, 416, 549, 599, 549, 262, 549, 348, 165, 549, 100, 462, 549, 549, 563, 328, 399, 383, 71, 558, 590, 549, 549, 359, 549, 549, 549, 549, 387, 375, 549, 346, 541, 549, 582, 549, 549, 96, 421, 324, 341, 549, 549, 184, 258, 549, 586, 568, 253, 337, 592, 336, 549, 539, 549, 389, 72, 549, 549, 31, 465, 27, 137, 166, 558, 324, 549, 294, 549, 355, 261, 22, 549, 148, 251, 345, 549, 178, 549, 524, 549, 131, 549, 186, 84, 148, 107, 21, 72, 65, 168, 481, 549}

Returns: 56
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Returns: 131
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Returns: 69
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Returns: 105
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Returns: 16
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Returns: 37
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Returns: 66
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Returns: 49
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Returns: 187
{13, 21, 6, 18, 18, 21, 3, 21, 12, 21, 2, 8, 18, 21, 2, 1, 17, 21, 21, 21, 17, 21, 12, 21, 11, 3, 21, 17, 15, 21, 2, 11, 19, 20, 21, 1, 21, 15, 27, 21, 21, 15, 9, 21, 18, 8, 21, 21, 21, 15, 20, 21, 29, 20, 16, 21, 21, 21, 21, 16, 15, 21, 21, 1, 19, 2, 15, 2, 21, 21, 12, 1, 10, 15, 20, 1, 10, 20, 8, 21, 22, 21, 21, 5, 2, 21, 20, 3, 14, 21, 6, 21, 6, 21, 13, 3, 15, 21, 2, 21, 18, 17, 1, 7, 2, 21, 21, 21, 22, 3, 21, 21, 20, 21, 4, 3, 19, 2, 17, 21, 21, 21, 18, 21, 10, 21, 19, 21, 1, 21, 3, 22, 6, 9, 24, 19, 3, 22, 21, 21, 5, 18, 21, 21, 12, 13, 30, 9, 19, 21, 4, 9, 17, 21, 22, 21, 19, 4, 21, 18, 4, 21, 9, 6, 13, 21, 29, 21, 21, 2, 20, 11, 29, 17, 21, 3, 21, 16, 21, 21, 29}

Returns: 111
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Returns: 53
{337629, 181930, 337629, 273155, 100972, 337629, 337629, 337629, 337629, 56621, 132672, 337629, 337629, 309996, 337629, 337629, 337629, 337629, 83713, 337629, 193594, 337629, 313642, 295977, 112520, 44994, 333844, 240400, 337629, 51099, 337629, 337629, 337629, 3785, 337629, 217082, 337629, 337629, 236657, 337629, 337629, 337629, 337629, 73289, 337629, 33101, 337629, 189050, 316814, 226999, 337629, 337629, 257640, 337629, 337629, 337629, 337629, 337629, 337629, 337629, 59052, 337629, 337629, 337629, 355814, 337629, 337629, 337629, 77300, 337629, 337629, 337629, 337629, 120547, 236104, 41652, 337629, 337629, 286530, 337629, 337629, 337629, 337629, 148579, 96830, 335385, 144035, 64474, 337629, 337629, 337629, 337629, 309473, 55215, 337629, 337629, 240799, 337629, 337629, 211875, 337629, 133622, 337629, 337629, 155699, 134091, 337629, 337629, 337629, 79989, 2244, 337629, 337629, 337629, 225109, 337629, 337629, 281008, 337629, 337629, 337629, 337629, 337629, 337629, 337629, 337629, 337629, 337629, 337629, 337629, 337629, 304528, 285933, 278577, 337629, 292635, 337629, 337629, 337629, 253916, 159111, 125754, 232205, 27633, 337629, 337629, 204007, 337629, 337629, 282414, 98811, 101525, 337629, 337629, 337629, 178518, 51696, 337629, 337629, 297187, 337629, 337629, 337629, 337629, 337629, 238818, 337629, 337629, 23987, 203538, 40442, 337629, 264340, 337629}

Returns: 136
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Returns: 81
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Returns: 7
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Returns: 11
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Returns: 85
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Returns: 71
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Returns: 101
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Returns: 110
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Returns: 20
{51, 166, 164, 93, 9, 164, 74, 164, 164, 164, 164, 102, 106, 45, 91, 164, 164, 164, 164, 34, 164, 109, 99, 86, 174, 40, 164, 164, 164, 164, 122, 164, 164, 144, 141, 73, 90, 164, 67, 164, 7, 164, 128, 140, 61, 97, 164, 164, 15, 164, 164, 164, 164, 61, 164, 138, 130, 164, 164, 164, 94, 164, 164, 179, 164, 62, 60, 164, 164, 164, 162, 164, 147, 186, 168, 164, 164, 164, 60, 13, 164, 111, 164, 164, 131, 164, 164, 164, 30, 164, 155, 172, 164, 135, 146, 144, 160, 39, 157, 69, 164, 73, 140, 29, 164, 153, 39, 164, 164, 152, 164, 164, 164, 95, 164, 151, 1, 164, 164, 164, 164, 164, 127, 164, 164, 164, 116, 148, 70, 164, 164, 164, 164, 164, 43, 110, 164, 164, 164, 1, 23, 164, 164, 164, 164, 164, 3, 164, 80, 24, 164}

Returns: 92
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Returns: 54
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Returns: 57
{891, 1800, 1367, 70, 812, 2423, 1563, 404, 2594, 1599, 1415, 665, 471, 606, 2632, 1208, 2678, 1936, 1793, 2200, 1995, 367, 1450, 452, 1004, 2596, 1792, 872, 1665, 337, 1369, 1076, 324, 2271, 1961, 1534, 1493, 1956, 2291, 1833, 1073, 1235, 766, 2096, 1230, 1708, 564, 441, 933, 1708, 590, 2103, 2331, 1734, 2013, 720, 1630, 2661, 1739, 2482, 2098, 1499, 1499, 1926, 1756, 9, 1848, 815, 76, 1196, 1381, 2090, 2359, 1356, 255, 380, 1722, 2284, 1309, 1651, 1839, 2132, 606, 955, 2237, 2283, 2520, 1622, 385, 1521, 1163, 1091, 1719, 701, 1273, 468, 2074, 395, 1798, 1535, 2627, 1479, 2117, 1953, 824, 1710, 358, 501, 94, 2186, 1104, 859, 1968, 2364, 1441, 352, 2050, 2069, 1905, 2560, 732, 1527, 1258, 1890, 2188, 524, 1350, 1976, 322, 1948, 866, 2199, 661, 1094, 2008, 1595, 2198, 2383, 330, 1397, 698, 1522, 95, 1504, 443, 662, 1128, 2286, 1291, 1828, 762, 1983, 2030, 1830, 1789, 1316, 92, 1753, 2361, 1326, 486, 450, 349, 1057, 656, 1443, 744, 955, 975, 123, 2692, 1509, 478, 2370, 205, 1098, 356, 1865, 615, 803, 832, 2087, 1128, 1570, 1563}

Returns: 45
{56, 17, 96, 11, 77, 122, 2, 87, 26, 27, 144, 72, 107, 72, 149, 124, 92, 117, 87, 4, 144, 21, 110, 144, 93, 4, 139, 55, 10, 73, 120, 45, 135, 92, 48, 38, 101, 106, 102, 57, 43, 99, 143, 127, 117, 142, 10, 40, 37, 77, 65, 6, 2, 17, 30, 61, 114, 83, 72, 130, 50, 71, 142, 72, 72, 72, 99, 72, 72, 121, 83, 5, 69, 56, 22, 138, 72, 72, 14, 143, 20, 17, 56, 32, 144, 144, 127, 14, 72, 135, 2, 89, 47, 137, 51, 72, 34, 79, 104, 128, 72, 61, 57, 125, 123, 76, 85, 133, 11, 16, 133, 134, 87, 144, 86, 88, 59, 61, 144, 72, 67, 57, 21, 42, 71, 68, 1, 140, 37, 72, 142, 130, 52, 51, 9, 97, 123, 140, 72, 144, 67, 133, 75, 1, 127, 72, 40, 23, 144, 9, 104, 52, 89, 101, 56, 140, 134, 43, 55, 24, 94, 118, 83, 19, 88, 72, 45, 72, 4, 11, 88, 58, 93, 47, 72}

Returns: 88
{5, 14, 13, 3, 15, 12, 16, 14, 4, 13, 6, 3, 5, 12, 6, 13, 8, 9, 8, 3, 16, 13, 2, 5, 7, 14, 14, 2, 4, 9, 13, 13, 10, 5, 3, 1, 10, 13, 10, 7, 5, 15, 11, 12, 15, 5, 4, 1, 14, 11, 11, 12, 11, 13, 16, 12, 9, 3, 2, 5, 16, 1, 10, 15, 3, 14, 7, 12, 2, 8, 4, 15, 1, 10, 4, 16, 6, 10, 1, 9, 2, 15, 10, 3, 9, 3, 7, 8, 15, 14, 12, 11, 2, 5, 15, 1, 6, 2, 14, 2, 5, 4, 3, 5, 2, 1, 2, 2, 10, 3, 14, 15, 14, 9, 9, 4, 7, 14, 7, 8, 13, 6, 1, 15, 15, 12, 7, 1, 4, 8, 8, 14, 6, 15, 5, 2, 9, 14, 13, 13, 9, 16, 3, 1, 2, 3, 14, 3, 14, 15, 8, 2, 4, 13, 10, 7, 9, 14, 11, 14, 1, 9, 3, 5, 7, 12, 10, 2, 10, 4, 7, 7, 1, 16, 8, 2, 5, 8, 6, 6, 13, 14, 3, 10, 15, 8, 6, 7, 7, 5, 1, 4, 1, 4}

Returns: 90
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Returns: 40
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Returns: 46
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Returns: 42
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Returns: 60
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Returns: 155
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Returns: 75
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Returns: 86
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Returns: 3
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Returns: 127
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Returns: 51
{2751907, 804177, 1594554, 601053, 1796874, 2146705, 1265624, 629045, 2312658, 824705, 916679, 629075, 526728, 346429, 1121205, 1688564, 1254863, 1636892, 404511, 972706, 1196256, 910794, 913340, 1527212, 1286046, 2047783, 1884897, 1663717, 489617, 1817972, 230091, 1233300, 920949, 1766422, 971343, 2574511, 1922684, 372691, 689614, 1657832, 282366, 261853, 840444, 459188, 1650495, 2323119, 2574511, 1579749, 1945466, 2574511, 2574511, 1319648, 1309090, 2167651, 2152467, 933796, 2626718, 2574511, 1305928, 1198143, 1453306, 1134244, 331505, 441759, 1702446, 2427863, 918666, 1440267, 278075, 2574511, 2522666, 839463, 2465511, 1288465, 2574511, 1045863, 2464267, 1268583, 1246599, 651827, 1047299, 942901, 2243006, 146648, 1631610, 406860, 2331085, 1973458, 233672, 2088537, 854569, 857327, 2132752, 2574511, 885947, 808181, 2201820, 844434, 1717184, 110244, 1528648, 1749806, 1766330, 1603168, 2574511, 640274, 2030305, 1341211, 2574511, 2574511, 2292145, 1398095, 1308887, 994762, 1601084, 109011, 1535060, 537546, 2149696, 1655845, 2228082, 835408, 1945436, 777637, 2574511, 1734067, 2296436, 424815, 544206, 1696833, 427806, 1176416, 1932197, 485974, 1735048, 251392, 243426, 872065, 1739103, 1601805, 937619, 642314, 1640715, 1417279, 973427, 1327912, 60972, 663693, 924016, 422044, 1265421, 979957, 1246988, 1770334, 2574511, 1730077, 2036965, 2227839, 2115323, 2456690}

Returns: 74
{9971, 9971, 9971, 6309, 10097, 2932, 9971, 3426, 323, 9971, 2350, 9971, 4769, 221, 9258, 9971, 9971, 6738, 129, 6877, 9971, 4554, 9971, 10720, 321, 9468, 4973, 5286, 9971, 3234, 2263, 9971, 9971, 9773, 9971, 7286, 9971, 2035, 1760, 9971, 9971, 1810, 8487, 9971, 9971, 9971, 9971, 3277, 9139, 9971, 6718, 9971, 5202, 5811, 9971, 7525, 9971, 503, 3761, 9971, 9971, 9971, 7486, 3287, 9971, 8500, 9971, 674, 316, 1974, 9971, 9971, 5104, 9303, 7593, 869, 9971, 9971, 9971, 9971, 9971, 9537, 9971, 3476, 6694, 9971, 9971, 9971, 9971, 9971, 9971, 1884, 8578, 9971, 9971, 3430, 5428, 9664, 9971, 9829, 9971, 6737, 8545, 9971, 9971, 9971, 7755, 9971, 832, 242, 9971, 2685, 6844, 2446, 9971, 9971, 776, 5324, 9971, 5740, 6041, 9971, 7597, 6210, 9971, 9568, 403, 2374, 8759, 9971, 9971, 1979, 3253, 9971, 9971, 9971, 1613, 713, 770, 8130, 4798, 9971, 4647, 9971, 9569, 8211, 9971, 9971, 7708, 5954, 3570, 1827, 2121, 4543, 6891, 3593, 10937, 9596, 437, 9971, 142, 9971, 9971, 7850, 9648, 9459, 4867, 9971, 6684, 5417, 4160, 6299, 5173, 826, 9971, 6537, 1691, 9971, 2520, 9971, 9971, 9971, 8123, 9971, 9971, 3745, 334, 9971}

Returns: 103
{9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 9, 4, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 11, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 16, 9, 9, 6, 9, 9, 4, 8, 5, 5, 6, 7, 9, 9, 9, 9, 9, 9, 5, 9, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 3, 9, 9, 16, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 6, 10, 9, 9, 16, 9, 9, 9, 9, 9, 7, 9, 9, 9, 2, 8, 9, 9, 9, 9, 9, 9, 6, 9, 9, 9, 9, 9, 9, 9, 2, 9, 9, 9, 3, 9, 9, 9, 9, 9, 3, 9, 9}

Returns: 145
{10, 6, 3, 7, 17, 6, 3, 1, 2, 9, 9, 10, 10, 10, 16, 10, 3, 9, 6, 10, 3, 10, 16, 11, 10, 1, 18, 7, 9, 1, 10, 14, 5, 10, 8, 5, 10, 12, 8, 10, 10, 10, 2, 10, 3, 10, 7, 6, 4, 5, 10, 4, 7, 8, 2, 6, 10, 10, 4, 4, 5, 16, 10, 6, 10, 5, 3, 4, 6, 10, 7, 10, 1, 7, 9, 6, 2, 3, 10, 12, 10, 10, 6, 8, 7, 10, 2, 3, 1, 4, 1, 15, 10, 10, 6, 10, 10, 3, 9, 16, 6, 9, 3, 16, 4, 8, 3, 10, 7, 10, 13, 1, 3, 2, 3, 5, 16, 6, 10, 3, 1, 2, 1, 10, 4, 4, 10, 11, 6, 7, 3, 18, 11, 8, 1, 7, 10, 13, 17, 10, 4, 7, 6, 9, 10, 10, 8, 10, 10, 3, 7, 10, 4, 10, 4, 13, 4}

Returns: 87
{9, 2, 9, 11, 1, 9, 8, 4, 5, 13, 3, 12, 2, 4, 1, 2, 11, 3, 6, 7, 1, 10, 2, 13, 9, 13, 3, 3, 10, 2, 4, 4, 3, 4, 3, 5, 6, 3, 1, 13, 2, 4, 2, 8, 12, 5, 5, 12, 7, 10, 3, 1, 3, 3, 7, 1, 12, 5, 6, 4, 9, 7, 2, 2, 13, 1, 3, 13, 14, 11, 12, 2, 1, 9, 3, 3, 2, 5, 6, 3, 13, 4, 7, 3, 8, 11, 7, 4, 12, 11, 5, 2, 11, 4, 1, 10, 11, 5, 11, 3, 1, 9, 4, 10, 1, 10, 9, 10, 2, 4, 8, 2, 14, 6, 8, 5, 4, 8, 14, 6, 2, 2, 5, 5, 13, 14, 9, 7, 10, 8, 13, 14, 2, 3, 3, 7, 3, 5, 14, 13, 7, 5, 4, 13, 10, 4, 5, 13, 7, 10, 5, 12, 5, 11, 1, 8, 13, 8, 2, 3, 12, 3, 6, 6, 4, 12, 3, 1, 4, 8, 5, 7, 12, 1, 1, 3, 8, 11, 1, 11, 3, 14, 1, 4, 6, 4, 3, 3, 6, 2, 2, 1, 5, 6, 10}

Returns: 77
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Returns: 119
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Returns: 114
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Returns: 148
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Returns: 125
{18, 49, 9, 37, 8, 24, 41, 59, 63, 4, 42, 75, 40, 13, 34, 58, 63, 39, 35, 58, 21, 39, 38, 39, 18, 13, 6, 73, 63, 56, 9, 76, 33, 75, 63, 40, 3, 37, 67, 46, 63, 63, 63, 40, 50, 60, 61, 16, 54, 23, 18, 6, 10, 63, 63, 45, 28, 45, 49, 63, 47, 28, 45, 7, 20, 76, 45, 4, 53, 26, 36, 63, 56, 32, 24, 28, 37, 59, 57, 63, 63, 1, 3, 63, 40, 63, 61, 63, 63, 2, 60, 42, 18, 63, 39, 50, 63, 6, 30, 61, 21, 35, 76, 25, 57, 3, 28, 25, 9, 34, 63, 63, 7, 39, 62, 63, 64, 47, 63, 33, 2, 2, 43, 63, 2, 45, 59, 15, 21, 5, 69, 32, 63, 61, 35, 40, 60, 63, 21, 16, 45, 76, 48, 56, 63, 50, 14, 10, 72, 63, 63, 2, 64, 15, 21, 17, 32, 6, 23, 63, 49, 18, 45, 22, 63, 61, 8, 55, 5, 18, 1, 18, 18, 38, 2, 35, 47, 70, 63, 14, 16, 55, 69, 63, 76, 43}

Returns: 86
{300151614, 300151614, 216145476, 300151614, 300151614, 300151614, 15090811, 300151614, 247759304, 300151614, 71284073, 189626585, 300151614, 36927157, 300151614, 60242093, 300151614, 300151614, 300151614, 122823392, 142075821, 27316995, 300151614, 300151614, 244410298, 33175584, 300151614, 88187186, 300151614, 300151614, 300151614, 128657662, 315586942, 57633037, 11069119, 300151614, 7001190, 300151614, 300151614, 70150437, 241814170, 210884540, 184470931, 118352542, 300151614, 300151614, 300151614, 300151614, 300151614, 300151614, 282632794, 300151614, 300151614, 300151614, 274525257, 21241049, 268325940, 300151614, 95543230, 99494395, 300151614, 275060382, 101901706, 178352609, 300151614, 23465534, 300151614, 300151614, 300151614, 225573116, 300151614, 300151614, 166894827, 300151614, 169422062, 300151614, 300151614, 300151614, 300151614, 300151614, 300151614, 300151614, 298200258, 106441282, 300151614, 135193345, 300151614, 148635070, 300151614, 43145289, 300151614, 300151614, 300151614, 300151614, 259986944, 300151614, 300151614, 203374222, 210865415, 183210274, 284867679, 300151614, 7560337, 46232966, 300151614, 300151614, 300151614, 300151614, 300151614, 298874727, 300151614, 300151614, 300151614, 2595266, 239970182, 300151614, 300151614, 200432582, 314172154, 300151614, 300151614, 19133547, 302034036, 300151614, 300151614, 253792702, 300151614, 300151614, 36905306, 82290752, 300151614, 266794055, 277560866, 300151614, 300151614, 300151614, 300151614, 300151614, 300151614, 146551669, 300151614, 194641690, 101466190, 300151614, 12882643, 300151614, 19019537, 115141589, 300151614, 285847791, 300151614, 21147135, 210983871, 300151614, 300151614, 300151614, 232880979, 70616362, 300151614, 63509022, 77710715, 300151614, 300151614, 300151614, 80440269, 300151614, 281210974, 85777501, 300151614, 174380262, 137417451, 300151614, 300151614, 300151614, 146611512, 300151614, 61906930, 300151614, 300151614, 300151614, 300151614, 300151614, 300151614, 300151614, 297071949, 141875438, 300151614, 300151614, 261345531, 235815627, 300151614, 300151614, 30232700}

Returns: 108
{90, 87, 95, 6, 45, 302, 273, 302, 169, 2, 270, 37, 269, 140, 172, 107, 22, 242, 85, 97, 147, 212, 253, 271, 68, 72, 242, 172, 35, 214, 19, 137, 252, 187, 243, 189, 279, 265, 18, 174, 212, 294, 36, 172, 143, 225, 137, 121, 233, 232, 183, 134, 68, 109, 115, 230, 183, 59, 86, 189, 53, 91, 178, 266, 63, 271, 79, 176, 45, 37, 174, 5, 173, 92, 183, 52, 39, 264, 205, 199, 167, 15, 74, 239, 48, 85, 127, 247, 46, 147, 191, 99, 140, 270, 69, 64, 80, 277, 126, 204, 80, 177, 269, 252, 42, 169, 312, 113, 312, 202, 313, 235, 31, 300, 229, 219, 139, 138, 292, 264, 177, 167, 187, 241, 257, 106, 81, 144, 95, 298, 34, 28, 67, 139, 97, 1, 19, 297, 157, 52, 8, 193, 248, 124, 223, 252, 263, 108, 313, 39, 102, 255, 280, 17, 266, 39, 146, 98, 175, 14, 309, 261, 197, 280, 231, 120, 52, 217, 199, 294, 40, 8, 37, 251, 84, 123, 190, 48, 199, 170, 38, 16, 239, 284, 209, 228, 98, 295, 65, 273, 278, 241, 232, 133, 41, 127}

Returns: 47
{3, 10, 6, 3, 9, 10, 9, 10, 3, 9, 10, 10, 2, 10, 10, 10, 10, 8, 5, 10, 1, 7, 3, 10, 10, 10, 5, 4, 10, 7, 10, 10, 8, 5, 10, 1, 3, 10, 10, 1, 10, 1, 2, 6, 1, 10, 15, 10, 10, 10, 10, 10, 10, 1, 8, 13, 1, 10, 10, 10, 10, 9, 10, 4, 10, 5, 4, 10, 10, 10, 1, 2, 11, 10, 8, 2, 10, 8, 1, 4, 10, 10, 6, 10, 4, 10, 4, 9, 10, 5, 10, 10, 10, 7, 10, 10, 5, 7, 10, 9, 10, 5, 10, 10, 10, 10, 10, 10, 10, 9, 8, 10, 10, 10, 10, 4, 6, 10, 9, 10, 10, 5, 10, 10, 1, 10, 5, 6, 4, 5, 9, 3, 5, 10, 6, 8, 2, 2, 2, 9, 10, 10, 10, 10, 10, 5, 10, 10, 10, 9, 10, 1, 2, 4, 10, 5, 10, 10, 10, 2, 4, 8, 7, 6, 7, 5, 1, 3, 5, 1, 10, 10, 10, 10, 10, 10, 3, 7, 9, 6, 9, 7}

Returns: 131
{59341682, 77754337, 248646488, 82602809, 217283834, 169287117, 133848926, 26173916, 142342775, 190218166, 139124727, 247873684, 252286928, 157050788, 252153019, 335228540, 191698577, 227453392, 271422815, 31136468, 27193557, 190343703, 5780435, 26766227, 210477661, 254759894, 170633854, 171938571, 138712590, 222459637, 218920437, 236347239, 66699571, 266343488, 174494684, 18854577, 2034997, 103623915, 118343602, 213399076, 335914386, 194493972, 188627139, 135815186, 144814459, 307240412, 112153644, 131753176, 53768058, 177988497, 332019117, 102162507, 229811508, 111190283, 102659752, 230502990, 240117899, 135272703, 229599411, 148744822, 92195606, 83598586, 289780784, 330335187, 250013296, 65455088, 282043030, 6625682, 201947932, 128709382, 183438832, 231498767, 290795409, 22112637, 131389859, 143097017, 230626957, 169366941, 252604921, 116821651, 47758088, 213338926, 21931859, 24525032, 250966200, 312559775, 25462222, 344204777, 171758801, 26986941, 164804570, 100702500, 23306167, 211441824, 253625403, 287335349, 19006757, 255233523, 44829569, 119307407, 8850462, 70965523, 21149373, 182711717, 138394928, 243136053, 174947827, 73983677, 242165281, 24741267, 204874359, 200290778, 298053926, 323283527, 125474437, 313676539, 149297006, 83071855, 290719392, 55027650, 88944744, 44609670, 103075645, 300077204, 305251114, 54976111, 287114635, 91060486, 157050788, 123757873, 157050788, 331172424, 71168477, 324402374, 105761931, 202725205, 61948557, 208339645, 157050788, 157050788, 63637312, 23787833, 140980466, 185392194, 132726457, 192676759, 146345360, 123883410, 270947505, 343771926, 54007254, 151780550, 61387902, 178993293, 109227217, 265549976, 232949089, 157050788, 98759075, 167756216, 7651696, 176995795, 309529070, 318614544, 157050788, 324412950, 120529372, 27059502, 147504387, 207682624, 232182370, 46483364, 226496522, 324595614, 266230761, 288639354, 195757974, 22409771, 341475899, 157050788, 176495619, 194167112, 12371840, 171924027}

Returns: 34
{3, 7, 8, 2, 4, 6, 5, 5, 5, 5}

Returns: 5

Here, pairing up the pieces in the given order gives us five planks of length 10. Alternately, we can build a fence using the four pieces of length 5 as planks and making the fifth plank as 2+3.
{3, 7, 3, 7, 3, 7, 8, 2, 4, 6, 5, 5, 5, 5}

Returns: 7
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

Returns: 5
{3, 4, 2, 3, 1, 2321312, 321312312, 321312312, 1221, 3213, 21312, 312, 43423, 432423, 432432, 3312, 321, 3213, 432432, 543543, 432, 312312, 3432423, 321312, 12321, 3214, 321312, 123123, 321312, 42432, 32312, 32, 23312312, 321312, 21312312, 213123, 31231, 1, 2, 3, 4, 5, 6, 4, 3, 2, 2, 2, 3, 423423, 432432, 3423423 }

Returns: 8

Statistics

Problem Statement for "ANewFence"

Problem Statement

Definition

Constraints

Examples