TopCoder Statistics - Problem Statement

Problem Statement

Two positive integers can be merged if and only if the last three digits of the first integer match the first three digits of the second integer. If they do, you can merge them together into one bigger integer by overlapping those digits.

For example, you can merge 7890 and 890123 into 7890123. Merging 100147 with 147 into 100147 is also valid. You cannot merge 12345 with 543789, the order of digits matters: the end "345" is not the same as the beginning "543".

It is not allowed to add extra leading zeros before merging. E.g., you are not allowed to merge 4007 with 759 by pretending that the second number is 00759.

Note that if a number has fewer than three digits, it cannot be merged with anything. E.g., there is no x such that you can merge x and 47, and there is no y such that you can merge 47 and y.

Suppose you have a collection of (not necessarily distinct) positive integers. In each step you can select any two numbers that can be merged and merge them - i.e., discard both of them from the collection and add the number you produced by merging them into the collection instead.

For example, if you collection is 1234, 1234, 1234, 2345, you can merge one of the 1234s with the 2345. Your new collection will be 1234, 1234, 12345.

The collection is called nice if there is a sequence of zero or more such steps after which the collection will consist of a single number.

The int[] numbers contains a collection of positive integers. If it is nice, return 0. Otherwise, if there is a positive integer X < 10^9 such that adding one X to the collection makes it nice, return any such X. Otherwise, return -1.

Definition

Class:: MergingNumbers
Method:: solve
Parameters:: int[]
Returns:: int
Method signature:: int solve(int[] numbers)
(be sure your method is public)

Constraints

numbers will contain between 1 and 300 elements, inclusive.
Each element of numbers will be between 1 and 10^9, inclusive.

Examples

{ 1234567 }

Returns: 0

We perform zero steps, as we already have a single number. Any single number clearly forms a nice collection.
{ 12345, 78901, 3456789 }

Returns: 0

We can first merge 3456789 and 78901 into 345678901, and then merge 12345 and 345678901 into 12345678901.
{ 22222, 22222, 22222, 22222, 22222, 22222, 22222 }

Returns: 0

The numbers in the collection are not necessarily distinct. We can merge these in any order and after six steps we will have a single number. That number will always be 22222222222222222.
{1, 2, 3, 11, 22, 3}

Returns: -1

No two of these six numbers can be merged.
{1234, 3456}

Returns: 2345

We cannot merge these two numbers, so the collection is not nice. If we add 2345 to the collection, we can then eventually merge everything into a single number, so 2345 is a valid return value. Other valid solutions include 234719345 and 45609123.
{1234, 5678, 3456}

Returns: -1

In order to turn this collection into a nice one we would need to add at least two new numbers.
{123123123, 1234, 1234, 1234, 1234, 1234, 234890123, 234890123}

Returns: -1

If the collection contains duplicates, their exact counts matter. The above collection is not nice and it cannot be made into a nice collection by adding any single number. However, adding two additional copies of 234890123 would make this collection nice.
{7}

Returns: 0
{57}

Returns: 0
{7, 1234}

Returns: -1
{1046, 46}

Returns: -1
{1046, 27104}

Returns: 0
{27045, 12009}

Returns: -1
{358359, 312313, 342343, 388389, 141142, 182183, 394395, 238239, 273274, 195196, 373374, 258259, 107108, 187188, 339340, 276277, 262263, 334335, 250251, 380381, 101102, 351352, 219220, 274275, 130131, 109110, 397398, 237238, 148149, 185186, 268269, 249250, 243244, 322323, 116117, 204205, 199200, 279280, 335336, 288289, 181182, 248249, 265266, 139140, 359360, 212213, 123124, 331332, 184185, 355356, 189190, 287288, 214215, 251252, 140141, 163164, 202203, 157158, 360361, 256257, 126127, 302303, 137138, 253254, 352353, 252253, 295296, 357358, 228229, 205206, 133134, 233234, 192193, 124125, 215216, 309310, 169170, 313314, 365366, 198199, 386387, 175176, 207208, 266267, 303304, 142143, 277278, 234235, 327328, 387388, 306307, 347348, 136137, 203204, 372373, 208209, 354355, 246247, 158159, 183184, 159160, 284285, 165166, 293294, 328329, 176177, 377378, 378379, 218219, 227228, 375376, 317318, 385386, 114115, 106107, 171172, 308309, 368369, 172173, 289290, 344345, 209210, 330331, 391392, 316317, 174175, 170171, 241242, 340341, 178179, 113114, 177178, 122123, 257258, 381382, 196197, 115116, 160161, 111112, 186187, 298299, 311312, 144145, 364365, 102103, 269270, 329330, 356357, 267268, 226227, 151152, 225226, 389390, 146147, 135136, 395396, 369370, 282283, 194195, 370371, 349350, 131132, 384385, 310311, 301302, 127128, 366367, 396397, 278279, 245246, 134135, 125126, 398399, 361362, 343344, 145146, 147148, 210211, 188189, 154155, 162163, 247248, 105106, 180181, 263264, 281282, 353354, 382383, 324325, 292293, 264265, 167168, 321322, 108109, 345346, 193194, 211212, 376377, 239240, 259260, 230231, 168169, 119120, 121122, 294295, 305306, 319320, 240241, 143144, 103104, 213214, 138139, 338339, 348349, 374375, 224225, 197198, 153154, 315316, 260261, 129130, 255256, 156157, 304305, 232233, 286287, 337338, 201202, 299300, 333334, 179180, 371372, 110111, 244245, 236237, 191192, 166167, 336337, 242243, 341342, 161162, 307308, 350351, 325326, 173174, 323324, 272273, 190191, 254255, 206207, 390391, 128129, 290291, 220221, 155156, 271272, 216217, 149150, 229230, 296297, 285286, 150151, 270271, 164165, 118119, 222223, 200201, 393394, 399400, 291292, 117118, 223224, 326327, 283284, 363364, 367368, 221222, 217218, 318319, 261262, 104105, 379380, 346347, 235236, 100101, 152153, 112113, 314315, 120121, 300301, 297298, 362363, 231232, 275276, 392393, 332333, 383384, 320321, 132133, 280281}

Returns: 0
{276693, 373790, 261678, 265682, 298715, 148565, 380797, 187604, 159576, 304721, 108525, 330747, 223640, 135552, 176593, 258675, 174591, 219636, 269686, 390807, 267684, 268685, 283700, 279696, 273690, 197614, 297714, 277694, 271688, 227644, 170587, 328745, 382799, 158575, 213630, 287704, 237654, 280697, 254671, 167584, 196613, 345762, 238655, 359776, 326743, 198615, 113530, 110527, 168585, 397814, 378795, 363780, 370787, 128545, 395812, 286703, 381798, 155572, 314731, 122539, 306723, 337754, 389806, 207624, 193610, 342759, 377794, 325742, 323740, 257674, 374791, 364781, 172589, 272689, 300717, 235652, 242659, 215632, 154571, 114531, 339756, 285702, 313730, 324741, 104521, 351768, 320737, 216633, 117534, 249666, 311728, 394811, 372789, 248665, 360777, 274691, 369786, 352769, 179596, 182599, 344761, 138555, 177594, 290707, 106523, 292709, 371788, 199616, 281698, 288705, 118535, 141558, 163580, 169586, 103520, 262679, 236653, 309726, 230647, 222639, 398815, 226643, 166583, 218635, 217634, 194611, 387804, 204621, 147564, 247664, 307724, 244661, 334751, 124541, 270687, 245662, 125542, 321738, 112529, 346763, 149566, 105522, 225642, 205622, 211628, 353770, 208625, 319736, 233650, 375792, 246663, 239656, 316733, 209626, 181598, 332749, 184601, 134551, 308725, 151568, 109526, 331748, 341758, 275692, 188605, 156573, 263680, 240657, 175592, 206623, 131548, 356773, 200617, 368785, 132549, 327744, 338755, 142559, 143560, 231648, 136553, 322739, 146563, 301718, 289706, 251668, 140557, 116533, 186603, 127544, 195612, 241658, 392809, 160577, 358775, 202619, 250667, 101518, 399816, 256673, 203620, 161578, 278695, 329746, 145562, 284701, 173590, 115532, 243660, 129546, 255672, 228645, 178595, 295712, 376793, 165582, 347764, 396813, 264681, 232649, 157574, 253670, 120537, 259676, 340757, 107524, 386803, 350767, 302719, 335752, 164581, 126543, 343760, 266683, 185602, 224641, 282699, 133550, 119536, 317734, 349766, 180597, 150567, 366783, 365782, 210627, 183600, 229646, 393810, 201618, 123540, 312729, 252669, 212629, 221638, 367784, 189606, 153570, 379796, 315732, 144561, 152569, 305722, 361778, 162579, 291708, 333750, 355772, 296713, 100517, 299716, 137554, 171588, 102519, 303720, 190607, 388805, 214631, 130547, 310727, 348765, 139556, 383800, 192609, 121538, 293710, 191608, 385802, 336753, 294711, 111528, 384801, 260677, 234651, 362779, 391808, 357774, 220637, 318735, 354771}

Returns: -1
{3992195, 48856413, 514957, 21437699, 7802384, 301900, 290465, 947386268, 285029213, 32464695, 756503, 1440252, 8537266, 5033620, 371419490, 118141, 60262, 101143815, 577812, 41257809, 668301, 217195, 79983414, 12894633, 783736, 87391432, 432806, 6993391, 54299113, 4290167, 195439, 3924198, 208417, 730385, 20399121, 73636, 271529, 55021730, 45666, 45136932, 882350187, 25695540, 7747536, 3687428, 90914898, 399476, 81761623, 39187367, 53601399, 62254534, 686533717, 26272739, 3504236, 255210177, 451255720, 152669994, 717806602, 520336, 428906315, 18760399, 90994584, 12840515, 553597702, 54811, 378584, 9170331, 222610651, 385172394, 17795, 623134863, 7957290, 17459392, 45454567, 581262322, 774744550, 736214, 90241683, 27111435, 809875, 13224802, 399528, 5082185, 56866499, 529302, 2012673, 725970337, 49460208, 30279412, 12104, 21660946, 3360240, 32966876, 364320886, 40525349, 461756300, 417194424, 160192583, 68346, 760806225, 739514, 2582160, 613228569, 228826203, 88668, 6737548, 30066702, 38876317, 8663459, 65126959, 810248553, 317811882, 8768947, 42453808, 43329, 87583455, 282789538, 439688191, 611787686, 567935, 25624995, 4932622, 117451, 601725, 113271, 22080195, 900400819, 528046000, 995876, 53461, 2136, 26663183, 217122, 7854398, 501783, 2777449, 38442, 225986205, 80279821, 2493774, 88130223, 8084739, 635001394, 183516760, 72607581, 6992548, 638454, 53453873, 736118, 6002255, 946416, 35501, 957015289, 274013145, 136114568, 819748564, 811567, 416718, 8127564, 367073128, 79850917, 38536174, 14525201, 3669735, 258378, 991983635, 39233613, 2500982, 1856794, 289152, 583553, 49968249, 138845902, 720465987, 394324, 666228, 56466392, 44963, 982514, 6246148, 41466, 62046508, 98737451, 49024570, 44271, 85304624, 25293, 654127399, 439566, 398111258, 62355128, 577433, 195440791, 632785, 663238494, 21876216, 3919439, 9592577, 821971, 718632, 414122138, 1224817, 849145101, 466909, 214538183, 847217, 476274, 238456, 3315424, 976272736, 37206, 26853, 58450271, 9025529, 73079220, 271429, 564991, 3159638, 94323759, 538798, 44179238, 514756, 404372, 566068736, 45585259, 70282, 259826488, 87218, 7393258, 66790, 18388623, 567022355, 413378611, 54025654, 81553132, 482600, 58418662, 9584391, 33775847, 8984902, 791828730, 42919, 74405, 2368978, 97874144, 919291542, 62444853, 70250, 459810, 636404, 4880534, 969112, 7260744, 806957, 529144767, 915774217, 584726, 96385, 863016707, 95711603, 790832780, 1673441, 39881, 1958, 695749368, 759429, 2231482, 4247909, 515432214, 5694366, 767866, 935051849, 7350222, 141774, 19161371, 104799, 19820388, 112915, 148789256, 9326584, 87607976, 3469493, 633624, 2935726, 20504277, 994809520, 66217398, 5706699, 707884256, 603510943, 46522872, 39497285, 97147601, 43573663, 548310969, 794382667, 20660577, 3492414, 240488, 55350, 32262117}

Returns: 104364
{9296502, 892533, 686974758, 992840, 931361, 899616, 53558, 228972, 17195761, 10490731, 5942229, 741349572, 74295765, 6599553, 58152361, 806240, 90252611, 852172, 2243542, 764247672, 739926597, 752907380, 23135, 573346479, 9748840, 88305541, 47423857, 41462, 354612, 503756757, 2029810, 93133929, 820757414, 9922982, 65956121, 4823445, 666540506, 667306230, 738582, 860820, 471767, 100391218, 54422, 69384231, 552901171, 7445, 37394238, 5344370, 77135424, 84036410, 902910, 5302719, 5824705, 66590, 3422496, 19658250, 41933, 708236, 257375189, 972279877, 17255902, 4456370, 810538637, 5904532, 69405992, 5023738, 21294686, 370150, 255653663, 9381230, 27060637, 616859, 982520, 20074689, 4510598, 10072892, 93455534, 767997463, 76424165, 717862, 9207931, 59688742, 45682524, 23667899, 98268142, 354595, 873751, 890514584, 731569471, 612163952, 520630594, 44521117, 5297400, 524296686, 28090590, 6722738, 533693, 744639126, 840552, 58344544, 902815100, 709981824, 54185, 51012709, 8081157, 93348502, 238869104, 807194, 532140, 353724, 862660413, 61182666, 40036473, 4134703, 11728803, 30706172, 126412, 776140, 72474, 270234593, 2503401, 58499872, 21616, 763216483, 758429, 1944899, 17212, 813168, 8666342, 6865171, 590337803, 2998147, 51454974, 81859, 946313, 4838910, 68062189, 463196, 397466, 857581, 271801333, 2409157, 1506742, 9066290, 8094665, 854878514, 542235418, 572629904, 53560724, 5538889, 16748100, 8512530, 4161120, 4451, 167975, 603583, 859255, 12196, 641657789, 1895873, 5021535, 91065353, 7787973, 168902, 221680, 5978883, 354431286, 66354, 75179983, 5249943, 49619808, 520796168, 313333757, 94397442, 473860, 572829742, 904656597, 4777345, 877948934, 4620923, 48355468, 70354, 3458641, 781822270, 46330764, 41066502, 8891739, 4689542, 422828820, 4421529, 2722462, 185676477, 7245581, 218502, 429776, 934659, 76525307, 5987534, 595992, 3806270, 983852, 8209463, 9042255, 1965251, 923137952, 479109535, 41213946, 952167, 89910709, 230782771, 973452, 58196255, 76165756, 59746937, 185200, 10922257, 43400595, 3619354, 2519741, 2299813, 353986778, 189382, 3062172, 7577526, 803212185, 7571818, 87274416, 526412, 773934, 68973456, 74251744, 709548520, 5935809, 4522890, 5428500, 1201931, 756956445, 9738109, 42421708, 616884, 5029902, 70532167, 172039573, 757845, 171757, 937596, 1864216, 418082764, 35419, 255642202, 4664221, 28640982, 82412752, 742946, 59500773, 333299, 168784933, 859841, 230744, 2903883, 74232510, 8837216, 14004938, 135186, 40161353, 7386781, 4680659, 1407483, 38280, 719806, 2164228, 462354, 2551603, 14221854, 15742, 500149271, 9333866, 637482, 538503, 412568717, 91066224, 147998397, 845334920, 97524, 84176851, 370306, 502157373, 95291763, 55824904, 518, 94640973, 637694, 53435667, 361042572, 50621807, 157538, 165093468, 88434, 80389906, 7892272}

Returns: 100518
{5961189, 42996354, 105890229, 415133, 9310827, 9497503, 42637, 751754717, 2572479, 560426, 3336432, 637172560, 689508, 474600321, 43286807, 907029818, 4121442, 660671, 6445694, 65759459, 5242789, 11316877, 573977771, 799880, 448494, 35477763, 923542784, 7954997, 40167471, 592804300, 24150910, 6562412, 58596, 241296, 305346852, 104909, 17705, 4486349, 896891377, 334210165, 1023135, 156901, 158207630, 105059657, 860522466, 59820, 784598, 418343104, 3465351, 79892539, 6833586, 231261718, 622592, 864303776, 9746973, 97881, 238290714, 820, 7267316, 152953382, 466149, 63028258, 15786432, 483883121, 109158, 189598378, 8201524, 6964724, 7393758, 4188264, 13305, 938718917, 64775293, 351881, 890929, 426586, 42252, 296054300, 80461, 46870907, 582656, 311403617, 52410, 47766, 5820135, 34981305, 7584448, 714914621, 667403, 973182795, 462864, 50807493, 30593, 54416, 671144949, 3217949, 929302, 881212, 8808212, 957978, 8891647, 80435972, 170827, 2519929, 598418, 96229598, 271607, 61766582, 82735113, 26566351, 30647, 30079514, 456663718, 7639113, 90749333, 97307754, 585964286, 5970687, 416717289, 32792617, 13515177, 8526975, 758429, 71843, 837981418, 617686, 689724652, 6471696, 983573, 880170, 964440585, 378980346, 244974, 96501202, 271896, 4034872, 909810, 264, 8106, 252216748, 949526358, 96478739, 895886938, 49462, 382053468, 189882334, 22941799, 465483, 617271, 336, 71810, 445689, 1942758, 2813622, 6174156, 5344957, 27599241, 520012895, 910421809, 503464194, 11457152, 2313627, 69459271, 616931, 58683, 113718, 8439593, 77102, 71860, 131726, 72615245, 63240105, 354671, 300637, 909829241, 40147, 158919, 258003632, 2125667, 22306, 43297617, 6076333, 37779311, 627354, 77609231, 1490306, 62113, 461784, 810644, 57368667, 58308, 717173901, 901223, 8955964, 2122414, 144114773, 49384757, 1504445, 678662, 47921469, 667158, 31616, 2003582, 78907, 6863157, 78415, 7548212, 949692694, 26425804, 512, 351148231, 748686, 683200, 87789, 593852, 662889, 51468238, 806301302, 165490741, 88133, 9418544, 7891477, 45965, 1893327, 70514, 30671, 144530, 7663290, 687491456, 298520, 9726573, 702067617, 686653357, 30262756, 202909, 333692150, 652296442, 29007251, 74131, 77303837, 87244890, 6940585, 2864384, 12123751, 135925962, 757390265, 593582, 917256257, 106465, 51412, 147585, 92920, 32142298, 471426, 74281, 9201983, 53909, 874726, 8189, 827306534, 80967321, 9090702, 807949, 90144, 275923, 293189583, 133597, 302895, 58575244, 997239401, 11378964, 3842109, 212650114, 442189, 756275, 41401, 35734474, 357448, 67117689, 827881941, 442742, 97566798, 35806, 852881, 30895683, 582357, 412481827, 53092806, 469841660, 4109880, 80625144, 245105, 2896804, 724964, 637973, 964173874, 919150524, 586422, 671910275, 881678}

Returns: -1
{42074561, 333146906, 66441935, 420, 325, 906742293, 31189382, 713727, 801472, 142651325, 311854325, 311172325, 221378, 8015546, 80674759, 221321713, 561210801, 325713, 56162, 3820657, 3337759, 32571311, 3335142, 47227869, 935821472, 80162, 11130546, 142336, 33367877, 664000, 86973472, 221382, 285685472, 2858178, 75543935, 42057169, 162416460, 20417285, 80631727, 293877, 935840285, 336378, 9359801, 46066664, 46065162, 293215142, 336293, 285178, 32523221, 3368293, 9069333, 336207333, 6019664, 29360142, 869664, 162111, 42071869, 221806, 33382, 546515755, 533180806, 3112293, 53327293, 8696420, 2216657, 90668336, 1693460, 29311, 3117378, 460561, 935771472, 472869, 72747906, 29376221, 2219759, 87759, 80182935, 162414664, 420, 7273333, 336, 14221, 378988142, 546523178, 806, 169058178, 221578336, 14287727, 755, 285503169, 311, 47292162, 17871162, 14276806, 66420, 806, 47293169, 759336, 806311, 311336, 75515801, 169711801, 806713, 111675801, 66472, 759402378, 1785204, 29363906, 869601, 11159460, 877533, 378206325, 420821285, 3253759, 142325, 877, 759164336, 178865204, 3364906, 333, 16204, 60111, 727610906, 80169, 664169, 336333, 460869, 204111, 75906, 460037801, 32594759, 1694601, 561472, 80154472, 755169, 664869, 75546, 657843221, 204664, 935869, 293221, 60102755, 93507420, 80103460, 37827221, 657293, 8014204, 5460, 111561, 178369204, 713657, 336, 178617935, 221806, 6573336, 204376162, 72748333, 37893142, 285111, 333271906, 221, 906585533, 657, 31133293, 759336, 7279657, 178285, 11169, 75945533, 11143935, 56188801, 759221, 4204, 877748333, 935420, 759443293, 935924755, 178640601, 285111, 38293, 4601, 601577935, 657261333, 86972204, 22145657, 162178, 71353533, 204178, 472169, 472178, 221, 20478111, 53382, 806, 80674378, 6577142, 56173935, 60195801, 935162, 29325, 162259546, 378180906, 60162, 204541601, 1697178, 162664, 759806, 378311, 53325, 5331877, 16964420, 9350111, 86981601, 169475601, 336375759, 420372285, 162420, 17812561, 7595877, 29321657, 47205561, 33325, 601414285, 8060533, 906378, 5460, 71336, 4202935, 16285, 169801, 54611755, 65727, 378221, 293877, 111, 162204178, 7558869, 3361311, 906759, 1117801, 801935, 2937713, 3253311, 657897333, 16935, 382146378, 906311, 533786906, 66409935, 325759, 37831333, 72759, 869580460, 33358727, 325229727, 285, 727006293, 311221, 33325, 75563601, 333293, 47204, 32533, 293796221, 80110755, 806, 5467169, 37830311, 46021755, 90657, 382279378, 935627285, 472420, 111546, 38236311, 11162, 28577755, 877716333, 9063806, 204645169, 54602111, 311806, 336325, 877382, 221293, 16960601, 906, 60162, 285438178, 80648293, 178863169, 9352472, 178420, 4202801, 325378, 601332664, 1696111, 75546, 293727, 801546}

Returns: 142935
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Returns: 111142
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Returns: -1
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Returns: -1
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Returns: -1
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Returns: 111221
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Returns: 755877
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Returns: -1
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Returns: 336221
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Returns: 336472
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Returns: 311336
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Returns: -1
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Returns: 111142
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Returns: -1
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Returns: -1
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Returns: 106856
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Returns: 175678
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Returns: -1
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Returns: 336212
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Returns: 336472
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Returns: 174336
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Returns: -1
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Returns: 100110
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 777112
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Returns: 375428
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Returns: 907143
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Returns: 316173
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Returns: 350839
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Returns: 148644
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Returns: 604470
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Returns: 536503
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Returns: 382554
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Returns: 359149
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Returns: 253516
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Returns: -1
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Returns: 142285
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Returns: 533755
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Returns: 378869
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Returns: 325472
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Returns: 713382
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Returns: 713293
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Returns: 472561
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Returns: 420311
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Returns: 142664
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Returns: 546325
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Returns: 0
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Returns: -1
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Returns: -1
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Returns: -1
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Returns: -1
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Returns: -1
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Returns: -1
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Returns: -1
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Returns: -1
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Returns: -1
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Returns: -1
{76452, 4525972, 972452, 452, 9722434, 452, 452, 434972, 4340764, 4348764, 434378972, 452, 972, 76434, 76452, 4521764, 97253434, 452825434, 972430764, 76452, 972998434, 76452, 764, 452, 43452, 4341972, 972764, 764972, 434, 76434, 972627764, 434, 9722434, 452699434, 452, 972, 434764, 434972, 76452, 76452, 76434, 76452, 43452, 9728434, 972, 76434, 434972, 764567972, 972434, 972798434, 452764, 452, 972492452, 7643972, 43460972, 452767434, 972, 76434, 452609434, 452434, 97218452, 452764, 9728764, 452764, 452, 43452, 452972, 9723764, 76434, 452, 972487434, 972452, 76434, 434764, 4343972, 972, 45221764, 97260452, 972, 972, 434, 43452, 972770434, 76452, 452, 43452, 7646972, 452895764, 434612972, 452, 972, 972434, 76452, 972452, 43402972, 764972, 764107972, 452, 452, 972, 4520972, 434386972, 45298972, 452, 452452, 972452, 452434, 764431972, 4348972, 76434, 76434, 764972, 452, 76434, 764972, 43452, 76461972, 452368434, 434, 9728434, 972506764, 76434, 452, 452764, 4348972, 972434, 45226434, 76452, 764972, 7640764, 45213764, 972, 76434, 452425764, 76434, 452972, 45217764, 452434, 76452, 76452, 972764, 97250764, 4345972, 452890434, 452434, 764848972, 76483972, 452764, 434361972, 434083764, 764, 43452, 764972, 434, 43452, 764, 76452, 4346764, 764, 4525972, 4522972, 43452, 43465972, 43452, 76439972, 97280764, 972434, 452826434, 43452, 434, 452764, 4528434, 76452, 76452, 4520764, 45271764, 43452, 43452, 972, 972452, 452, 434972, 4526434, 972452, 972, 972, 972, 76434, 7647972, 76434, 452972, 9720452, 452, 4524764, 7641972, 76452, 452764, 4521434, 4521434, 9722452, 764, 434, 4348972, 45200452, 972, 76434, 43452, 972764, 45292434, 434, 9720434, 452388434, 452576434, 972764, 434956764, 76434, 764, 972452, 76497972, 97218764, 972764, 4522972, 764, 452972, 434, 4348764, 76434, 764097764, 4523434, 764434, 972247452, 434764, 9724434, 972247434, 452, 97200059, 4341764, 764452, 43452, 9725434, 434884972, 452067972, 972, 972434, 76452, 972, 434972, 764, 764144972, 7644972, 7643434, 76434, 452884764, 434226972, 76407972, 43491764, 452, 764310972, 76452, 972764, 972408434, 452740764, 76434, 452754972, 9723764, 972, 452764, 972434, 97220434, 43452, 452, 76434, 434972, 764, 43490972, 434579972, 452, 452189434, 4529764, 452096764, 972046764, 452115434, 43425764, 9727434, 452, 76451972, 452, 452263434, 76452, 434305764, 4345972, 972434, 452, 7645764, 972866434, 97293764, 97244434, 452506764, 972173764, 76452}

Returns: -1
{33523942, 81652335, 663942, 485780663, 81663, 663317816, 485, 9424335, 942, 942821335, 485612942, 663159942, 663485, 94259663, 335942, 8166335, 6634816, 6639942, 81663, 33589816, 335, 942289485, 9426335, 66335, 6638816, 663816, 816, 816, 33583816, 942948335, 816730485, 942942663, 335, 816485, 335192942, 335094942, 94217663, 663, 485663, 3354485, 816, 942203816, 942816, 485, 816335, 485, 485612335, 942, 33520942, 66350485, 663537485, 33540663, 9423663, 942208816, 816, 485989335, 816, 335663, 335485, 942569335, 335, 335490816, 4859663, 9427485, 942331485, 48572816, 81616942, 663285942, 942335, 816719335, 663816, 663, 6638485, 942335, 663113485, 816, 3351663, 33516663, 816774335, 335314335, 9423663, 485695663, 663, 485, 663485, 81663, 81676485, 485370335, 485506942, 942, 33502485, 66335, 94231485, 942, 94299485, 3350485, 942816, 942663663, 942485, 66335, 48551663, 94251663, 485071663, 335, 485475942, 8164335, 663942, 335942, 663832942, 4853942, 335485, 9423485, 816942, 485232335, 942663, 6631485, 485663, 942184335, 485335, 33552942, 663816, 6638485, 33593485, 663816, 6638816, 816942, 335816, 3359485, 663023485, 81663, 485, 942485, 335814942, 816335, 81663, 94289335, 9425816, 663635942, 335085663, 94207485, 6631816, 663485, 942124663, 485056335, 335348485, 6639816, 335, 94223663, 66335, 663485, 66335, 335663, 485, 816942, 663, 942353335, 335104942, 94291485, 3350485, 942235485, 33544816, 942434485, 485816, 9428335, 816447485, 4857816, 485, 485951942, 48559663, 663485, 81663, 4853942, 485, 335, 485705663, 335, 66335, 942, 942, 663, 6631816, 663434816, 942816, 81606942, 94204663, 485, 942799663, 9425816, 942100485, 335485, 335, 335942, 8163485, 663485, 663, 66335, 816103335, 4859816, 9420335, 9428485, 663, 663942, 81622942, 48527485, 816067335, 66377816, 942816, 66335, 816, 816, 9428816, 335238485, 335883485, 335, 81663, 4854942, 66307816, 663630485, 663945816, 942485, 485335, 663, 8168942, 81663, 81657942, 485816, 9422816, 816898335, 485, 48539335, 485, 335, 816, 485764816, 3358485, 48529335, 81663, 66351485, 66335, 816485, 8169485, 33597485, 94256663, 663146942, 3356485, 942, 942663, 663833816, 485663, 816634942, 33518663, 942489485, 485942, 81663, 4852816, 81687335, 942099663, 816, 942043335, 942312485, 942, 485, 663816, 816, 81652335, 335, 81677942, 485816, 66394485, 942308663, 485, 816504335, 485, 9428485, 485732335, 3355816, 485, 663, 485, 485335, 816, 3356663, 663670942, 942485, 9422816, 663, 9428816, 48598816, 485816, 663663, 335439942, 485835816, 663663, 663485, 33583816, 663, 9428663, 485816, 33546942, 8163485}

Returns: -1
{485, 816, 66335, 663, 6635485, 33521816, 663566816, 816942, 9427485, 335, 48533663, 942, 66389663, 94230335, 9420663, 48568816, 335, 485340942, 335, 6630816, 335485, 485942, 8163942, 663485, 816, 94253663, 335485, 94262335, 9424816, 33529485, 485, 942, 335, 942077335, 33569942, 663, 81612942, 663, 485505816, 335485, 663911816, 663, 485663, 94234485, 663942, 9424663, 663340816, 663942, 485, 942613335, 335544942, 94273663, 6637485, 942775485, 4854942, 485, 81626335, 485335, 816335, 663942, 485, 335942, 816824335, 3359942, 816335, 663816, 485789485, 485335, 6632942, 33560663, 942878816, 816485, 816, 485663, 942051, 942816, 942816, 335942, 485335, 81663, 942, 663942, 33536942, 6635485, 942816, 942663, 485465816, 48571663, 66355663, 663652816, 942663, 942362663, 942021816, 66361485, 816834335, 942, 485, 3359485, 335264485, 942607816, 816942, 485663, 663503942, 81663, 485, 9429942, 485942, 942816, 8162942, 816335, 3351335, 816581942, 485255816, 335861485, 6636816, 66316485, 3355485, 94206663, 942663, 663, 48595663, 942816, 81663, 4854663, 816, 66335, 335485, 663485, 33550485, 9420663, 94292335, 663942, 485515335, 335, 942929335, 942242663, 816335, 9422335, 48562816, 485, 48540335, 942353816, 6634942, 485942, 8168816, 81663, 335705816, 942485, 81663, 485144816, 4851816, 335789663, 816, 94207485, 335, 942137663, 816335, 942382485, 94243816, 663744816, 66335, 663, 663, 9421335, 663663, 81663, 485, 33536942, 4856663, 663816, 485, 9422485, 4855335, 663485, 33529485, 335335, 942, 663816, 8167942, 335845663, 335823816, 663644485, 663322816, 6633942, 66335, 66335, 485942, 816335, 335942, 66335, 33597663, 942992485, 663705485, 33539816, 9425485, 816, 485816, 94286485, 81663, 942485, 8164485, 48586816, 485550816, 9423335, 663, 66346942, 942335, 335, 335917816, 485, 94296335, 8167335, 942333816, 9422485, 81663, 9429485, 8160942, 335, 4852335, 66335, 485271335, 485, 4854663, 48571335, 335942, 33519816, 663262485, 485636816, 942335, 66378485, 4854942, 3355485, 81663, 66317816, 335242663, 6632816, 485, 4858335, 816597485, 942, 9427485, 485, 942644663, 9420485, 66320485, 816, 66335, 94246663, 94288485, 9427942, 485, 66399485, 3356485, 94210663, 8163485, 485335, 8165335, 335, 816, 4857816, 9425335, 335663, 663, 81642485, 48510942, 816816, 3355485, 335, 663194663, 94251485, 663630816, 81693942, 81630485, 335832942, 66373485, 816936485, 9424663, 8168485, 485663, 8165335, 81663, 663827816, 66380485, 816942, 9422663, 94257485, 3356485, 816077335, 33525942, 942244485, 6634816, 33539816, 816816, 6635485, 33542663, 485826485, 6636816, 816, 335663, 66335}

Returns: -1
{17347283, 7603882, 873687556, 882688873, 873768173, 283932760, 760277173, 88466556, 760, 760283, 88410760, 17322884, 556873, 173649884, 882173, 8739884, 760283, 87305283, 87343884, 882313884, 760173, 882884, 760139283, 173884, 173882, 28352173, 873396882, 873173, 884283, 556757283, 873, 5566882, 760283, 873556, 8735882, 283283173, 28379283, 28394173, 283109873, 7608884, 882, 760760, 76041173, 7604173, 556, 873882, 88277760, 88412873, 283882, 8842882, 884, 28352556, 1738884, 760126760, 283760, 88283, 760882, 8735882, 55698173, 28300760, 873882, 873, 283884, 173556, 760318884, 882173, 283419760, 556283, 2831760, 8733884, 5568884, 2832873, 884, 760882, 7605873, 882556, 760760, 28376882, 873487556, 882873, 760, 882534760, 28308884, 873856556, 2832882, 283, 873, 28323760, 882556, 28359873, 2833884, 760873, 882, 76085283, 556106283, 55684884, 76037283, 28320760, 173, 88200884, 8845173, 884556, 283, 873882, 760434283, 882, 55639882, 8737173, 873590882, 8827173, 884556, 173283, 8829884, 556884, 283, 873556, 884, 1734556, 8738173, 884, 283, 8849882, 760895882, 8739882, 884173, 882556873, 173456873, 173388873, 760, 87390884, 556040283, 173873, 88296884, 8735884, 88409760, 87305882, 8734556, 8734556, 173882, 884585760, 884572173, 8732760, 882, 283346173, 760556, 87391173, 2835884, 873707283, 882, 88445873, 173470283, 87309884, 873928556, 556884, 873396283, 283760, 873091283, 76063882, 8847873, 28378760, 882556, 2834173, 884283, 2834173, 882, 882, 760681882, 173, 55604173, 1739884, 283283, 884556, 283173, 884, 884, 556882, 8730884, 873086283, 283760, 28379760, 1739283, 173, 2839760, 55676873, 8840873, 2835884, 884, 882630760, 7606283, 556760, 173873, 760882, 283, 17366283, 8849556, 873760, 173, 873035882, 283371760, 55661884, 884399283, 8845283, 760173, 88283, 7608556, 283145173, 88283, 283882, 8848873, 873760, 884882, 283882, 556884, 88474283, 884, 28399556, 873763884, 884527556, 8829760, 2837873, 873974884, 2835556, 7603283, 283716760, 760884, 28390873, 873157173, 873, 5567873, 173882, 760, 873842283, 173, 884873, 7608760, 873346556, 173, 760523884, 28300873, 173350882, 760, 76069873, 1730882, 76071556, 88424173, 7600556, 8844556, 88235884, 283, 884, 882884, 173071760, 55675283, 173002283, 873760, 873, 760884, 884873, 283, 87390283, 76045283, 8826556, 1732760, 873760, 88441760, 8739882, 173, 556, 884102173, 873041884, 283977760, 55607283, 283760, 884264882, 760873, 7608173, 87369760, 882, 873, 87303760, 884283, 556, 87352556, 556884, 55653760, 8827884, 88283, 873, 88486760, 2830760, 1732873, 173873, 556, 882010760, 882337556, 884, 76048556, 556517173, 884, 556873}

Returns: -1
{556, 17392760, 556884, 884584556, 760882, 884283, 173433283, 87348760, 88275173, 283760, 28377882, 87306173, 760956283, 556107873, 760, 76008283, 283760, 556, 873556, 556556, 7603283, 884, 873677173, 283694882, 173886556, 283873, 28305760, 873595884, 882, 882712173, 173, 873884, 8732882, 88451173, 760, 873882, 8739283, 760173, 760, 28397873, 884, 173283, 2835760, 873882, 882873, 760173, 873477884, 873982873, 173, 760, 884993556, 173, 8736283, 873283, 882425760, 873556, 88404173, 882, 87342556, 873825882, 88283, 7601882, 882556, 17377882, 28378760, 7602884, 7601882, 884556, 884873, 882, 7600173, 55679283, 760, 882556, 760942173, 882884, 5568882, 88486173, 884356882, 5563884, 283760, 8841556, 173, 760173, 556877873, 283760, 873760, 283, 8825760, 283, 884, 884457873, 55621173, 2835884, 88236884, 760824873, 882066884, 8730882, 17363882, 760708882, 2835882, 873884, 5565283, 760, 556884, 760, 873044283, 283873, 8848283, 873882, 283173, 882221884, 88451283, 87312760, 760899882, 2830556, 173789760, 873335556, 882556, 556884, 884556, 556005, 88478760, 760517556, 873884, 556776882, 8843882, 882, 173, 760884, 55636884, 8829760, 882, 1738882, 556760, 88432873, 283302760, 2832556, 2831173, 28364884, 1735884, 5565283, 884882, 882760, 2837873, 76060873, 17395884, 556173, 556259173, 283173, 55683760, 173556, 8840760, 884760, 1738283, 873, 7600283, 882884, 87351882, 8848760, 283378882, 884364760, 873760, 556091283, 283, 873, 8736556, 88283, 173, 2837556, 88420873, 884, 884532556, 7607283, 760, 283081760, 882, 884173, 8738556, 873556, 8734760, 882884, 1738882, 173381873, 873211884, 884, 873884, 173873, 2839760, 8846873, 8734283, 873884556, 283, 88432873, 882, 760283, 76040556, 882254873, 55624283, 760283, 88453173, 283199760, 283141884, 88283, 5569873, 873760, 8739884, 1731873, 88239556, 873, 76077283, 882837173, 2831173, 2838760, 884556, 873, 88259556, 283868173, 556873, 283698884, 884, 1733873, 760556, 884, 873682173, 7605556, 556884, 283926283, 173283, 1739882, 1737884, 556283, 8730882, 28317173, 873250283, 884, 87374173, 87319882, 8844283, 7601884, 76058882, 556884, 87367760, 283195882, 873, 760173, 882, 173385283, 87374882, 5561882, 283, 884882, 283760, 884, 283173, 5569556, 884, 2836873, 87399884, 283, 760873, 76072873, 76056556, 873, 28328760, 283, 17391873, 8739882, 87322173, 7600283, 283942873, 873245556, 873252173, 2834760, 884379283, 760882, 173, 8730283, 7601283, 283616173, 8826283, 760, 283, 882122884, 8823873, 28343760, 8847873, 88280760, 873395556, 760884, 8730884, 1735283, 1739873, 884, 283151760, 882884, 1739884, 283917884, 884283, 760507884}

Returns: -1
{100000, 200002 }

Returns: -1
{10000, 10000 }

Returns: -1
{1 }

Returns: 0
{123456, 456123, 234567, 567234 }

Returns: 123234
{100200, 100200, 300400, 300400, 200400, 400200 }

Returns: -1
{123321, 321123, 456654, 654456 }

Returns: 123456

Statistics

Problem Statement for "MergingNumbers"

Problem Statement

Definition

Constraints

Examples