Statistics

Problem Statement for "TellBagsApart"

Problem Statement

Lucy has two bags. The bags have numbers 1 and 2 on them. One of them (but we do not know which one) contains four white and four black marbles, the other contains twenty white and twenty black marbles. The bags are opaque, so we cannot see what's inside.

We would like to determine which bag is which.


Consider the following experiment:

  1. We choose a bag.
  2. Lucy draws a random marble from the chosen bag.
  3. She shows us the marble.
  4. She returns the marble back into the bag.

It should be clear that in terms of our goal the above experiment is useless: even if we are allowed to repeat it multiple times, we cannot use it to learn anything useful about the two bags.


Perhaps surprisingly, the situation changes completely once we modify the experiment slightly:

  1. We choose a bag.
  2. Lucy draws two random marbles from the chosen bag, one after another.
  3. She shows us the two marbles in the order in which she drew them.
  4. She returns both marbles back into the bag.

We have performed the two-marble version of the experiment exactly 2500 times. For each round we recorded the number of the bag we chose (1 or 2) and the colors of the two marbles Lucy drew (WW, BW, WB, or BB).

Note that while the marbles were always drawn at random (with all random choices being uniform and mutually independent), the bag from which Lucy drew in each round was chosen by us, and not necessarily uniformly at random. You do not know anything about how we selected the bag from which Lucy should draw in each round. In particular, you should not expect that each bag was chosen approximately 50 percent of the time.


There are eight possible records for a single experiment: 1WW, 1BW, 1WB, 1BB, 2WW, 2BW, 2WB, 2BB. As different draws are mutually independent and their order does not matter, we just kept a count for each record.

You are given these counts: eight integers that correspond to the eight records in the order given above. Given this information, determine the number of the bag that contains the smaller number of marbles.


-----------------------------------


Each test case contains N independent queries. In the examples we have N = 4 and N = 20, in each other test case N = 100. In each query you are given the eight counts as described above, and your task is to determine which bag has the smaller number of marbles.

The input is given as the int[] records with 8*N elements: the first 8 elements of records form the first query, the next 8 elements the second query, and so on.

Return a String with N characters, each being '1' or '2': for each query, the number of the bag with the smaller number of marbles.


Your answer for a test case will be accepted if and only if its accuracy is at least 94 percent.

(I.e., you need to get Example 0 completely correct, you can make up to 1 mistake in Example 1, and in each other test case you can make up to 6 mistakes.)

Definition

Class:
TellBagsApart
Method:
whichBagIsSmaller
Parameters:
int[]
Returns:
String
Method signature:
String whichBagIsSmaller(int[] records)
(be sure your method is public)

Notes

  • All tests for this problem were prepared before the round by actually simulating the process from the problem statement. More precisely, we prepared the generator, ran it exactly once and used the tests it generated.
  • Custom challenges for this problem will not be allowed, as we cannot guarantee that you generated them in a fair way.
  • During the challenge phase you can only use the example tests as possible challenge inputs.
  • There are exactly 20 test cases. (This includes the two examples.)
  • Under these conditions, the reference solution would pass system tests with probability significantly over 99.99 percent.

Constraints

  • In the test case in Example 0, records contains 4*8 elements.
  • In the test case in Example 1, records contains 20*8 elements.
  • In each other test case, records contains 100*8 elements.
  • All elements of records are non-negative.
  • If we break records into groups of 8, the sum of each such group is exactly 2500.
  • Each query in records was generated as described in the problem statement.

Examples

  1. {262, 371, 340, 277, 303, 304, 333, 310, 296, 326, 370, 275, 312, 329, 284, 308, 265, 402, 372, 279, 279, 317, 307, 279, 112, 160, 121, 102, 497, 497, 505, 506}

    Returns: "1111"

    When generating this test case, we used the following strategies to select the bag for Lucy: Query 0: we first chose bag 1 exactly 1250 times and then bag 2 exactly 1250 times. (Note that 262+371+340+277 = 303+304+333+310 = 1250.) Query 1: in each round of the experiment we chose the bag at random. Query 2: we started by choosing bag 1, and each time Lucy drew two black marbles, we flipped to the other bag. Query 3: we were choosing the bags in the cyclic order 1,2,2,2,2. The return value is correct: in each query bag 1 was the one with fewer marbles.

  2. {401, 405, 345, 358, 203, 295, 284, 209, 348, 380, 396, 361, 221, 274, 307, 213, 361, 347, 410, 347, 246, 287, 298, 204, 301, 389, 412, 304, 253, 289, 280, 272, 303, 450, 388, 290, 270, 286, 246, 267, 328, 354, 326, 362, 254, 305, 309, 262, 290, 362, 391, 296, 285, 282, 313, 281, 338, 335, 345, 335, 220, 338, 335, 254, 309, 356, 348, 323, 239, 344, 343, 238, 264, 368, 365, 258, 301, 312, 328, 304, 256, 368, 343, 295, 296, 323, 319, 300, 275, 318, 383, 258, 320, 340, 306, 300, 275, 301, 323, 309, 273, 372, 366, 281, 263, 331, 290, 309, 277, 358, 395, 277, 261, 310, 291, 259, 301, 407, 379, 292, 256, 318, 297, 257, 325, 358, 366, 323, 284, 287, 274, 286, 294, 406, 358, 311, 266, 271, 282, 256, 282, 395, 429, 319, 270, 274, 278, 268, 308, 396, 404, 302, 203, 283, 299, 229, 368, 401, 377, 340}

    Returns: "22211212211122212221"

    For each i from 0 to 19, inclusive, when generating query i we used the strategy that in each round bag 1 was chosen with probability (60-i) percent. The return value is correct for each of the 20 queries.

  3. {42, 52, 64, 40, 605, 572, 576, 549, 556, 581, 616, 546, 46, 61, 56, 38, 214, 290, 281, 207, 380, 352, 401, 375, 288, 366, 391, 291, 269, 301, 304, 290, 310, 457, 401, 307, 263, 277, 240, 245, 253, 315, 341, 271, 308, 339, 320, 353, 225, 230, 226, 213, 330, 471, 463, 342, 128, 200, 153, 130, 468, 453, 501, 467, 309, 407, 424, 301, 279, 247, 286, 247, 346, 467, 468, 337, 203, 229, 237, 213, 117, 139, 113, 122, 400, 568, 591, 450, 69, 116, 111, 74, 526, 546, 547, 511, 565, 605, 647, 590, 19, 32, 19, 23, 28, 45, 63, 44, 550, 614, 607, 549, 313, 486, 452, 329, 230, 232, 239, 219, 352, 428, 401, 413, 198, 250, 286, 172, 633, 607, 647, 613, 0, 0, 0, 0, 567, 609, 599, 585, 26, 36, 47, 31, 178, 179, 183, 175, 380, 512, 503, 390, 157, 214, 235, 161, 425, 433, 450, 425, 420, 525, 562, 385, 156, 145, 148, 159, 286, 316, 322, 251, 331, 343, 350, 301, 262, 402, 370, 283, 291, 296, 320, 276, 388, 467, 511, 360, 197, 190, 225, 162, 367, 533, 532, 382, 173, 174, 176, 163, 221, 299, 312, 247, 327, 380, 329, 385, 7, 7, 3, 4, 613, 632, 616, 618, 178, 247, 241, 201, 417, 395, 440, 381, 94, 93, 106, 75, 471, 612, 597, 452, 76, 82, 85, 72, 495, 564, 593, 533, 0, 0, 0, 0, 524, 747, 717, 512, 401, 561, 584, 395, 134, 155, 152, 118, 29, 27, 31, 40, 520, 673, 682, 498, 180, 220, 200, 197, 395, 494, 478, 336, 165, 241, 243, 168, 389, 445, 430, 419, 226, 304, 287, 224, 358, 374, 374, 353, 470, 642, 647, 483, 63, 60, 66, 69, 52, 66, 65, 53, 532, 602, 565, 565, 388, 399, 361, 366, 193, 299, 289, 205, 372, 372, 419, 377, 197, 270, 274, 219, 261, 351, 343, 273, 297, 317, 329, 329, 573, 587, 605, 522, 44, 70, 53, 46, 426, 462, 411, 481, 165, 197, 225, 133, 530, 688, 713, 515, 9, 15, 10, 20, 25, 26, 26, 28, 515, 699, 700, 481, 251, 356, 334, 271, 292, 346, 308, 342, 216, 162, 217, 181, 364, 507, 472, 381, 367, 507, 505, 400, 211, 159, 188, 163, 525, 642, 672, 485, 42, 49, 44, 41, 397, 536, 583, 401, 146, 165, 138, 134, 470, 604, 624, 442, 89, 86, 85, 100, 170, 229, 225, 178, 450, 444, 439, 365, 175, 169, 193, 165, 374, 506, 508, 410, 319, 492, 395, 342, 248, 257, 243, 204, 387, 379, 340, 376, 209, 303, 293, 213, 603, 672, 629, 596, 0, 0, 0, 0, 33, 34, 44, 28, 508, 689, 674, 490, 376, 534, 508, 380, 164, 161, 203, 174, 251, 326, 332, 239, 358, 343, 330, 321, 34, 58, 38, 57, 519, 607, 684, 503, 577, 559, 601, 579, 29, 61, 48, 46, 502, 728, 695, 575, 0, 0, 0, 0, 263, 300, 292, 253, 328, 348, 363, 353, 167, 151, 146, 148, 411, 584, 496, 397, 31, 37, 36, 36, 577, 563, 626, 594, 118, 142, 141, 129, 422, 555, 579, 414, 185, 198, 208, 205, 362, 489, 491, 362, 479, 510, 482, 385, 114, 203, 193, 134, 583, 612, 631, 598, 20, 14, 22, 20, 354, 404, 441, 401, 205, 250, 247, 198, 294, 438, 431, 299, 249, 281, 265, 243, 187, 202, 200, 178, 375, 498, 507, 353, 289, 409, 434, 290, 265, 284, 274, 255, 332, 412, 442, 265, 262, 263, 288, 236, 185, 218, 231, 148, 431, 453, 444, 390, 167, 160, 160, 139, 383, 547, 550, 394, 31, 29, 34, 31, 513, 696, 665, 501, 556, 557, 577, 517, 56, 107, 64, 66, 389, 389, 397, 359, 199, 261, 288, 218, 214, 316, 308, 260, 324, 337, 370, 371, 246, 380, 349, 277, 296, 336, 299, 317, 357, 394, 428, 372, 197, 292, 264, 196, 228, 238, 227, 231, 319, 464, 439, 354, 365, 456, 507, 327, 203, 219, 222, 201, 239, 293, 321, 243, 320, 349, 379, 356, 496, 675, 687, 494, 44, 38, 38, 28, 146, 148, 129, 133, 400, 576, 553, 415, 69, 91, 103, 96, 544, 537, 561, 499, 287, 362, 365, 282, 290, 341, 284, 289, 60, 82, 71, 71, 479, 644, 612, 481, 362, 407, 391, 392, 228, 265, 249, 206, 212, 274, 292, 218, 397, 371, 352, 384, 7, 15, 16, 9, 505, 719, 696, 533, 251, 249, 252, 199, 332, 438, 438, 341, 460, 608, 615, 468, 77, 94, 92, 86, 485, 637, 680, 476, 60, 56, 55, 51, 0, 0, 0, 0, 576, 699, 692, 533, 112, 126, 120, 115, 433, 576, 577, 441, 593, 645, 646, 584, 5, 12, 9, 6, 457, 665, 658, 463, 52, 74, 71, 60}

    Returns: "1211112111212112222111111111212122111122122121211111212221122112122222121112222112211121122122112221"

  4. {595, 587, 624, 551, 34, 36, 42, 31, 530, 549, 605, 581, 47, 63, 68, 57, 506, 682, 675, 486, 33, 36, 47, 35, 606, 629, 608, 549, 29, 33, 29, 17, 502, 710, 772, 516, 0, 0, 0, 0, 536, 597, 601, 557, 41, 68, 47, 53, 569, 627, 668, 570, 15, 22, 14, 15, 489, 653, 643, 500, 57, 44, 58, 56, 614, 609, 614, 578, 26, 14, 28, 17, 484, 641, 666, 539, 35, 51, 39, 45, 558, 600, 559, 611, 34, 51, 58, 29, 636, 604, 627, 614, 7, 6, 1, 5, 609, 562, 570, 552, 51, 65, 53, 38, 575, 597, 643, 588, 24, 28, 30, 15, 580, 612, 593, 585, 24, 30, 39, 37, 582, 687, 602, 576, 15, 15, 8, 15, 521, 686, 665, 477, 35, 32, 40, 44, 589, 577, 544, 561, 47, 55, 73, 54, 533, 653, 674, 471, 37, 44, 47, 41, 580, 568, 639, 560, 35, 41, 43, 34, 603, 624, 610, 562, 20, 29, 27, 25, 609, 647, 615, 607, 5, 4, 4, 9, 593, 621, 633, 627, 6, 10, 4, 6, 528, 648, 658, 541, 36, 30, 29, 30, 596, 587, 640, 528, 31, 45, 41, 32, 526, 683, 672, 521, 27, 27, 22, 22, 558, 639, 688, 615, 0, 0, 0, 0, 571, 591, 584, 604, 30, 39, 45, 36, 589, 630, 683, 571, 6, 7, 8, 6, 493, 657, 643, 498, 48, 53, 58, 50, 469, 692, 692, 476, 44, 47, 33, 47, 514, 690, 718, 528, 12, 18, 11, 9, 569, 609, 626, 617, 21, 15, 23, 20, 555, 690, 677, 496, 18, 19, 24, 21, 498, 677, 687, 512, 30, 36, 29, 31, 534, 698, 703, 538, 5, 7, 9, 6, 549, 567, 586, 584, 46, 61, 56, 51, 634, 643, 619, 604, 0, 0, 0, 0, 528, 653, 643, 504, 34, 43, 51, 44, 487, 630, 707, 457, 50, 46, 55, 68, 474, 635, 675, 481, 48, 73, 52, 62, 554, 587, 575, 562, 50, 63, 58, 51, 569, 642, 619, 583, 14, 20, 36, 17, 488, 628, 688, 495, 51, 49, 54, 47, 519, 665, 657, 492, 32, 52, 42, 41, 537, 731, 738, 494, 0, 0, 0, 0, 502, 682, 692, 551, 18, 17, 18, 20, 483, 640, 666, 544, 36, 33, 40, 58, 526, 680, 620, 476, 48, 53, 54, 43, 572, 619, 564, 528, 55, 60, 58, 44, 503, 617, 695, 493, 39, 54, 56, 43, 563, 686, 672, 532, 19, 9, 4, 15, 589, 649, 599, 640, 10, 4, 4, 5, 556, 653, 619, 580, 21, 25, 19, 27, 499, 695, 664, 534, 22, 28, 32, 26, 595, 568, 610, 611, 25, 31, 32, 28, 607, 649, 645, 567, 5, 9, 11, 7, 504, 665, 657, 463, 49, 51, 56, 55, 601, 604, 596, 603, 20, 33, 25, 18, 579, 661, 607, 561, 17, 37, 24, 14, 601, 581, 645, 583, 20, 23, 27, 20, 534, 582, 621, 566, 44, 45, 59, 49, 531, 679, 706, 502, 20, 27, 17, 18, 504, 641, 683, 494, 49, 38, 38, 53, 517, 634, 676, 502, 37, 42, 46, 46, 488, 658, 664, 504, 43, 44, 51, 48, 525, 748, 704, 493, 9, 9, 5, 7, 533, 617, 664, 483, 52, 49, 51, 51, 581, 659, 611, 632, 9, 1, 6, 1, 538, 601, 579, 572, 47, 73, 46, 44, 643, 650, 620, 587, 0, 0, 0, 0, 547, 565, 630, 576, 35, 53, 52, 42, 495, 622, 693, 490, 48, 48, 52, 52, 544, 593, 616, 522, 52, 56, 70, 47, 524, 610, 602, 537, 37, 75, 54, 61, 499, 700, 689, 540, 23, 20, 17, 12, 503, 688, 718, 532, 19, 17, 14, 9, 502, 697, 667, 509, 28, 32, 34, 31, 598, 641, 634, 590, 6, 8, 12, 11, 550, 722, 687, 524, 8, 4, 4, 1, 558, 595, 556, 562, 46, 66, 61, 56, 594, 628, 624, 596, 16, 11, 18, 13, 479, 664, 685, 505, 43, 37, 44, 43, 527, 639, 557, 608, 43, 51, 31, 44, 613, 616, 599, 536, 31, 39, 36, 30, 596, 641, 672, 591, 0, 0, 0, 0, 498, 688, 613, 481, 61, 57, 53, 49, 525, 638, 639, 508, 48, 46, 49, 47, 493, 679, 674, 527, 24, 32, 40, 31, 566, 582, 576, 554, 44, 56, 68, 54, 606, 593, 620, 548, 26, 35, 37, 35, 495, 648, 648, 480, 60, 56, 56, 57, 472, 630, 676, 534, 39, 41, 54, 54, 560, 582, 604, 549, 39, 60, 60, 46, 471, 698, 663, 504, 47, 38, 30, 49, 530, 739, 645, 560, 10, 5, 5, 6, 599, 584, 643, 601, 18, 16, 27, 12, 589, 666, 598, 618, 5, 5, 11, 8, 509, 638, 693, 490, 39, 41, 50, 40, 483, 689, 732, 512, 22, 21, 18, 23}

    Returns: "2212122121222222121222212122211121112211122111111211221221222211111122221221112122122211122112112211"

  5. {19, 18, 13, 18, 530, 686, 732, 484, 59, 66, 59, 56, 461, 690, 668, 441, 48, 43, 37, 54, 500, 693, 629, 496, 52, 67, 58, 51, 591, 567, 565, 549, 18, 38, 37, 20, 584, 611, 616, 576, 12, 14, 19, 8, 572, 624, 628, 623, 40, 69, 75, 49, 544, 594, 564, 565, 0, 0, 0, 0, 547, 746, 712, 495, 0, 0, 0, 0, 614, 633, 643, 610, 0, 0, 0, 0, 628, 628, 592, 652, 28, 42, 54, 39, 550, 633, 592, 562, 61, 48, 69, 64, 486, 637, 639, 496, 4, 7, 10, 6, 545, 655, 732, 541, 23, 56, 41, 38, 544, 643, 590, 565, 49, 64, 48, 47, 558, 576, 589, 569, 20, 29, 21, 26, 533, 687, 703, 481, 9, 10, 14, 6, 490, 746, 689, 536, 4, 7, 11, 5, 526, 713, 686, 548, 38, 34, 26, 25, 488, 698, 670, 521, 46, 48, 63, 45, 549, 600, 560, 589, 22, 22, 20, 22, 514, 662, 700, 538, 24, 22, 32, 19, 589, 618, 628, 568, 19, 15, 19, 20, 535, 682, 679, 531, 55, 65, 64, 58, 575, 578, 575, 530, 21, 49, 42, 32, 582, 588, 595, 591, 51, 45, 49, 48, 483, 630, 688, 506, 14, 13, 14, 8, 520, 694, 718, 519, 7, 7, 7, 4, 642, 635, 611, 587, 0, 0, 0, 0, 619, 645, 639, 597, 25, 33, 35, 26, 597, 637, 569, 578, 28, 33, 45, 32, 572, 596, 618, 576, 24, 25, 28, 21, 588, 596, 602, 616, 33, 49, 60, 37, 569, 611, 610, 531, 40, 42, 57, 28, 490, 658, 699, 486, 13, 11, 8, 14, 517, 722, 711, 504, 44, 58, 60, 70, 573, 547, 595, 553, 25, 44, 50, 29, 509, 689, 680, 474, 35, 42, 51, 36, 508, 676, 622, 530, 27, 31, 22, 20, 653, 582, 601, 564, 23, 25, 25, 17, 545, 644, 650, 571, 3, 5, 7, 8, 615, 629, 645, 588, 19, 24, 33, 19, 593, 632, 628, 552, 13, 25, 18, 15, 499, 700, 728, 502, 21, 19, 10, 23, 633, 589, 630, 575, 44, 62, 67, 53, 558, 590, 540, 586, 48, 47, 57, 50, 482, 671, 623, 522, 19, 19, 34, 18, 570, 636, 615, 589, 45, 38, 37, 29, 522, 737, 638, 454, 5, 5, 3, 4, 532, 706, 718, 527, 13, 16, 19, 22, 469, 727, 726, 508, 22, 17, 25, 23, 476, 736, 651, 550, 9, 20, 23, 9, 619, 608, 647, 565, 30, 35, 39, 30, 573, 628, 607, 558, 21, 17, 20, 23, 526, 712, 662, 519, 24, 22, 22, 26, 503, 678, 696, 529, 2, 7, 5, 7, 600, 641, 640, 598, 20, 37, 37, 31, 577, 618, 587, 593, 8, 13, 13, 10, 536, 720, 704, 496, 0, 0, 0, 0, 624, 660, 650, 566, 15, 14, 14, 8, 529, 688, 727, 505, 50, 46, 66, 50, 564, 615, 635, 474, 5, 9, 8, 3, 576, 626, 657, 616, 31, 37, 32, 28, 611, 568, 594, 599, 30, 40, 29, 31, 496, 686, 663, 525, 25, 27, 40, 30, 608, 628, 574, 568, 43, 22, 38, 39, 489, 697, 673, 499, 24, 37, 29, 29, 513, 694, 691, 483, 44, 48, 57, 41, 568, 603, 601, 538, 40, 61, 53, 39, 568, 617, 613, 509, 12, 24, 21, 24, 536, 716, 690, 477, 21, 43, 34, 28, 571, 652, 620, 531, 54, 51, 54, 34, 556, 611, 573, 567, 51, 52, 57, 46, 488, 678, 678, 450, 50, 44, 37, 57, 476, 672, 672, 492, 52, 63, 56, 41, 557, 588, 600, 543, 24, 21, 32, 25, 577, 618, 634, 569, 40, 36, 46, 26, 566, 571, 639, 576, 25, 45, 36, 22, 579, 654, 566, 573, 24, 34, 30, 27, 549, 689, 646, 501, 7, 18, 10, 9, 569, 638, 631, 618, 31, 26, 27, 21, 493, 710, 669, 523, 35, 49, 36, 33, 492, 632, 723, 500, 9, 9, 4, 5, 577, 631, 690, 575, 35, 35, 29, 39, 489, 682, 710, 481, 8, 12, 9, 8, 547, 701, 702, 513, 6, 13, 11, 5, 621, 629, 637, 578, 19, 16, 16, 16, 569, 665, 654, 545, 28, 29, 36, 36, 514, 659, 700, 498, 51, 47, 54, 38, 502, 664, 680, 464, 41, 44, 64, 50, 537, 618, 576, 570, 17, 27, 23, 21, 596, 605, 632, 579, 28, 36, 32, 42, 507, 648, 684, 523, 0, 0, 0, 0, 644, 646, 611, 599, 17, 14, 13, 7, 479, 736, 674, 560, 0, 0, 0, 0, 545, 720, 698, 537, 31, 37, 22, 28, 524, 680, 682, 496, 65, 58, 58, 55, 507, 648, 639, 470, 15, 28, 36, 25, 583, 640, 621, 552, 13, 15, 14, 12, 601, 657, 603, 585, 0, 0, 0, 0, 638, 652, 615, 595}

    Returns: "2221111211122112222121211221111112212211112112122221122112122112122112112211112122122122211212222111"

  6. {262, 343, 348, 259, 301, 348, 335, 304, 319, 325, 320, 292, 260, 364, 362, 258, 304, 361, 318, 332, 250, 331, 334, 270, 260, 367, 356, 252, 301, 345, 303, 316, 298, 332, 339, 300, 273, 340, 344, 274, 251, 355, 352, 278, 297, 320, 348, 299, 291, 326, 346, 289, 245, 384, 334, 285, 301, 319, 342, 295, 273, 333, 380, 257, 267, 351, 382, 262, 293, 298, 338, 309, 324, 317, 311, 343, 235, 341, 368, 261, 323, 337, 321, 278, 273, 353, 336, 279, 251, 353, 353, 257, 320, 320, 361, 285, 312, 335, 302, 300, 279, 342, 374, 256, 334, 286, 329, 314, 253, 360, 346, 278, 314, 336, 321, 284, 275, 341, 360, 269, 289, 344, 369, 288, 305, 315, 281, 309, 253, 344, 364, 265, 334, 329, 285, 326, 320, 323, 300, 293, 267, 344, 369, 284, 272, 355, 367, 284, 299, 340, 296, 287, 288, 360, 329, 284, 305, 338, 301, 295, 303, 307, 305, 316, 276, 370, 344, 279, 277, 343, 364, 250, 294, 318, 363, 291, 251, 340, 317, 297, 323, 337, 338, 297, 266, 349, 347, 275, 316, 288, 327, 332, 303, 325, 326, 325, 249, 366, 329, 277, 317, 310, 323, 277, 264, 339, 387, 283, 259, 354, 348, 270, 317, 306, 345, 301, 314, 350, 323, 300, 281, 336, 348, 248, 257, 386, 356, 234, 302, 305, 347, 313, 261, 360, 393, 274, 281, 333, 327, 271, 316, 315, 303, 280, 258, 366, 390, 272, 288, 357, 346, 277, 273, 322, 344, 293, 280, 359, 327, 251, 301, 334, 309, 339, 306, 336, 355, 220, 323, 339, 328, 293, 327, 294, 324, 302, 265, 365, 340, 283, 263, 366, 370, 264, 272, 326, 331, 308, 316, 320, 309, 302, 283, 358, 341, 271, 310, 327, 332, 303, 277, 341, 348, 262, 326, 328, 307, 280, 282, 359, 352, 266, 287, 328, 296, 291, 296, 345, 378, 279, 307, 321, 339, 318, 244, 353, 361, 257, 292, 311, 318, 307, 291, 335, 354, 292, 287, 321, 297, 301, 265, 377, 375, 277, 288, 318, 350, 297, 258, 339, 383, 267, 281, 322, 326, 270, 274, 384, 371, 272, 296, 342, 318, 305, 289, 336, 365, 249, 262, 350, 362, 275, 315, 300, 333, 303, 312, 325, 339, 307, 265, 329, 351, 272, 285, 320, 296, 289, 305, 369, 365, 271, 336, 323, 322, 300, 289, 354, 326, 250, 316, 301, 316, 319, 268, 348, 360, 272, 264, 340, 345, 245, 337, 336, 330, 303, 281, 357, 372, 267, 285, 350, 285, 303, 296, 369, 352, 251, 313, 328, 320, 271, 262, 358, 369, 282, 277, 318, 324, 310, 276, 336, 382, 263, 292, 323, 320, 308, 257, 362, 361, 258, 315, 303, 324, 320, 287, 339, 371, 251, 284, 340, 347, 281, 319, 257, 329, 334, 255, 365, 372, 269, 324, 328, 302, 305, 290, 346, 350, 255, 260, 371, 341, 278, 294, 336, 334, 286, 298, 332, 292, 289, 286, 367, 370, 266, 285, 332, 326, 338, 273, 362, 350, 234, 315, 331, 348, 295, 279, 356, 320, 256, 251, 356, 379, 278, 306, 290, 346, 294, 243, 406, 354, 241, 311, 311, 313, 321, 273, 363, 366, 268, 291, 303, 329, 307, 295, 305, 320, 293, 286, 383, 366, 252, 304, 304, 306, 331, 263, 363, 362, 267, 281, 409, 340, 244, 294, 309, 319, 304, 297, 314, 353, 316, 268, 314, 370, 268, 310, 325, 321, 321, 272, 351, 340, 260, 314, 303, 300, 314, 279, 365, 342, 283, 282, 348, 375, 264, 329, 309, 339, 254, 298, 348, 305, 300, 254, 334, 360, 301, 259, 354, 354, 236, 362, 307, 329, 299, 259, 350, 356, 285, 287, 317, 332, 314, 247, 356, 324, 283, 340, 319, 317, 314, 264, 353, 381, 245, 305, 336, 320, 296, 252, 362, 357, 281, 290, 310, 308, 340, 323, 328, 323, 305, 222, 398, 330, 271, 308, 317, 302, 285, 269, 381, 380, 258, 342, 316, 323, 276, 265, 356, 354, 268, 283, 368, 336, 262, 319, 333, 296, 303, 260, 337, 374, 275, 310, 355, 295, 294, 305, 297, 310, 321, 258, 357, 375, 277, 263, 322, 360, 274, 327, 328, 287, 339, 308, 329, 327, 288, 264, 369, 355, 260, 296, 316, 326, 314, 270, 346, 375, 257, 260, 362, 345, 275, 297, 302, 346, 313, 301, 337, 312, 311, 288, 357, 344, 250, 261, 334, 309, 318, 276, 377, 359, 266, 340, 329, 298, 327, 270, 328, 339, 269, 280, 340, 365, 271, 288, 333, 325, 298, 325, 322, 345, 268, 263, 360, 362, 255, 316, 320, 324, 297, 266, 352, 329, 296, 291, 355, 350, 289, 271, 349, 292, 303, 323, 308, 300, 313, 252, 365, 344, 295, 266, 366, 318, 285, 297, 330, 332, 306, 332, 328, 315, 296, 272, 331, 353, 273}

    Returns: "1221212212212221121121112212112111212222222222122221111111221222111221222121111122211212212221221212"

  7. {605, 631, 618, 582, 11, 21, 21, 11, 570, 695, 653, 527, 11, 15, 14, 15, 0, 0, 0, 0, 533, 746, 726, 495, 13, 13, 14, 9, 526, 657, 693, 575, 596, 637, 653, 614, 0, 0, 0, 0, 568, 604, 632, 623, 11, 27, 21, 14, 6, 7, 5, 5, 533, 719, 700, 525, 585, 648, 602, 639, 8, 9, 4, 5, 570, 678, 637, 615, 0, 0, 0, 0, 3, 5, 6, 4, 511, 723, 717, 531, 541, 736, 697, 497, 14, 3, 9, 3, 0, 0, 0, 0, 605, 642, 637, 616, 514, 709, 716, 476, 25, 17, 26, 17, 27, 29, 18, 19, 546, 695, 648, 518, 504, 646, 742, 593, 4, 4, 2, 5, 524, 724, 711, 541, 0, 0, 0, 0, 639, 604, 570, 602, 16, 28, 24, 17, 606, 668, 606, 598, 6, 3, 9, 4, 9, 12, 13, 15, 596, 647, 636, 572, 524, 726, 718, 532, 0, 0, 0, 0, 535, 713, 677, 543, 10, 7, 9, 6, 591, 632, 658, 619, 0, 0, 0, 0, 556, 747, 676, 496, 5, 6, 6, 8, 23, 19, 17, 17, 578, 616, 639, 591, 9, 14, 16, 18, 524, 722, 688, 509, 527, 696, 702, 519, 12, 11, 21, 12, 638, 604, 593, 624, 8, 12, 11, 10, 19, 28, 20, 15, 577, 607, 639, 595, 605, 652, 638, 605, 0, 0, 0, 0, 507, 716, 702, 524, 11, 11, 13, 16, 0, 0, 0, 0, 549, 713, 705, 533, 0, 0, 0, 0, 548, 737, 713, 502, 5, 3, 5, 6, 503, 724, 733, 521, 619, 631, 636, 614, 0, 0, 0, 0, 513, 753, 687, 530, 5, 5, 4, 3, 607, 630, 612, 599, 12, 15, 18, 7, 0, 0, 0, 0, 587, 661, 652, 600, 600, 654, 623, 600, 4, 7, 6, 6, 507, 714, 707, 508, 16, 17, 19, 12, 13, 14, 23, 16, 576, 595, 672, 591, 625, 644, 627, 604, 0, 0, 0, 0, 648, 603, 641, 608, 0, 0, 0, 0, 6, 5, 9, 3, 598, 619, 633, 627, 527, 691, 723, 559, 0, 0, 0, 0, 613, 623, 606, 581, 11, 19, 33, 14, 555, 738, 719, 488, 0, 0, 0, 0, 540, 673, 660, 551, 23, 15, 23, 15, 500, 689, 724, 568, 5, 4, 6, 4, 13, 9, 14, 8, 491, 745, 689, 531, 524, 713, 711, 552, 0, 0, 0, 0, 594, 634, 615, 630, 4, 5, 14, 4, 576, 617, 620, 641, 7, 17, 14, 8, 641, 605, 648, 569, 3, 15, 11, 8, 638, 656, 599, 585, 4, 9, 5, 4, 0, 0, 0, 0, 579, 623, 670, 628, 600, 586, 647, 595, 15, 23, 19, 15, 542, 666, 682, 560, 15, 12, 11, 12, 532, 702, 689, 560, 3, 2, 7, 5, 10, 22, 15, 18, 540, 704, 684, 507, 622, 637, 631, 587, 3, 8, 7, 5, 615, 643, 619, 602, 3, 6, 6, 6, 11, 10, 17, 19, 553, 650, 726, 514, 601, 649, 626, 597, 8, 3, 9, 7, 530, 677, 675, 526, 24, 22, 16, 30, 526, 684, 696, 521, 16, 18, 18, 21, 570, 680, 699, 497, 15, 14, 12, 13, 20, 19, 16, 13, 538, 675, 695, 524, 601, 651, 616, 571, 14, 12, 21, 14, 581, 647, 624, 615, 7, 13, 9, 4, 506, 700, 691, 580, 8, 4, 8, 3, 16, 18, 13, 14, 598, 607, 611, 623, 603, 631, 598, 594, 13, 18, 27, 16, 13, 18, 24, 10, 593, 642, 607, 593, 0, 0, 0, 0, 536, 719, 688, 557, 556, 698, 721, 525, 0, 0, 0, 0, 537, 711, 712, 496, 10, 9, 11, 14, 0, 0, 0, 0, 530, 714, 691, 565, 616, 588, 643, 602, 7, 19, 13, 12, 564, 606, 619, 627, 19, 30, 24, 11, 524, 719, 719, 512, 9, 5, 5, 7, 0, 0, 0, 0, 601, 634, 675, 590, 629, 618, 637, 567, 9, 10, 16, 14, 0, 0, 0, 0, 530, 734, 708, 528, 16, 19, 20, 17, 595, 628, 622, 583, 606, 632, 651, 588, 3, 9, 7, 4, 16, 26, 15, 15, 537, 714, 670, 507, 622, 631, 598, 649, 0, 0, 0, 0, 5, 7, 8, 3, 588, 629, 630, 630, 7, 7, 7, 3, 509, 750, 686, 531, 565, 614, 658, 617, 11, 14, 9, 12, 4, 7, 6, 10, 545, 708, 688, 532, 8, 14, 27, 13, 613, 635, 593, 597, 544, 719, 732, 505, 0, 0, 0, 0, 510, 690, 691, 534, 14, 22, 25, 14, 598, 607, 645, 598, 15, 7, 19, 11, 12, 16, 12, 6, 584, 653, 615, 602, 0, 0, 0, 0, 640, 627, 631, 602, 542, 693, 679, 509, 12, 24, 18, 23, 592, 613, 647, 624, 8, 5, 7, 4, 23, 26, 17, 17, 590, 630, 590, 607}

    Returns: "2122222222111211221112112121212222121211221121112122221211222221112221121211222112212221222111211121"

  8. {0, 0, 0, 0, 545, 721, 685, 549, 622, 658, 631, 589, 0, 0, 0, 0, 599, 666, 640, 595, 0, 0, 0, 0, 0, 0, 0, 0, 653, 625, 641, 581, 0, 0, 0, 0, 589, 622, 690, 599, 0, 0, 0, 0, 590, 675, 657, 578, 635, 635, 654, 576, 0, 0, 0, 0, 592, 663, 673, 572, 0, 0, 0, 0, 616, 676, 640, 568, 0, 0, 0, 0, 618, 650, 614, 618, 0, 0, 0, 0, 0, 0, 0, 0, 582, 624, 669, 625, 0, 0, 0, 0, 611, 624, 643, 622, 0, 0, 0, 0, 540, 728, 722, 510, 0, 0, 0, 0, 506, 716, 724, 554, 0, 0, 0, 0, 491, 746, 741, 522, 0, 0, 0, 0, 518, 700, 720, 562, 497, 742, 728, 533, 0, 0, 0, 0, 0, 0, 0, 0, 616, 666, 605, 613, 0, 0, 0, 0, 599, 620, 648, 633, 0, 0, 0, 0, 533, 742, 700, 525, 0, 0, 0, 0, 597, 608, 661, 634, 0, 0, 0, 0, 618, 632, 656, 594, 540, 707, 746, 507, 0, 0, 0, 0, 608, 640, 648, 604, 0, 0, 0, 0, 0, 0, 0, 0, 639, 625, 606, 630, 0, 0, 0, 0, 573, 639, 686, 602, 0, 0, 0, 0, 606, 663, 603, 628, 546, 729, 690, 535, 0, 0, 0, 0, 624, 653, 616, 607, 0, 0, 0, 0, 593, 644, 676, 587, 0, 0, 0, 0, 633, 647, 626, 594, 0, 0, 0, 0, 0, 0, 0, 0, 555, 716, 712, 517, 0, 0, 0, 0, 533, 733, 696, 538, 602, 696, 698, 504, 0, 0, 0, 0, 609, 619, 642, 630, 0, 0, 0, 0, 0, 0, 0, 0, 594, 642, 625, 639, 530, 742, 725, 503, 0, 0, 0, 0, 0, 0, 0, 0, 548, 678, 716, 558, 0, 0, 0, 0, 518, 740, 734, 508, 0, 0, 0, 0, 631, 614, 656, 599, 0, 0, 0, 0, 573, 728, 667, 532, 0, 0, 0, 0, 499, 714, 735, 552, 0, 0, 0, 0, 540, 715, 699, 546, 625, 661, 664, 550, 0, 0, 0, 0, 0, 0, 0, 0, 627, 621, 643, 609, 595, 668, 634, 603, 0, 0, 0, 0, 0, 0, 0, 0, 609, 647, 636, 608, 522, 715, 706, 557, 0, 0, 0, 0, 575, 642, 628, 655, 0, 0, 0, 0, 510, 740, 686, 564, 0, 0, 0, 0, 0, 0, 0, 0, 597, 665, 629, 609, 551, 748, 691, 510, 0, 0, 0, 0, 0, 0, 0, 0, 626, 606, 649, 619, 546, 738, 704, 512, 0, 0, 0, 0, 565, 689, 709, 537, 0, 0, 0, 0, 597, 680, 709, 514, 0, 0, 0, 0, 583, 666, 655, 596, 0, 0, 0, 0, 543, 664, 722, 571, 0, 0, 0, 0, 589, 626, 663, 622, 0, 0, 0, 0, 603, 647, 656, 594, 0, 0, 0, 0, 0, 0, 0, 0, 600, 660, 619, 621, 551, 702, 697, 550, 0, 0, 0, 0, 0, 0, 0, 0, 522, 717, 726, 535, 551, 702, 729, 518, 0, 0, 0, 0, 0, 0, 0, 0, 544, 713, 743, 500, 600, 647, 637, 616, 0, 0, 0, 0, 616, 634, 666, 584, 0, 0, 0, 0, 518, 765, 697, 520, 0, 0, 0, 0, 0, 0, 0, 0, 557, 659, 671, 613, 614, 615, 658, 613, 0, 0, 0, 0, 535, 712, 721, 532, 0, 0, 0, 0, 0, 0, 0, 0, 530, 744, 707, 519, 620, 640, 590, 650, 0, 0, 0, 0, 0, 0, 0, 0, 593, 663, 648, 596, 0, 0, 0, 0, 608, 641, 617, 634, 0, 0, 0, 0, 622, 617, 668, 593, 0, 0, 0, 0, 502, 745, 707, 546, 0, 0, 0, 0, 662, 625, 601, 612, 0, 0, 0, 0, 549, 736, 704, 511, 519, 703, 739, 539, 0, 0, 0, 0, 0, 0, 0, 0, 513, 706, 733, 548, 616, 635, 628, 621, 0, 0, 0, 0, 0, 0, 0, 0, 603, 635, 640, 622, 0, 0, 0, 0, 620, 657, 618, 605, 549, 675, 773, 503, 0, 0, 0, 0, 615, 627, 658, 600, 0, 0, 0, 0, 566, 749, 698, 487, 0, 0, 0, 0, 579, 706, 690, 525, 0, 0, 0, 0, 592, 690, 719, 499, 0, 0, 0, 0, 518, 727, 707, 548, 0, 0, 0, 0, 577, 615, 687, 621, 0, 0, 0, 0, 0, 0, 0, 0, 625, 611, 674, 590, 0, 0, 0, 0, 525, 730, 718, 527, 0, 0, 0, 0, 563, 713, 695, 529, 0, 0, 0, 0, 577, 663, 670, 590, 587, 704, 695, 514, 0, 0, 0, 0, 0, 0, 0, 0, 630, 655, 628, 587, 566, 709, 682, 543, 0, 0, 0, 0, 545, 746, 645, 564, 0, 0, 0, 0, 552, 744, 717, 487, 0, 0, 0, 0}

    Returns: "2221112222112222111211121111222221211221222212112111111121221121222112122111212122111211112122111111"

  9. {99, 137, 155, 103, 524, 483, 506, 493, 0, 0, 0, 0, 603, 668, 611, 618, 639, 606, 645, 610, 0, 0, 0, 0, 45, 50, 71, 59, 498, 614, 627, 536, 57, 69, 62, 64, 524, 588, 589, 547, 195, 303, 283, 233, 358, 396, 352, 380, 308, 328, 328, 302, 256, 351, 372, 255, 65, 61, 69, 73, 492, 662, 605, 473, 516, 498, 524, 508, 74, 142, 144, 94, 309, 412, 446, 325, 226, 262, 277, 243, 568, 577, 596, 524, 50, 71, 61, 53, 618, 637, 663, 582, 0, 0, 0, 0, 434, 457, 448, 408, 156, 222, 212, 163, 497, 517, 502, 487, 118, 118, 156, 105, 628, 618, 628, 626, 0, 0, 0, 0, 582, 555, 557, 554, 59, 68, 72, 53, 485, 539, 471, 503, 108, 138, 157, 99, 621, 641, 648, 590, 0, 0, 0, 0, 253, 261, 234, 233, 321, 445, 424, 329, 103, 153, 141, 138, 494, 486, 504, 481, 202, 289, 297, 214, 365, 367, 408, 358, 343, 413, 393, 361, 221, 270, 293, 206, 482, 664, 616, 500, 60, 65, 62, 51, 490, 651, 624, 472, 78, 67, 61, 57, 0, 0, 0, 0, 616, 645, 638, 601, 196, 194, 181, 181, 378, 464, 535, 371, 304, 290, 325, 304, 278, 374, 345, 280, 421, 589, 568, 409, 126, 137, 134, 116, 148, 250, 209, 154, 386, 445, 451, 457, 175, 177, 187, 166, 396, 481, 520, 398, 181, 308, 301, 211, 331, 421, 384, 363, 240, 251, 257, 225, 331, 423, 446, 327, 0, 0, 0, 0, 581, 657, 639, 623, 419, 602, 584, 415, 109, 126, 116, 129, 159, 212, 204, 141, 448, 477, 443, 416, 170, 212, 215, 147, 429, 469, 442, 416, 234, 263, 251, 245, 326, 438, 414, 329, 337, 409, 386, 340, 245, 263, 267, 253, 504, 595, 550, 611, 51, 62, 74, 53, 0, 0, 0, 0, 554, 703, 741, 502, 580, 537, 546, 586, 59, 69, 67, 56, 495, 633, 650, 475, 57, 65, 65, 60, 0, 0, 0, 0, 570, 710, 710, 510, 108, 139, 138, 109, 510, 514, 500, 482, 203, 311, 276, 205, 344, 373, 385, 403, 241, 259, 293, 207, 352, 433, 357, 358, 273, 385, 332, 268, 322, 326, 305, 289, 252, 352, 367, 249, 291, 371, 323, 295, 481, 515, 528, 490, 101, 137, 143, 105, 466, 507, 495, 523, 115, 149, 135, 110, 554, 615, 541, 553, 38, 69, 69, 61, 0, 0, 0, 0, 592, 648, 641, 619, 624, 629, 646, 601, 0, 0, 0, 0, 207, 258, 307, 204, 332, 428, 384, 380, 48, 66, 82, 53, 544, 582, 573, 552, 0, 0, 0, 0, 593, 642, 645, 620, 222, 266, 280, 248, 294, 435, 432, 323, 513, 672, 644, 463, 60, 47, 50, 51, 53, 83, 95, 63, 547, 551, 569, 539, 338, 394, 417, 307, 245, 268, 275, 256, 175, 207, 171, 186, 375, 481, 518, 387, 243, 256, 251, 249, 324, 460, 402, 315, 387, 380, 381, 373, 227, 307, 249, 196, 526, 580, 589, 566, 48, 68, 75, 48, 257, 276, 266, 212, 346, 427, 402, 314, 138, 133, 106, 115, 454, 526, 571, 457, 179, 203, 210, 200, 359, 483, 491, 375, 299, 429, 421, 341, 235, 220, 274, 281, 480, 514, 508, 471, 110, 145, 152, 120, 547, 712, 713, 528, 0, 0, 0, 0, 62, 61, 65, 53, 499, 611, 676, 473, 109, 133, 137, 109, 490, 548, 509, 465, 485, 505, 525, 476, 109, 149, 144, 107, 293, 312, 330, 281, 276, 343, 358, 307, 45, 99, 70, 45, 541, 557, 581, 562, 171, 215, 214, 184, 352, 503, 485, 376, 231, 269, 245, 230, 300, 437, 475, 313, 482, 515, 505, 498, 113, 153, 127, 107, 551, 516, 593, 576, 45, 84, 83, 52, 108, 150, 134, 107, 467, 537, 512, 485, 0, 0, 0, 0, 476, 747, 748, 529, 167, 201, 205, 158, 453, 432, 466, 418, 516, 602, 651, 465, 78, 69, 65, 54, 263, 355, 349, 242, 317, 314, 319, 341, 521, 492, 529, 480, 116, 126, 149, 87, 158, 232, 206, 163, 424, 462, 469, 386, 155, 220, 225, 178, 422, 480, 412, 408, 466, 632, 684, 467, 60, 71, 56, 64, 111, 130, 150, 139, 401, 563, 571, 435, 432, 441, 460, 402, 155, 220, 223, 167, 308, 300, 318, 313, 302, 336, 367, 256, 121, 124, 141, 127, 424, 572, 590, 401, 423, 448, 417, 450, 167, 197, 249, 149, 218, 298, 291, 196, 404, 328, 360, 405, 258, 247, 259, 235, 335, 419, 432, 315, 57, 63, 91, 45, 531, 594, 564, 555, 54, 69, 76, 67, 464, 648, 640, 482, 378, 378, 374, 360, 214, 275, 299, 222, 175, 184, 216, 170, 442, 440, 426, 447, 434, 570, 548, 429, 106, 152, 124, 137}

    Returns: "1122112221222222222112111221121211112122212111112221211121112222222121212212222121112111222221212211"

  10. {270, 361, 311, 257, 319, 314, 371, 297, 529, 752, 683, 536, 0, 0, 0, 0, 277, 346, 363, 270, 287, 361, 294, 302, 251, 353, 373, 269, 303, 363, 309, 279, 0, 0, 0, 0, 528, 735, 690, 547, 255, 373, 374, 279, 279, 317, 302, 321, 277, 333, 345, 280, 314, 323, 309, 319, 306, 348, 334, 306, 238, 349, 361, 258, 0, 0, 0, 0, 596, 629, 646, 629, 287, 353, 358, 286, 308, 286, 312, 310, 297, 338, 361, 270, 322, 291, 316, 305, 499, 738, 713, 550, 0, 0, 0, 0, 0, 0, 0, 0, 598, 626, 689, 587, 270, 352, 358, 276, 294, 336, 321, 293, 515, 722, 742, 521, 0, 0, 0, 0, 0, 0, 0, 0, 609, 647, 638, 606, 286, 367, 378, 252, 266, 323, 310, 318, 585, 636, 644, 635, 0, 0, 0, 0, 0, 0, 0, 0, 542, 728, 704, 526, 245, 372, 360, 259, 325, 324, 321, 294, 613, 645, 653, 589, 0, 0, 0, 0, 281, 375, 326, 278, 324, 293, 325, 298, 550, 704, 715, 531, 0, 0, 0, 0, 310, 320, 297, 307, 298, 368, 343, 257, 0, 0, 0, 0, 596, 640, 650, 614, 0, 0, 0, 0, 547, 672, 730, 551, 0, 0, 0, 0, 635, 598, 655, 612, 311, 295, 312, 286, 268, 377, 374, 277, 584, 678, 625, 613, 0, 0, 0, 0, 0, 0, 0, 0, 556, 737, 701, 506, 0, 0, 0, 0, 578, 651, 631, 640, 298, 294, 311, 310, 268, 363, 358, 298, 534, 761, 681, 524, 0, 0, 0, 0, 297, 332, 308, 311, 279, 352, 358, 263, 631, 609, 632, 628, 0, 0, 0, 0, 0, 0, 0, 0, 542, 732, 711, 515, 0, 0, 0, 0, 587, 652, 626, 635, 336, 289, 303, 321, 266, 352, 352, 281, 274, 361, 368, 268, 292, 289, 322, 326, 241, 373, 354, 285, 324, 337, 305, 281, 0, 0, 0, 0, 503, 718, 730, 549, 0, 0, 0, 0, 555, 701, 741, 503, 0, 0, 0, 0, 526, 725, 692, 557, 513, 730, 706, 551, 0, 0, 0, 0, 283, 348, 361, 275, 298, 318, 301, 316, 277, 350, 354, 239, 320, 343, 320, 297, 603, 637, 675, 585, 0, 0, 0, 0, 0, 0, 0, 0, 551, 701, 707, 541, 333, 306, 305, 295, 238, 393, 351, 279, 313, 311, 296, 324, 271, 351, 351, 283, 0, 0, 0, 0, 593, 686, 614, 607, 0, 0, 0, 0, 579, 644, 677, 600, 0, 0, 0, 0, 593, 642, 667, 598, 0, 0, 0, 0, 612, 614, 661, 613, 312, 341, 309, 302, 270, 348, 332, 286, 0, 0, 0, 0, 569, 656, 729, 546, 524, 754, 694, 528, 0, 0, 0, 0, 0, 0, 0, 0, 612, 650, 624, 614, 530, 689, 728, 553, 0, 0, 0, 0, 534, 694, 730, 542, 0, 0, 0, 0, 520, 726, 740, 514, 0, 0, 0, 0, 289, 359, 291, 320, 227, 374, 372, 268, 266, 394, 336, 244, 303, 333, 316, 308, 300, 367, 313, 298, 252, 365, 347, 258, 640, 627, 627, 606, 0, 0, 0, 0, 253, 363, 339, 279, 319, 326, 323, 298, 509, 699, 741, 551, 0, 0, 0, 0, 521, 725, 714, 540, 0, 0, 0, 0, 307, 315, 307, 294, 309, 348, 370, 250, 0, 0, 0, 0, 579, 726, 691, 504, 0, 0, 0, 0, 528, 747, 701, 524, 515, 725, 731, 529, 0, 0, 0, 0, 275, 384, 358, 248, 316, 332, 302, 285, 323, 324, 326, 271, 269, 336, 382, 269, 594, 636, 696, 574, 0, 0, 0, 0, 0, 0, 0, 0, 597, 650, 638, 615, 286, 352, 372, 234, 293, 347, 306, 310, 0, 0, 0, 0, 603, 646, 686, 565, 257, 370, 374, 286, 270, 326, 314, 303, 0, 0, 0, 0, 540, 694, 736, 530, 264, 308, 328, 304, 271, 396, 352, 277, 569, 663, 659, 609, 0, 0, 0, 0, 0, 0, 0, 0, 519, 691, 728, 562, 0, 0, 0, 0, 574, 639, 730, 557, 0, 0, 0, 0, 597, 630, 643, 630, 320, 309, 292, 321, 252, 351, 375, 280, 0, 0, 0, 0, 601, 676, 605, 618, 548, 733, 728, 491, 0, 0, 0, 0, 599, 644, 634, 623, 0, 0, 0, 0, 250, 358, 381, 245, 295, 336, 352, 283, 260, 369, 355, 257, 292, 341, 310, 316, 511, 722, 708, 559, 0, 0, 0, 0, 333, 327, 323, 323, 283, 339, 312, 260, 290, 314, 331, 293, 271, 355, 384, 262, 634, 595, 636, 635, 0, 0, 0, 0, 491, 759, 731, 519, 0, 0, 0, 0, 266, 354, 376, 259, 300, 324, 319, 302, 0, 0, 0, 0, 554, 701, 700, 545, 537, 709, 714, 540, 0, 0, 0, 0, 0, 0, 0, 0, 600, 652, 668, 580}

    Returns: "1111211211111111122121121212221212221211222111222211112211111212211122211221111222221211211122211211"

  11. {500, 663, 652, 497, 40, 50, 58, 40, 372, 516, 465, 373, 186, 194, 208, 186, 292, 405, 437, 298, 256, 289, 279, 244, 463, 453, 533, 480, 138, 181, 154, 98, 472, 681, 628, 472, 52, 63, 61, 71, 358, 480, 472, 338, 199, 224, 221, 208, 544, 590, 592, 575, 39, 66, 50, 44, 479, 547, 515, 462, 122, 123, 144, 108, 373, 418, 429, 373, 204, 254, 220, 229, 463, 636, 651, 469, 79, 69, 70, 63, 333, 352, 333, 321, 256, 351, 331, 223, 318, 375, 394, 285, 263, 280, 316, 269, 449, 475, 451, 469, 127, 178, 187, 164, 384, 495, 459, 377, 169, 188, 223, 205, 323, 412, 424, 332, 241, 256, 254, 258, 394, 400, 405, 362, 212, 278, 263, 186, 465, 427, 425, 433, 141, 229, 220, 160, 456, 450, 458, 439, 153, 214, 184, 146, 430, 553, 573, 454, 106, 124, 126, 134, 470, 633, 647, 452, 78, 71, 86, 63, 453, 597, 640, 400, 102, 101, 98, 109, 522, 570, 553, 527, 74, 94, 96, 64, 518, 618, 581, 554, 65, 55, 69, 40, 401, 476, 477, 389, 177, 216, 194, 170, 351, 406, 414, 389, 201, 253, 295, 191, 465, 636, 635, 475, 68, 78, 73, 70, 416, 416, 464, 396, 175, 237, 218, 178, 371, 517, 505, 383, 170, 178, 183, 193, 362, 529, 515, 397, 169, 179, 167, 182, 495, 491, 513, 480, 112, 159, 148, 102, 359, 348, 376, 389, 198, 295, 309, 226, 317, 460, 433, 331, 225, 272, 214, 248, 511, 560, 507, 503, 106, 100, 129, 84, 494, 540, 556, 547, 74, 106, 99, 84, 324, 374, 385, 298, 293, 292, 261, 273, 452, 600, 606, 446, 92, 108, 93, 103, 438, 619, 593, 443, 86, 91, 116, 114, 490, 522, 550, 548, 76, 117, 105, 92, 433, 482, 441, 450, 132, 218, 211, 133, 447, 516, 485, 503, 106, 155, 172, 116, 435, 575, 570, 457, 117, 124, 101, 121, 418, 510, 572, 403, 144, 172, 134, 147, 474, 604, 622, 457, 88, 86, 81, 88, 301, 387, 430, 266, 243, 295, 286, 292, 507, 638, 613, 505, 70, 60, 49, 58, 410, 448, 446, 417, 176, 220, 232, 151, 353, 381, 350, 388, 217, 305, 278, 228, 467, 610, 580, 436, 94, 119, 104, 90, 429, 415, 421, 432, 181, 228, 211, 183, 302, 408, 404, 303, 282, 258, 269, 274, 342, 476, 454, 349, 205, 227, 236, 211, 367, 426, 438, 346, 183, 287, 248, 205, 400, 541, 500, 417, 170, 152, 174, 146, 407, 455, 490, 373, 198, 197, 174, 206, 495, 612, 673, 492, 51, 54, 63, 60, 416, 614, 551, 454, 120, 113, 117, 115, 484, 501, 485, 465, 118, 161, 160, 126, 512, 559, 563, 527, 83, 88, 93, 75, 367, 483, 514, 388, 188, 202, 190, 168, 413, 597, 623, 469, 90, 97, 99, 112, 322, 418, 444, 306, 225, 265, 280, 240, 398, 512, 548, 426, 145, 178, 143, 150, 512, 520, 562, 507, 95, 113, 109, 82, 385, 445, 416, 402, 195, 243, 236, 178, 400, 448, 468, 463, 164, 203, 198, 156, 560, 571, 575, 536, 51, 64, 79, 64, 458, 604, 581, 464, 108, 89, 99, 97, 402, 557, 525, 397, 148, 123, 188, 160, 536, 583, 591, 548, 56, 65, 69, 52, 445, 470, 447, 467, 142, 197, 188, 144, 333, 424, 419, 303, 257, 240, 267, 257, 365, 470, 566, 314, 207, 206, 184, 188, 462, 463, 502, 466, 126, 185, 150, 146, 436, 537, 535, 431, 139, 145, 134, 143, 411, 424, 409, 439, 180, 216, 232, 189, 576, 512, 592, 529, 54, 86, 87, 64, 387, 498, 545, 397, 162, 177, 163, 171, 426, 573, 584, 445, 121, 119, 118, 114, 436, 580, 635, 485, 74, 93, 90, 107, 490, 501, 482, 523, 121, 134, 142, 107, 428, 594, 555, 382, 153, 144, 138, 106, 398, 553, 557, 419, 147, 160, 131, 135, 416, 609, 563, 385, 127, 132, 136, 132, 436, 476, 468, 417, 144, 182, 210, 167, 438, 467, 473, 431, 138, 202, 219, 132, 426, 488, 520, 435, 158, 153, 169, 151, 382, 388, 441, 398, 199, 238, 273, 181, 292, 430, 362, 311, 279, 309, 268, 249, 394, 429, 390, 353, 201, 245, 290, 198, 313, 402, 423, 316, 237, 264, 276, 269, 547, 562, 598, 535, 61, 78, 71, 48, 455, 604, 613, 429, 100, 130, 90, 79, 523, 558, 536, 572, 64, 103, 84, 60, 407, 474, 405, 438, 153, 228, 223, 172, 329, 481, 481, 367, 219, 211, 202, 210, 526, 584, 595, 532, 57, 58, 85, 63, 364, 345, 338, 353, 223, 332, 306, 239, 336, 353, 378, 372, 238, 289, 309, 225, 477, 614, 612, 468, 96, 86, 70, 77, 369, 458, 432, 386, 186, 246, 236, 187}

    Returns: "1112112211212112221112212121122122111222111112212112111122111122221122112122111211122121212122122212"

  12. {264, 287, 272, 296, 269, 420, 398, 294, 160, 211, 240, 156, 427, 459, 416, 431, 195, 248, 278, 209, 373, 403, 401, 393, 215, 242, 242, 221, 384, 413, 451, 332, 198, 275, 289, 202, 373, 430, 381, 352, 229, 298, 332, 231, 357, 343, 364, 346, 259, 272, 310, 237, 353, 354, 368, 347, 159, 241, 251, 182, 413, 447, 416, 391, 247, 270, 292, 196, 380, 392, 353, 370, 300, 289, 280, 292, 283, 364, 396, 296, 210, 226, 236, 223, 364, 446, 453, 342, 206, 298, 279, 261, 352, 368, 390, 346, 222, 295, 342, 240, 308, 381, 348, 364, 189, 215, 215, 173, 437, 438, 420, 413, 216, 200, 190, 186, 374, 469, 481, 384, 191, 257, 245, 175, 398, 399, 417, 418, 223, 215, 219, 210, 340, 441, 514, 338, 216, 220, 214, 197, 351, 473, 495, 334, 144, 210, 219, 152, 440, 438, 486, 411, 210, 237, 241, 227, 335, 443, 455, 352, 248, 245, 276, 273, 298, 389, 449, 322, 198, 190, 193, 214, 366, 512, 471, 356, 235, 326, 329, 212, 341, 333, 379, 345, 198, 246, 267, 229, 373, 414, 409, 364, 242, 286, 318, 230, 312, 350, 382, 380, 202, 249, 259, 201, 416, 402, 407, 364, 184, 260, 252, 219, 408, 398, 413, 366, 222, 225, 225, 217, 354, 453, 466, 338, 270, 283, 278, 299, 293, 396, 378, 303, 190, 240, 228, 243, 339, 457, 467, 336, 250, 262, 278, 253, 313, 423, 421, 300, 279, 270, 269, 303, 302, 392, 390, 295, 197, 250, 259, 190, 405, 369, 434, 396, 233, 228, 225, 197, 306, 482, 483, 346, 266, 311, 299, 234, 342, 365, 335, 348, 245, 250, 245, 212, 321, 437, 465, 325, 155, 240, 227, 147, 428, 435, 469, 399, 217, 244, 232, 232, 320, 437, 499, 319, 203, 287, 303, 201, 377, 366, 420, 343, 227, 266, 247, 195, 371, 402, 393, 399, 251, 261, 257, 214, 313, 428, 450, 326, 211, 224, 235, 213, 312, 479, 475, 351, 200, 235, 253, 217, 388, 388, 409, 410, 237, 333, 317, 249, 349, 348, 350, 317, 246, 269, 252, 240, 324, 428, 418, 323, 197, 184, 213, 184, 385, 515, 483, 339, 223, 195, 235, 223, 383, 460, 442, 339, 249, 293, 330, 248, 349, 352, 354, 325, 233, 250, 270, 239, 331, 430, 452, 295, 293, 267, 287, 279, 305, 399, 367, 303, 262, 249, 245, 274, 319, 431, 400, 320, 181, 187, 193, 203, 367, 512, 490, 367, 257, 280, 326, 276, 278, 402, 365, 316, 228, 248, 221, 227, 316, 419, 476, 365, 210, 318, 317, 236, 390, 377, 352, 300, 216, 308, 262, 214, 355, 378, 365, 402, 219, 330, 301, 215, 340, 353, 361, 381, 205, 214, 219, 202, 352, 460, 495, 353, 175, 198, 229, 145, 422, 438, 438, 455, 185, 214, 227, 159, 412, 424, 460, 419, 259, 221, 263, 230, 325, 446, 438, 318, 230, 279, 335, 245, 334, 347, 363, 367, 241, 240, 253, 229, 325, 446, 425, 341, 201, 232, 208, 185, 378, 434, 465, 397, 236, 295, 320, 206, 340, 396, 370, 337, 263, 304, 264, 276, 314, 402, 377, 300, 203, 214, 206, 181, 361, 483, 504, 348, 167, 256, 220, 173, 389, 448, 445, 402, 180, 182, 193, 191, 367, 507, 503, 377, 165, 257, 237, 180, 389, 394, 468, 410, 161, 233, 223, 166, 434, 418, 413, 452, 251, 329, 292, 246, 328, 379, 364, 311, 241, 299, 303, 242, 349, 362, 388, 316, 244, 266, 269, 222, 300, 410, 444, 345, 258, 237, 241, 260, 309, 440, 422, 333, 202, 259, 265, 179, 417, 432, 379, 367, 200, 205, 185, 179, 349, 493, 519, 370, 187, 260, 236, 205, 409, 392, 412, 399, 186, 267, 282, 216, 359, 403, 390, 397, 233, 218, 251, 209, 371, 411, 460, 347, 168, 197, 211, 185, 386, 476, 498, 379, 209, 234, 245, 216, 328, 462, 453, 353, 172, 248, 243, 182, 424, 408, 437, 386, 191, 283, 261, 191, 376, 404, 404, 390, 173, 220, 260, 151, 403, 458, 438, 397, 227, 311, 301, 235, 340, 346, 371, 369, 251, 246, 248, 246, 334, 420, 440, 315, 273, 263, 253, 244, 292, 389, 469, 317, 219, 248, 213, 204, 344, 459, 488, 325, 240, 271, 274, 251, 351, 410, 411, 292, 201, 259, 265, 205, 406, 419, 389, 356, 212, 296, 293, 218, 357, 412, 341, 371, 173, 196, 212, 202, 346, 503, 501, 367, 165, 245, 236, 173, 385, 426, 454, 416, 248, 304, 318, 244, 346, 340, 337, 363, 260, 297, 313, 258, 295, 376, 405, 296, 201, 266, 307, 207, 365, 395, 373, 386, 244, 337, 292, 210, 359, 361, 344, 353, 199, 237, 262, 177, 372, 414, 434, 405, 200, 263, 293, 200, 347, 419, 393, 385}

    Returns: "2112111112211121221222111112222212121211221122212222221112112121122121111221211222111122221121121111"

  13. {219, 270, 261, 224, 333, 396, 446, 351, 176, 158, 214, 173, 380, 518, 481, 400, 165, 211, 227, 163, 424, 448, 414, 448, 166, 233, 227, 181, 430, 437, 415, 411, 234, 254, 269, 247, 296, 428, 436, 336, 195, 169, 207, 192, 352, 515, 484, 386, 176, 243, 259, 184, 417, 399, 419, 403, 159, 227, 205, 178, 428, 423, 449, 431, 210, 281, 276, 201, 367, 387, 409, 369, 149, 246, 264, 159, 389, 427, 456, 410, 266, 255, 261, 233, 301, 405, 431, 348, 242, 275, 233, 256, 330, 418, 423, 323, 245, 268, 245, 252, 333, 453, 420, 284, 188, 249, 245, 180, 386, 409, 429, 414, 252, 233, 291, 230, 328, 400, 432, 334, 221, 259, 274, 260, 324, 435, 409, 318, 226, 262, 229, 219, 346, 481, 436, 301, 225, 260, 280, 232, 321, 454, 436, 292, 168, 218, 223, 160, 416, 464, 423, 428, 189, 225, 221, 226, 349, 487, 439, 364, 209, 216, 237, 224, 357, 445, 466, 346, 163, 240, 219, 164, 416, 454, 435, 409, 176, 174, 161, 194, 382, 537, 516, 360, 219, 276, 246, 198, 383, 404, 374, 400, 154, 207, 185, 157, 420, 455, 462, 460, 226, 278, 300, 208, 353, 375, 396, 364, 272, 270, 267, 272, 275, 437, 408, 299, 155, 188, 175, 178, 378, 496, 539, 391, 187, 231, 181, 188, 364, 487, 511, 351, 199, 285, 283, 220, 338, 379, 415, 381, 173, 170, 231, 190, 392, 486, 506, 352, 230, 264, 270, 224, 352, 392, 370, 398, 180, 225, 233, 181, 339, 495, 477, 370, 203, 217, 213, 172, 353, 491, 487, 364, 200, 190, 222, 191, 343, 495, 509, 350, 177, 229, 229, 172, 405, 418, 449, 421, 203, 216, 218, 190, 319, 533, 483, 338, 235, 304, 318, 219, 354, 357, 359, 354, 261, 259, 301, 241, 346, 367, 400, 325, 251, 254, 277, 252, 281, 435, 437, 313, 176, 215, 224, 203, 419, 410, 451, 402, 213, 249, 237, 231, 329, 451, 464, 326, 167, 198, 213, 149, 410, 462, 485, 416, 192, 272, 278, 223, 341, 397, 408, 389, 228, 218, 214, 219, 341, 492, 438, 350, 161, 176, 198, 147, 397, 461, 474, 486, 179, 166, 184, 143, 432, 510, 526, 360, 235, 226, 258, 235, 361, 450, 413, 322, 194, 220, 235, 199, 329, 499, 471, 353, 214, 294, 302, 209, 350, 389, 352, 390, 206, 285, 269, 220, 365, 420, 377, 358, 170, 185, 199, 181, 369, 522, 481, 393, 158, 222, 217, 164, 415, 419, 457, 448, 175, 179, 238, 172, 424, 454, 430, 428, 143, 191, 205, 148, 463, 452, 467, 431, 152, 189, 156, 176, 389, 516, 533, 389, 209, 229, 232, 196, 343, 486, 470, 335, 228, 323, 284, 219, 375, 393, 341, 337, 279, 264, 263, 282, 311, 409, 381, 311, 166, 217, 202, 165, 436, 434, 462, 418, 271, 261, 232, 219, 338, 414, 420, 345, 186, 193, 233, 176, 393, 468, 433, 418, 195, 207, 189, 199, 374, 474, 495, 367, 206, 254, 245, 213, 394, 395, 428, 365, 188, 251, 260, 204, 403, 428, 376, 390, 208, 199, 230, 181, 367, 463, 481, 371, 205, 198, 183, 196, 375, 498, 477, 368, 212, 202, 219, 189, 363, 491, 453, 371, 238, 242, 252, 226, 355, 405, 446, 336, 148, 208, 223, 182, 439, 449, 450, 401, 197, 200, 202, 170, 393, 476, 475, 387, 186, 218, 213, 194, 360, 478, 486, 365, 162, 210, 195, 163, 413, 451, 469, 437, 172, 253, 261, 209, 374, 432, 408, 391, 209, 253, 261, 214, 386, 402, 394, 381, 260, 247, 256, 253, 317, 421, 436, 310, 161, 167, 163, 192, 402, 513, 506, 396, 189, 193, 226, 207, 361, 508, 493, 323, 235, 243, 241, 242, 351, 439, 424, 325, 235, 287, 297, 224, 357, 381, 376, 343, 238, 240, 240, 239, 328, 447, 477, 291, 218, 255, 214, 217, 331, 456, 465, 344, 184, 254, 246, 189, 419, 429, 401, 378, 195, 227, 216, 232, 348, 465, 464, 353, 232, 262, 242, 201, 342, 429, 464, 328, 210, 241, 239, 170, 395, 455, 419, 371, 211, 284, 318, 222, 352, 371, 392, 350, 144, 224, 222, 160, 415, 453, 440, 442, 224, 296, 292, 239, 364, 367, 386, 332, 210, 304, 283, 223, 377, 370, 368, 365, 147, 216, 213, 140, 435, 440, 451, 458, 278, 277, 265, 245, 270, 430, 420, 315, 236, 315, 286, 234, 317, 362, 400, 350, 264, 246, 277, 226, 316, 440, 425, 306, 154, 205, 232, 141, 417, 461, 487, 403, 260, 254, 259, 237, 319, 393, 455, 323, 192, 256, 240, 183, 402, 414, 412, 401, 162, 203, 208, 163, 442, 449, 438, 435, 227, 243, 235, 245, 354, 417, 433, 346, 139, 217, 227, 174, 412, 477, 468, 386}

    Returns: "2211221111222122221221211122212122212122121121222112111221212121122221221112222122122111111212121121"

  14. {352, 382, 409, 383, 220, 282, 269, 203, 359, 487, 459, 380, 216, 202, 226, 171, 308, 406, 410, 326, 231, 261, 288, 270, 395, 377, 431, 413, 201, 232, 256, 195, 359, 491, 463, 339, 224, 217, 211, 196, 346, 374, 369, 347, 221, 314, 287, 242, 394, 361, 395, 338, 210, 310, 309, 183, 324, 374, 356, 360, 248, 292, 312, 234, 418, 414, 401, 388, 200, 241, 228, 210, 344, 355, 359, 361, 203, 350, 306, 222, 371, 397, 390, 370, 219, 270, 277, 206, 367, 376, 384, 382, 191, 298, 285, 217, 301, 443, 418, 351, 226, 217, 283, 261, 413, 434, 441, 423, 179, 236, 216, 158, 367, 347, 384, 347, 212, 310, 308, 225, 358, 416, 419, 437, 172, 243, 251, 204, 363, 383, 380, 364, 228, 311, 255, 216, 381, 378, 373, 370, 206, 264, 302, 226, 389, 399, 405, 403, 201, 253, 260, 190, 319, 408, 436, 328, 246, 260, 260, 243, 379, 411, 395, 357, 204, 257, 260, 237, 365, 453, 516, 352, 220, 206, 207, 181, 351, 475, 467, 371, 207, 200, 211, 218, 342, 512, 464, 347, 199, 195, 220, 221, 319, 448, 401, 325, 263, 277, 229, 238, 323, 381, 424, 301, 275, 273, 259, 264, 338, 438, 428, 318, 227, 275, 253, 223, 345, 406, 435, 330, 229, 251, 249, 255, 320, 399, 394, 291, 270, 275, 268, 283, 334, 470, 471, 298, 229, 238, 246, 214, 350, 492, 495, 306, 224, 226, 213, 194, 360, 347, 396, 378, 207, 303, 272, 237, 396, 409, 443, 369, 200, 223, 264, 196, 297, 411, 414, 340, 271, 269, 262, 236, 354, 495, 492, 352, 186, 189, 213, 219, 407, 464, 481, 394, 182, 204, 179, 189, 325, 417, 449, 329, 220, 264, 242, 254, 357, 417, 432, 429, 189, 254, 223, 199, 344, 385, 364, 327, 223, 318, 313, 226, 383, 425, 372, 419, 194, 263, 247, 197, 337, 448, 425, 345, 230, 246, 243, 226, 385, 355, 360, 377, 205, 284, 314, 220, 415, 431, 402, 377, 184, 291, 217, 183, 375, 442, 457, 416, 184, 221, 225, 180, 372, 402, 403, 406, 221, 254, 271, 171, 314, 461, 431, 321, 228, 242, 261, 242, 335, 454, 471, 313, 244, 254, 221, 208, 413, 418, 455, 409, 165, 261, 218, 161, 299, 462, 427, 296, 237, 278, 265, 236, 312, 395, 424, 302, 267, 278, 271, 251, 324, 422, 434, 345, 241, 267, 234, 233, 331, 469, 441, 341, 240, 211, 221, 246, 364, 455, 485, 350, 211, 215, 218, 202, 312, 460, 433, 326, 205, 241, 287, 236, 309, 430, 434, 300, 229, 280, 265, 253, 309, 407, 413, 297, 270, 249, 306, 249, 325, 425, 393, 313, 270, 272, 259, 243, 349, 430, 397, 442, 179, 250, 252, 201, 389, 372, 407, 362, 198, 272, 301, 199, 315, 429, 428, 351, 233, 247, 235, 262, 399, 447, 472, 381, 179, 213, 246, 163, 440, 436, 423, 420, 161, 219, 225, 176, 425, 416, 445, 407, 171, 223, 230, 183, 348, 429, 429, 345, 223, 242, 267, 217, 345, 463, 471, 329, 223, 242, 229, 198, 304, 434, 441, 294, 260, 248, 270, 249, 325, 439, 424, 305, 245, 261, 252, 249, 298, 394, 411, 288, 287, 303, 270, 249, 353, 476, 455, 355, 195, 227, 230, 209, 342, 455, 406, 326, 238, 250, 232, 251, 413, 444, 389, 396, 182, 267, 244, 165, 399, 416, 425, 395, 174, 249, 259, 183, 334, 446, 418, 302, 245, 259, 241, 255, 333, 425, 463, 310, 245, 253, 246, 225, 418, 414, 402, 421, 188, 249, 235, 173, 359, 447, 481, 361, 223, 203, 225, 201, 374, 395, 436, 377, 174, 300, 263, 181, 363, 468, 487, 397, 171, 200, 220, 194, 369, 370, 409, 381, 216, 278, 284, 193, 340, 388, 393, 351, 210, 274, 308, 236, 324, 409, 438, 317, 246, 265, 277, 224, 328, 393, 411, 296, 246, 266, 272, 288, 402, 352, 402, 392, 223, 260, 274, 195, 312, 417, 395, 295, 262, 307, 284, 228, 350, 345, 397, 353, 250, 287, 294, 224, 318, 399, 409, 302, 259, 297, 268, 248, 392, 417, 390, 385, 199, 255, 257, 205, 348, 362, 374, 380, 211, 306, 291, 228, 395, 421, 418, 420, 159, 222, 265, 200, 397, 430, 405, 370, 201, 256, 264, 177, 427, 407, 419, 415, 183, 213, 236, 200, 411, 417, 427, 407, 161, 252, 238, 187, 345, 458, 492, 354, 211, 219, 216, 205, 330, 428, 436, 339, 219, 254, 247, 247, 415, 400, 417, 408, 179, 229, 264, 188, 353, 459, 448, 336, 225, 228, 235, 216, 398, 436, 416, 426, 170, 255, 222, 177, 371, 440, 466, 357, 204, 216, 223, 223, 304, 431, 430, 354, 228, 239, 257, 257, 371, 407, 413, 368, 201, 273, 275, 192}

    Returns: "2112122222221222222121111111111221111222122221121111111112212221111111221121212211212122222211212112"

  15. {212, 252, 226, 202, 335, 421, 494, 358, 265, 367, 354, 269, 283, 320, 328, 314, 304, 300, 334, 305, 251, 366, 375, 265, 262, 353, 371, 262, 322, 312, 323, 295, 237, 247, 214, 201, 336, 452, 446, 367, 309, 253, 286, 267, 287, 398, 389, 311, 280, 282, 305, 281, 271, 415, 385, 281, 242, 266, 286, 256, 317, 426, 401, 306, 213, 316, 289, 237, 387, 371, 360, 327, 247, 251, 271, 246, 328, 413, 427, 317, 316, 368, 344, 256, 303, 308, 299, 306, 226, 236, 260, 231, 301, 407, 447, 392, 220, 254, 259, 261, 340, 452, 384, 330, 217, 273, 310, 216, 367, 387, 368, 362, 275, 346, 379, 264, 289, 314, 330, 303, 278, 355, 347, 268, 295, 323, 329, 305, 284, 272, 273, 253, 309, 418, 395, 296, 207, 280, 325, 218, 342, 390, 380, 358, 248, 257, 283, 241, 342, 414, 407, 308, 315, 330, 329, 274, 264, 372, 348, 268, 252, 343, 328, 255, 339, 330, 331, 322, 262, 274, 274, 267, 302, 372, 431, 318, 259, 268, 287, 259, 295, 420, 433, 279, 217, 284, 292, 238, 336, 409, 356, 368, 258, 331, 377, 270, 292, 309, 321, 342, 205, 246, 252, 189, 419, 434, 401, 354, 221, 230, 266, 243, 333, 440, 441, 326, 201, 306, 300, 201, 386, 382, 360, 364, 225, 261, 291, 214, 306, 435, 422, 346, 158, 266, 260, 180, 395, 431, 416, 394, 222, 281, 301, 196, 376, 380, 381, 363, 243, 262, 236, 229, 338, 455, 423, 314, 243, 253, 217, 218, 328, 433, 471, 337, 260, 309, 354, 224, 317, 353, 353, 330, 254, 266, 264, 263, 321, 395, 435, 302, 220, 227, 176, 228, 362, 495, 444, 348, 282, 359, 308, 271, 263, 378, 337, 302, 288, 305, 307, 317, 258, 373, 381, 271, 300, 341, 291, 297, 275, 373, 334, 289, 291, 343, 367, 283, 305, 293, 327, 291, 332, 303, 263, 306, 285, 365, 356, 290, 277, 298, 310, 264, 280, 413, 360, 298, 304, 330, 305, 274, 293, 362, 355, 277, 256, 227, 240, 270, 310, 439, 424, 334, 221, 275, 297, 219, 343, 378, 402, 365, 179, 279, 252, 191, 373, 415, 418, 393, 266, 327, 336, 310, 281, 381, 343, 256, 282, 303, 352, 323, 244, 354, 383, 259, 260, 303, 320, 299, 285, 392, 381, 260, 248, 301, 252, 248, 294, 428, 434, 295, 324, 327, 305, 304, 269, 350, 367, 254, 229, 305, 316, 237, 360, 368, 358, 327, 240, 349, 352, 267, 317, 339, 328, 308, 217, 297, 289, 212, 372, 372, 383, 358, 265, 262, 266, 286, 299, 428, 386, 308, 217, 275, 294, 236, 306, 403, 463, 306, 288, 317, 332, 247, 358, 327, 332, 299, 308, 314, 303, 287, 291, 343, 388, 266, 250, 323, 368, 280, 313, 314, 318, 334, 204, 264, 273, 237, 377, 378, 396, 371, 198, 256, 263, 199, 380, 407, 405, 392, 231, 325, 309, 238, 344, 381, 348, 324, 275, 342, 365, 276, 287, 327, 310, 318, 269, 281, 254, 249, 311, 414, 433, 289, 257, 359, 360, 268, 323, 318, 314, 301, 224, 219, 205, 231, 351, 452, 494, 324, 253, 288, 313, 284, 306, 362, 413, 281, 267, 281, 297, 264, 288, 405, 397, 301, 186, 269, 239, 199, 393, 409, 400, 405, 227, 293, 305, 229, 309, 363, 387, 387, 310, 321, 314, 294, 292, 350, 353, 266, 194, 209, 234, 239, 353, 478, 469, 324, 310, 346, 345, 318, 244, 350, 343, 244, 220, 266, 281, 189, 365, 407, 405, 367, 282, 328, 326, 261, 298, 358, 354, 293, 224, 304, 319, 242, 362, 373, 362, 314, 298, 285, 328, 271, 312, 342, 401, 263, 272, 378, 363, 275, 305, 292, 330, 285, 225, 316, 347, 223, 298, 379, 388, 324, 289, 344, 364, 268, 312, 313, 311, 299, 202, 299, 292, 213, 359, 382, 391, 362, 260, 344, 372, 265, 302, 355, 284, 318, 220, 281, 281, 184, 351, 392, 423, 368, 245, 317, 317, 252, 317, 372, 346, 334, 239, 312, 329, 240, 331, 360, 362, 327, 180, 262, 245, 211, 389, 418, 425, 370, 267, 285, 284, 271, 275, 410, 412, 296, 215, 328, 306, 218, 359, 355, 369, 350, 278, 285, 317, 302, 303, 353, 379, 283, 304, 306, 338, 333, 264, 346, 341, 268, 238, 230, 277, 189, 383, 383, 410, 390, 246, 238, 273, 245, 336, 430, 402, 330, 200, 238, 256, 184, 393, 443, 400, 386, 322, 321, 353, 305, 246, 332, 361, 260, 208, 258, 258, 251, 333, 440, 430, 322, 189, 277, 243, 201, 369, 421, 401, 399, 201, 293, 263, 235, 366, 382, 367, 393, 294, 264, 295, 285, 274, 406, 385, 297, 261, 332, 300, 297, 271, 388, 392, 259, 291, 321, 316, 312, 276, 375, 353, 256}

    Returns: "2121222212122111212212211121211221222221222211222221112212111112122211222121211111111121221212211222"

  16. {158, 224, 240, 156, 390, 448, 460, 424, 245, 367, 323, 247, 300, 336, 341, 341, 196, 224, 186, 188, 384, 490, 493, 339, 206, 257, 216, 168, 402, 443, 412, 396, 213, 341, 338, 237, 351, 339, 360, 321, 169, 256, 233, 165, 378, 423, 453, 423, 259, 247, 256, 260, 317, 416, 427, 318, 235, 287, 283, 260, 306, 420, 417, 292, 316, 304, 318, 296, 272, 375, 366, 253, 175, 195, 241, 174, 411, 467, 432, 405, 139, 146, 158, 140, 393, 582, 552, 390, 163, 233, 216, 165, 428, 426, 441, 428, 243, 238, 270, 221, 353, 418, 472, 285, 185, 247, 259, 206, 381, 414, 423, 385, 197, 283, 256, 194, 397, 386, 389, 398, 186, 175, 175, 196, 365, 504, 513, 386, 204, 291, 303, 187, 404, 381, 345, 385, 250, 327, 359, 248, 339, 316, 343, 318, 197, 229, 216, 204, 386, 440, 471, 357, 267, 298, 317, 276, 295, 385, 386, 276, 143, 138, 159, 140, 389, 523, 568, 440, 214, 269, 270, 199, 370, 422, 383, 373, 247, 231, 245, 262, 313, 445, 442, 315, 105, 161, 178, 120, 480, 524, 486, 446, 271, 342, 368, 246, 299, 325, 355, 294, 215, 260, 247, 226, 317, 432, 451, 352, 202, 240, 303, 204, 356, 387, 405, 403, 192, 260, 259, 205, 379, 402, 438, 365, 224, 299, 279, 209, 371, 379, 383, 356, 309, 310, 317, 313, 253, 336, 373, 289, 152, 233, 236, 156, 428, 430, 436, 429, 191, 189, 213, 190, 375, 480, 519, 343, 260, 249, 249, 239, 323, 435, 435, 310, 211, 218, 235, 210, 362, 442, 457, 365, 136, 195, 212, 144, 461, 464, 460, 428, 121, 153, 168, 124, 460, 491, 499, 484, 249, 329, 342, 231, 333, 338, 343, 335, 229, 244, 257, 253, 319, 441, 436, 321, 136, 140, 146, 140, 420, 551, 576, 391, 179, 158, 162, 149, 394, 480, 574, 404, 222, 344, 321, 231, 302, 378, 354, 348, 127, 145, 126, 135, 419, 580, 575, 393, 197, 335, 331, 230, 334, 354, 368, 351, 223, 252, 253, 247, 336, 434, 414, 341, 297, 299, 291, 288, 288, 378, 377, 282, 166, 187, 180, 175, 401, 527, 499, 365, 263, 350, 359, 263, 346, 319, 323, 277, 275, 355, 382, 268, 301, 312, 312, 295, 234, 220, 258, 222, 340, 458, 429, 339, 274, 298, 279, 285, 275, 419, 377, 293, 166, 166, 183, 156, 379, 527, 537, 386, 123, 149, 157, 129, 464, 483, 501, 494, 256, 334, 314, 282, 316, 324, 358, 316, 269, 316, 312, 277, 305, 403, 335, 283, 187, 169, 159, 157, 412, 487, 556, 373, 212, 349, 345, 221, 350, 345, 350, 328, 130, 190, 184, 116, 446, 499, 477, 458, 196, 176, 160, 164, 400, 503, 507, 394, 166, 235, 204, 170, 380, 444, 472, 429, 228, 234, 240, 220, 323, 461, 461, 333, 199, 269, 279, 197, 363, 392, 418, 383, 156, 237, 226, 179, 421, 447, 436, 398, 165, 203, 180, 177, 364, 517, 523, 371, 185, 193, 208, 198, 355, 470, 517, 374, 208, 281, 289, 203, 360, 378, 416, 365, 171, 191, 200, 165, 424, 491, 462, 396, 274, 297, 280, 260, 324, 425, 361, 279, 226, 225, 240, 205, 349, 437, 454, 364, 220, 245, 238, 204, 356, 471, 448, 318, 209, 231, 246, 237, 349, 466, 440, 322, 184, 254, 226, 176, 417, 447, 427, 369, 209, 288, 294, 219, 375, 375, 355, 385, 183, 187, 182, 174, 394, 493, 505, 382, 233, 226, 254, 217, 345, 469, 433, 323, 220, 252, 245, 261, 319, 436, 443, 324, 236, 284, 251, 252, 347, 406, 399, 325, 243, 224, 209, 206, 356, 462, 450, 350, 200, 256, 286, 199, 406, 387, 376, 390, 282, 305, 268, 257, 296, 385, 373, 334, 177, 199, 169, 156, 415, 502, 485, 397, 193, 225, 221, 208, 352, 462, 482, 357, 282, 347, 333, 260, 298, 306, 343, 331, 234, 292, 305, 224, 350, 374, 371, 350, 269, 334, 317, 234, 356, 357, 338, 295, 238, 253, 263, 239, 307, 463, 433, 304, 117, 156, 176, 123, 466, 493, 521, 448, 257, 272, 296, 248, 302, 417, 406, 302, 182, 247, 258, 169, 407, 391, 431, 415, 272, 301, 278, 295, 292, 397, 362, 303, 269, 313, 294, 249, 344, 363, 367, 301, 219, 320, 296, 214, 392, 366, 358, 335, 325, 304, 313, 299, 264, 360, 358, 277, 285, 299, 281, 268, 288, 400, 369, 310, 286, 298, 299, 274, 291, 383, 387, 282, 138, 144, 151, 144, 406, 535, 570, 412, 125, 150, 143, 135, 478, 491, 511, 467, 223, 239, 244, 193, 350, 463, 451, 337, 260, 285, 269, 267, 287, 406, 397, 329, 149, 125, 140, 128, 386, 572, 566, 434, 304, 322, 332, 268, 264, 388, 339, 283}

    Returns: "1121112221212112112221211211121222111222121222112221122112121122112222112222212221112121211222212222"

  17. {457, 575, 588, 448, 104, 111, 105, 112, 273, 365, 352, 277, 284, 344, 309, 296, 255, 383, 320, 261, 328, 305, 346, 302, 429, 590, 489, 399, 140, 163, 149, 141, 417, 556, 526, 446, 122, 138, 160, 135, 319, 379, 353, 315, 240, 317, 329, 248, 316, 440, 472, 367, 231, 210, 215, 249, 334, 326, 332, 306, 252, 356, 352, 242, 332, 446, 372, 377, 230, 287, 267, 189, 417, 425, 430, 406, 185, 248, 219, 170, 463, 524, 530, 477, 100, 157, 133, 116, 337, 415, 352, 393, 201, 310, 272, 220, 235, 398, 352, 286, 295, 336, 304, 294, 373, 512, 543, 374, 159, 170, 185, 184, 384, 536, 484, 393, 174, 196, 174, 159, 478, 645, 626, 418, 93, 79, 79, 82, 417, 455, 482, 452, 154, 205, 191, 144, 494, 524, 505, 489, 97, 147, 147, 97, 490, 526, 487, 471, 119, 136, 161, 110, 408, 445, 417, 395, 167, 251, 224, 193, 359, 378, 380, 333, 208, 294, 317, 231, 526, 459, 490, 425, 108, 165, 208, 119, 259, 306, 346, 266, 308, 362, 342, 311, 476, 527, 488, 472, 109, 172, 135, 121, 459, 558, 566, 396, 143, 125, 135, 118, 301, 420, 425, 323, 262, 267, 251, 251, 341, 473, 458, 353, 204, 226, 218, 227, 396, 589, 545, 434, 120, 130, 149, 137, 318, 472, 398, 319, 217, 257, 240, 279, 439, 439, 452, 419, 154, 212, 204, 181, 399, 431, 400, 427, 177, 255, 238, 173, 256, 356, 332, 266, 322, 331, 315, 322, 412, 391, 389, 376, 204, 264, 263, 201, 554, 635, 632, 564, 18, 33, 39, 25, 449, 535, 578, 388, 123, 139, 147, 141, 408, 481, 534, 390, 180, 171, 171, 165, 529, 537, 526, 492, 89, 126, 122, 79, 301, 346, 328, 306, 253, 323, 361, 282, 430, 544, 568, 447, 135, 131, 116, 129, 317, 333, 359, 306, 252, 315, 352, 266, 426, 455, 431, 369, 177, 232, 249, 161, 516, 508, 518, 500, 92, 131, 145, 90, 371, 561, 568, 433, 158, 128, 139, 142, 271, 343, 390, 294, 292, 301, 324, 285, 493, 620, 623, 507, 63, 64, 69, 61, 399, 527, 531, 410, 162, 148, 170, 153, 431, 586, 581, 420, 115, 120, 126, 121, 269, 355, 357, 279, 297, 317, 302, 324, 365, 438, 477, 332, 217, 221, 225, 225, 518, 554, 573, 534, 73, 93, 91, 64, 259, 396, 354, 251, 299, 337, 317, 287, 283, 372, 354, 244, 288, 341, 309, 309, 469, 491, 538, 482, 119, 150, 133, 118, 434, 477, 479, 454, 138, 194, 166, 158, 284, 338, 364, 275, 301, 307, 334, 297, 463, 599, 635, 467, 74, 90, 82, 90, 300, 294, 339, 311, 259, 352, 369, 276, 479, 500, 482, 467, 134, 167, 158, 113, 391, 497, 512, 365, 167, 198, 192, 178, 306, 393, 417, 313, 262, 259, 287, 263, 403, 557, 528, 418, 156, 156, 120, 162, 292, 365, 377, 288, 307, 317, 293, 261, 433, 458, 462, 464, 157, 198, 191, 137, 536, 588, 589, 536, 54, 67, 67, 63, 501, 537, 506, 497, 104, 130, 120, 105, 320, 364, 350, 326, 241, 326, 328, 245, 319, 310, 337, 324, 261, 341, 360, 248, 511, 665, 656, 502, 44, 48, 34, 40, 593, 613, 572, 599, 29, 32, 35, 27, 457, 618, 568, 451, 88, 116, 100, 102, 360, 380, 418, 396, 191, 294, 253, 208, 452, 457, 419, 408, 166, 213, 216, 169, 432, 478, 414, 427, 162, 206, 224, 157, 279, 405, 370, 279, 271, 321, 296, 279, 308, 368, 353, 311, 292, 307, 285, 276, 310, 413, 432, 355, 235, 286, 234, 235, 460, 647, 625, 471, 69, 73, 78, 77, 447, 570, 603, 443, 101, 118, 110, 108, 479, 594, 626, 421, 100, 96, 95, 89, 295, 364, 370, 240, 323, 292, 325, 291, 489, 639, 688, 513, 45, 50, 41, 35, 578, 590, 613, 562, 28, 42, 55, 32, 392, 536, 559, 415, 145, 154, 158, 141, 282, 336, 304, 320, 247, 377, 352, 282, 294, 282, 284, 297, 315, 370, 351, 307, 386, 556, 515, 375, 156, 175, 171, 166, 366, 381, 386, 377, 209, 281, 281, 219, 453, 590, 596, 452, 87, 118, 88, 116, 391, 450, 432, 408, 161, 230, 247, 181, 445, 636, 557, 412, 114, 114, 102, 120, 471, 649, 625, 488, 73, 61, 65, 68, 445, 546, 565, 418, 118, 122, 141, 145, 391, 443, 429, 431, 176, 215, 240, 175, 476, 655, 607, 492, 70, 79, 64, 57, 517, 580, 563, 508, 65, 90, 99, 78, 351, 379, 355, 330, 245, 322, 313, 205, 422, 435, 447, 432, 152, 233, 218, 161, 322, 357, 359, 310, 233, 362, 319, 238, 422, 551, 564, 391, 138, 158, 143, 133, 541, 495, 513, 474, 91, 141, 117, 128}

    Returns: "1111121222221111222222121111122122112212221111111211221122111122222121222111111112122121211121222212"

  18. {594, 581, 616, 606, 18, 28, 27, 30, 569, 643, 610, 568, 24, 29, 34, 23, 315, 449, 439, 280, 234, 265, 266, 252, 409, 539, 526, 389, 167, 146, 161, 163, 305, 268, 319, 321, 266, 367, 380, 274, 381, 481, 576, 399, 168, 169, 168, 158, 121, 139, 125, 110, 424, 612, 562, 407, 152, 154, 164, 172, 389, 549, 533, 387, 429, 567, 597, 442, 114, 97, 122, 132, 266, 266, 281, 255, 332, 413, 394, 293, 182, 274, 291, 243, 378, 393, 400, 339, 570, 598, 615, 589, 28, 31, 39, 30, 226, 279, 283, 239, 323, 431, 415, 304, 365, 358, 341, 334, 223, 313, 329, 237, 286, 266, 280, 263, 315, 401, 370, 319, 98, 96, 107, 82, 472, 590, 586, 469, 276, 324, 330, 320, 254, 350, 365, 281, 419, 406, 454, 384, 174, 233, 251, 179, 258, 370, 345, 246, 325, 323, 318, 315, 187, 251, 225, 175, 411, 441, 441, 369, 386, 461, 424, 392, 158, 246, 262, 171, 357, 392, 363, 345, 213, 324, 291, 215, 297, 445, 391, 289, 242, 280, 278, 278, 126, 217, 187, 164, 441, 432, 483, 450, 547, 682, 702, 480, 18, 26, 27, 18, 221, 319, 275, 205, 339, 376, 387, 378, 388, 412, 410, 382, 193, 251, 267, 197, 586, 592, 591, 564, 38, 49, 47, 33, 508, 566, 561, 555, 66, 88, 95, 61, 179, 177, 225, 177, 457, 440, 428, 417, 263, 287, 283, 241, 315, 424, 402, 285, 470, 631, 702, 480, 58, 66, 35, 58, 308, 284, 330, 269, 270, 401, 368, 270, 322, 334, 370, 288, 282, 298, 342, 264, 202, 252, 269, 196, 380, 386, 417, 398, 565, 612, 630, 566, 23, 47, 34, 23, 199, 233, 226, 201, 366, 469, 443, 363, 294, 277, 311, 286, 274, 373, 394, 291, 240, 235, 260, 238, 305, 465, 432, 325, 244, 333, 357, 246, 313, 317, 356, 334, 226, 307, 296, 263, 373, 333, 354, 348, 106, 115, 148, 138, 432, 594, 541, 426, 93, 115, 107, 91, 442, 590, 608, 454, 429, 611, 565, 418, 133, 102, 131, 111, 294, 404, 338, 293, 294, 287, 320, 270, 154, 131, 145, 147, 399, 531, 588, 405, 470, 455, 489, 487, 129, 168, 170, 132, 510, 701, 682, 497, 28, 25, 33, 24, 343, 408, 418, 334, 252, 251, 270, 224, 229, 310, 272, 253, 352, 372, 373, 339, 400, 408, 371, 369, 183, 288, 274, 207, 599, 589, 638, 545, 30, 31, 38, 30, 123, 183, 172, 165, 494, 463, 471, 429, 200, 178, 205, 163, 379, 503, 535, 337, 468, 493, 504, 468, 115, 151, 173, 128, 331, 423, 472, 337, 217, 215, 246, 259, 200, 169, 180, 195, 389, 521, 487, 359, 100, 154, 146, 112, 485, 520, 500, 483, 271, 422, 383, 300, 268, 290, 291, 275, 305, 439, 436, 323, 234, 264, 248, 251, 229, 276, 277, 212, 371, 413, 368, 354, 109, 110, 118, 105, 442, 565, 672, 379, 259, 375, 376, 246, 307, 309, 327, 301, 350, 370, 375, 369, 198, 300, 295, 243, 548, 552, 545, 535, 61, 97, 94, 68, 242, 264, 267, 251, 324, 415, 437, 300, 396, 391, 365, 375, 202, 264, 288, 219, 329, 330, 345, 333, 249, 339, 338, 237, 300, 342, 314, 289, 270, 347, 361, 277, 577, 556, 559, 545, 67, 70, 66, 60, 136, 132, 105, 106, 427, 604, 580, 410, 618, 576, 581, 567, 41, 39, 44, 34, 180, 260, 248, 200, 377, 424, 415, 396, 576, 643, 639, 555, 14, 24, 28, 21, 159, 272, 245, 199, 360, 441, 438, 386, 170, 196, 190, 170, 382, 485, 487, 420, 417, 517, 490, 464, 123, 180, 178, 131, 340, 438, 468, 337, 245, 219, 251, 202, 148, 187, 159, 134, 437, 544, 434, 457, 180, 229, 211, 170, 398, 479, 469, 364, 263, 353, 327, 283, 335, 315, 325, 299, 226, 276, 277, 211, 359, 385, 388, 378, 516, 683, 679, 515, 24, 30, 25, 28, 99, 158, 139, 106, 475, 511, 535, 477, 544, 688, 684, 524, 11, 19, 15, 15, 412, 540, 511, 449, 140, 146, 164, 138, 276, 283, 283, 266, 281, 400, 389, 322, 399, 465, 515, 361, 193, 199, 174, 194, 358, 509, 460, 351, 176, 196, 236, 214, 391, 437, 403, 440, 167, 256, 249, 157, 235, 326, 317, 216, 339, 346, 381, 340, 276, 426, 361, 277, 266, 307, 289, 298, 289, 276, 306, 303, 270, 356, 410, 290, 204, 239, 287, 184, 378, 439, 389, 380, 259, 357, 353, 258, 324, 310, 326, 313, 339, 378, 339, 306, 263, 325, 316, 234, 138, 178, 184, 140, 447, 498, 464, 451, 205, 269, 255, 185, 380, 430, 388, 388, 271, 390, 366, 239, 307, 305, 329, 293, 399, 427, 417, 409, 152, 240, 270, 186}

    Returns: "2211212212122222221122111122212122122221122112211122122121111212222222221212211211111121121121121112"

  19. {578, 593, 596, 546, 30, 58, 49, 50, 508, 675, 704, 520, 24, 24, 20, 25, 613, 610, 601, 592, 13, 28, 24, 19, 610, 585, 636, 610, 11, 23, 13, 12, 507, 699, 675, 516, 34, 25, 26, 18, 519, 639, 687, 538, 37, 25, 26, 29, 556, 623, 610, 597, 16, 40, 32, 26, 589, 613, 601, 593, 23, 31, 30, 20, 539, 694, 695, 572, 0, 0, 0, 0, 442, 639, 660, 498, 58, 65, 65, 73, 524, 688, 712, 544, 6, 9, 7, 10, 562, 609, 607, 550, 28, 56, 55, 33, 576, 546, 591, 514, 73, 76, 73, 51, 518, 657, 631, 488, 50, 45, 55, 56, 557, 613, 626, 566, 28, 41, 42, 27, 477, 666, 684, 541, 32, 39, 37, 24, 623, 640, 625, 595, 4, 6, 3, 4, 463, 654, 680, 490, 58, 53, 55, 47, 558, 598, 584, 581, 40, 45, 52, 42, 514, 620, 650, 502, 60, 45, 55, 54, 547, 561, 568, 536, 58, 84, 84, 62, 587, 577, 556, 530, 48, 66, 77, 59, 502, 704, 735, 528, 5, 9, 4, 13, 506, 588, 577, 532, 61, 92, 90, 54, 479, 619, 638, 458, 64, 90, 87, 65, 533, 688, 660, 530, 26, 17, 23, 23, 556, 596, 591, 591, 30, 54, 45, 37, 479, 669, 635, 513, 52, 44, 52, 56, 611, 633, 605, 651, 0, 0, 0, 0, 610, 598, 639, 627, 3, 10, 7, 6, 586, 623, 610, 587, 19, 38, 19, 18, 511, 712, 691, 510, 19, 19, 21, 17, 586, 610, 587, 563, 30, 45, 50, 29, 522, 698, 694, 533, 13, 18, 10, 12, 488, 586, 556, 543, 79, 94, 99, 55, 531, 568, 593, 580, 45, 48, 69, 66, 512, 704, 662, 536, 27, 18, 21, 20, 569, 693, 670, 479, 16, 27, 23, 23, 563, 689, 681, 517, 17, 10, 12, 11, 480, 639, 648, 501, 56, 47, 71, 58, 481, 646, 647, 466, 56, 72, 68, 64, 528, 695, 667, 503, 28, 32, 20, 27, 551, 604, 596, 581, 32, 57, 35, 44, 624, 646, 597, 590, 4, 13, 13, 13, 525, 673, 678, 513, 26, 25, 29, 31, 491, 641, 662, 488, 57, 63, 47, 51, 559, 572, 583, 515, 67, 75, 71, 58, 482, 611, 624, 492, 68, 69, 71, 83, 499, 597, 561, 516, 82, 94, 78, 73, 476, 640, 657, 488, 68, 55, 61, 55, 500, 663, 694, 503, 39, 37, 34, 30, 495, 652, 681, 453, 56, 48, 58, 57, 608, 583, 593, 575, 31, 38, 41, 31, 505, 630, 653, 515, 56, 53, 44, 44, 503, 727, 710, 515, 14, 8, 16, 7, 533, 579, 577, 548, 69, 70, 64, 60, 518, 671, 728, 540, 8, 9, 10, 16, 550, 719, 660, 527, 13, 12, 9, 10, 525, 707, 651, 504, 24, 31, 29, 29, 545, 703, 742, 510, 0, 0, 0, 0, 528, 562, 587, 534, 65, 80, 87, 57, 488, 721, 672, 476, 34, 41, 37, 31, 582, 586, 580, 516, 49, 68, 62, 57, 481, 712, 700, 541, 17, 19, 16, 14, 547, 662, 679, 473, 33, 28, 44, 34, 499, 642, 679, 426, 60, 63, 67, 64, 519, 687, 669, 502, 28, 26, 33, 36, 488, 666, 680, 523, 35, 41, 34, 33, 594, 636, 614, 582, 11, 14, 26, 23, 579, 664, 614, 643, 0, 0, 0, 0, 551, 662, 575, 567, 28, 37, 44, 36, 520, 703, 724, 533, 6, 6, 3, 5, 573, 638, 569, 546, 39, 45, 52, 38, 484, 710, 688, 508, 30, 32, 24, 24, 540, 628, 604, 575, 44, 42, 33, 34, 500, 669, 663, 469, 59, 35, 57, 48, 586, 715, 666, 508, 5, 8, 8, 4, 595, 610, 675, 593, 4, 8, 11, 4, 507, 695, 757, 541, 0, 0, 0, 0, 555, 582, 598, 570, 41, 69, 56, 29, 488, 639, 613, 502, 54, 80, 61, 63, 550, 578, 547, 526, 63, 66, 92, 78, 614, 635, 629, 572, 7, 17, 18, 8, 501, 637, 640, 470, 61, 59, 63, 69, 614, 610, 590, 606, 24, 16, 22, 18, 592, 564, 597, 625, 23, 35, 40, 24, 503, 582, 605, 575, 52, 58, 58, 67, 494, 668, 637, 484, 49, 63, 64, 41, 500, 623, 654, 475, 63, 60, 71, 54, 541, 571, 589, 521, 46, 76, 85, 71, 536, 587, 598, 525, 60, 86, 65, 43, 555, 660, 669, 495, 32, 32, 32, 25, 536, 721, 685, 536, 5, 7, 4, 6, 559, 568, 578, 528, 51, 81, 70, 65, 521, 685, 691, 522, 15, 20, 27, 19, 484, 632, 627, 513, 66, 52, 56, 70, 609, 619, 565, 570, 26, 48, 35, 28, 614, 629, 597, 559, 18, 26, 31, 26, 578, 606, 585, 581, 27, 45, 45, 33, 461, 639, 639, 472, 78, 68, 63, 80}

    Returns: "2122112211122121212122121121222121221111112211212111211211112121111122212121121212212221122112112221"

  20. {347, 332, 313, 303, 264, 366, 323, 252, 283, 324, 305, 312, 281, 368, 357, 270, 342, 477, 460, 357, 207, 233, 204, 220, 322, 304, 320, 305, 274, 339, 331, 305, 314, 390, 382, 304, 259, 300, 281, 270, 265, 294, 263, 246, 300, 438, 383, 311, 383, 412, 427, 367, 191, 270, 245, 205, 411, 434, 413, 393, 176, 242, 257, 174, 270, 348, 321, 277, 288, 345, 327, 324, 331, 406, 407, 301, 267, 290, 244, 254, 266, 295, 303, 284, 300, 367, 406, 279, 248, 290, 279, 250, 320, 422, 393, 298, 309, 408, 388, 304, 267, 281, 281, 262, 285, 349, 346, 303, 264, 341, 339, 273, 291, 379, 450, 322, 253, 288, 290, 227, 344, 330, 396, 335, 238, 305, 313, 239, 216, 299, 281, 210, 384, 352, 402, 356, 260, 281, 280, 287, 316, 377, 376, 323, 287, 276, 266, 280, 310, 432, 343, 306, 253, 338, 301, 247, 320, 380, 348, 313, 312, 348, 346, 309, 257, 340, 324, 264, 257, 358, 362, 241, 323, 319, 319, 321, 340, 326, 349, 326, 255, 319, 328, 257, 192, 327, 283, 236, 348, 350, 402, 362, 342, 459, 485, 353, 200, 208, 228, 225, 349, 438, 427, 314, 227, 246, 242, 257, 260, 288, 324, 217, 349, 362, 337, 363, 359, 386, 419, 398, 196, 270, 260, 212, 302, 357, 326, 299, 248, 360, 349, 259, 397, 411, 422, 386, 193, 233, 276, 182, 282, 398, 388, 285, 270, 287, 299, 291, 362, 436, 419, 365, 209, 250, 275, 184, 184, 289, 285, 230, 369, 372, 404, 367, 315, 318, 296, 316, 262, 350, 367, 276, 277, 410, 441, 353, 231, 241, 287, 260, 242, 377, 342, 242, 307, 344, 329, 317, 253, 339, 354, 274, 312, 312, 347, 309, 302, 417, 429, 333, 261, 265, 260, 233, 348, 447, 467, 329, 248, 216, 223, 222, 259, 337, 346, 259, 293, 335, 325, 346, 372, 420, 393, 371, 192, 243, 288, 221, 381, 427, 441, 395, 189, 226, 238, 203, 278, 431, 417, 274, 268, 282, 280, 270, 282, 271, 263, 256, 300, 409, 441, 278, 272, 435, 402, 295, 280, 272, 276, 268, 269, 355, 375, 292, 275, 307, 329, 298, 301, 395, 394, 297, 256, 294, 307, 256, 261, 347, 326, 270, 315, 344, 346, 291, 340, 385, 374, 310, 225, 308, 324, 234, 260, 302, 317, 247, 286, 402, 406, 280, 384, 393, 390, 342, 203, 284, 279, 225, 305, 272, 271, 283, 292, 384, 403, 290, 308, 324, 316, 301, 269, 366, 342, 274, 387, 393, 450, 367, 181, 257, 270, 195, 301, 362, 356, 285, 298, 333, 279, 286, 237, 298, 340, 227, 343, 395, 325, 335, 374, 410, 383, 402, 189, 243, 276, 223, 286, 318, 304, 285, 268, 400, 359, 280, 441, 409, 428, 397, 185, 248, 217, 175, 317, 349, 381, 318, 255, 338, 317, 225, 327, 364, 337, 300, 277, 331, 326, 238, 381, 405, 364, 348, 233, 287, 268, 214, 365, 350, 341, 322, 250, 308, 321, 243, 358, 378, 395, 389, 191, 304, 295, 190, 328, 298, 362, 340, 244, 352, 322, 254, 371, 457, 437, 316, 222, 224, 241, 232, 378, 464, 470, 369, 210, 215, 207, 187, 203, 251, 287, 223, 402, 383, 387, 364, 271, 385, 363, 266, 319, 324, 297, 275, 361, 340, 329, 315, 220, 328, 342, 265, 368, 443, 393, 355, 184, 277, 274, 206, 330, 439, 469, 342, 241, 238, 225, 216, 266, 300, 283, 275, 286, 411, 390, 289, 219, 319, 300, 218, 372, 347, 379, 346, 299, 332, 308, 294, 253, 373, 362, 279, 233, 254, 260, 258, 341, 426, 430, 298, 310, 350, 345, 302, 231, 326, 352, 284, 263, 346, 286, 239, 329, 371, 327, 339, 324, 321, 378, 326, 247, 334, 324, 246, 346, 390, 376, 338, 230, 286, 317, 217, 340, 340, 387, 313, 233, 300, 351, 236, 324, 450, 464, 361, 213, 226, 227, 235, 274, 416, 384, 329, 280, 289, 282, 246, 290, 306, 268, 266, 285, 398, 388, 299, 326, 269, 301, 297, 286, 355, 379, 287, 383, 493, 465, 342, 203, 193, 220, 201, 264, 274, 264, 229, 304, 399, 469, 297, 340, 314, 309, 302, 257, 362, 347, 269, 379, 425, 474, 419, 166, 208, 245, 184, 304, 404, 388, 294, 257, 281, 296, 276, 267, 294, 279, 294, 315, 378, 414, 259, 283, 340, 345, 241, 319, 349, 327, 296, 356, 322, 353, 354, 234, 310, 332, 239, 334, 333, 328, 326, 256, 324, 343, 256, 353, 396, 373, 327, 227, 310, 311, 203, 287, 404, 416, 246, 288, 270, 298, 291, 373, 380, 386, 371, 211, 282, 254, 243, 314, 386, 390, 284, 271, 309, 278, 268, 217, 278, 300, 238, 364, 366, 368, 369, 208, 265, 273, 211, 375, 388, 387, 393}

    Returns: "2212122211221212122121211112221212111111221211112222221122222222211112212122212221122122212122212111"

  21. {401, 405, 345, 358, 203, 295, 284, 209, 348, 380, 396, 361, 221, 274, 307, 213, 361, 347, 410, 347, 246, 287, 298, 204, 301, 389, 412, 304, 253, 289, 280, 272, 303, 450, 388, 290, 270, 286, 246, 267, 328, 354, 326, 362, 254, 305, 309, 262, 290, 362, 391, 296, 285, 282, 313, 281, 338, 335, 345, 335, 220, 338, 335, 254, 309, 356, 348, 323, 239, 344, 343, 238, 264, 368, 365, 258, 301, 312, 328, 304, 256, 368, 343, 295, 296, 323, 319, 300, 275, 318, 383, 258, 320, 340, 306, 300, 275, 301, 323, 309, 273, 372, 366, 281, 263, 331, 290, 309, 277, 358, 395, 277, 261, 310, 291, 259, 301, 407, 379, 292, 256, 318, 297, 257, 325, 358, 366, 323, 284, 287, 274, 286, 294, 406, 358, 311, 266, 271, 282, 256, 282, 395, 429, 319, 270, 274, 278, 268, 308, 396, 404, 302, 203, 283, 299, 229, 368, 401, 377, 340 }

    Returns: "22211212211122212221"

  22. {262, 371, 340, 277, 303, 304, 333, 310, 296, 326, 370, 275, 312, 329, 284, 308, 265, 402, 372, 279, 279, 317, 307, 279, 112, 160, 121, 102, 497, 497, 505, 506 }

    Returns: "1111"

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