TopCoder Statistics - Problem Statement

Problem Statement

In Magic: the Gathering, some cards have the ability "cascade" that allows the player to play another cheaper card for free. Without using too many terms specific to this card game, we can rephrase this ability as follows:

When you play a card X with 'cascade', reveal cards from the top of your deck of cards until you either reveal a card C with a strictly smaller cost than card X, or reveal the entire deck.
If you revealed the entire deck without finding a card cheaper than card X, terminate the process.
Shuffle all the revealed cards other than card C, and place them onto the bottom of the deck.
Play card C. (This card can also have cascade. If it does, resolve it in the same way.)

Your deck contains N cards. Each of those cards has three properties: it has some non-negative integer cost cost[i], it has some non-negative integer power power[i], and it may have cascade (cascade[i] is either true or false). In the beginning, the entire deck is shuffled and you know nothing about the order of cards in the deck.

(Note that already after you resolve the first cascade you know which cards were put to the bottom of the deck and thus the order of the cards in the deck is no longer completely random. E.g., if there is a second cascade, the cards revealed first will be the cards that weren't revealed during the first cascade.)

You have just played another card (not from your deck). The cost of this card is greater than the cost of any card in your deck, the power of this card is 0, and it does have cascade. Calculate and return the expected total power of cards you will play. More precisely, the answer is a rational number P/Q. Return PQ^(-1), where Q^(-1) is the inverse element to Q modulo 10^9 + 7.

Please use the following pseudocode to generate the arrays cost, power, cascade:


L = len(costPrefix)
for i = 0 .. L-1:
    cost[i] = costPrefix[i]
    power[i] = powerPrefix[i]
    cascade[i] = (cascadePrefix[i] == 'Y')

state = seed
for i = L .. N-1:
    state = (state * 1103515245 + 12345) modulo 2^31
    cost[i] = state mod CM
    state = (state * 1103515245 + 12345) modulo 2^31
    power[i] = state mod PM
    state = (state * 1103515245 + 12345) modulo 2^31
    cascade[i] = (state &lt; CT)

Definition

Class:: Cascade
Method:: expectedPower
Parameters:: int, int[], int[], String, int, int, int, int
Returns:: int
Method signature:: int expectedPower(int N, int[] costPrefix, int[] powerPrefix, String cascadePrefix, int seed, int CM, int PM, int CT)
(be sure your method is public)

Notes

"Shuffle" means "rearrange into a permutation chosen uniformly at random from all possible permutations". All shuffles are mutually independent.
It can be shown that for each valid test case the answer P/Q (as a reduced fraction) has the property that Q and 10^9 + 7 are relatively prime.

Constraints

N will be between 1 and 100,000, inclusive.
L will be between 0 and min(N, 500), inclusive.
costPrefix, powerPrefix and cascadePrefix will each have length L.
seed will be between 0 and 2^31 - 1, inclusive.
CM will be between 1 and 10^6, inclusive.
PM will be between 1 and 10^6, inclusive.
CT will be between 0 and 2^31 - 1, inclusive.
Each element of costPrefix will be between 0 and 10^6 - 1, inclusive.
Each element of powerPrefix will be between 0 and 10^6 - 1, inclusive.
Each character of cascadePrefix will be either 'Y' or 'N'.

Examples

2

{10, 20}

{100, 200}

"NN"

0

1

1

0

Returns: 150

Two cards: one has cost 10 and power 100, the other has cost 20 and power 200, neither has cascade. When we resolve the initial cascade, we will reveal the top card of the deck and play it, and that's all. The expected total power of the cards played is therefore (100 + 200) / 2 = 150.
2

{10, 20}

{100, 201}

"NN"

0

1

1

0

Returns: 500000154

The same test case as before, but now the expected total power of the cards played is 301/2, which is not an integer. The returned value is (301 * 2^(-1)) mod (10^9 + 7) = (301 * 500,000,004) mod (10^9 + 7) = 500,000,154.
2

{10, 20}

{100, 200}

"NY"

0

1

1

0

Returns: 200

The same test case as Example 0, but now the more expensive card has cascade. If we reveal that one first, we will also cascade into the cheaper one. Thus, with probability 1/2 we will just play the cheaper card (power 100) and with probability 1/2 we will play both cards (total power 100+200 = 300).
6

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

{10, 20, 30, 40, 50, 60}

"NNNYNY"

0

1

1

0

Returns: 666666712

The fact that the last card (cost 0, power 60) has cascade does not matter - if we play this card and resolve its cascade, it certainly won't do anything because there are no cards cheaper than this one. The exact answer as a reduced fraction is 122/3.
10

{4, 7}

{47, 42}

"YN"

474747

10

100

1250000000

Returns: 487500069

The full test case should look as follows: cost: 4, 7, 0, 9, 0, 5, 8, 5, 6, 5, power: 47, 42, 49, 60, 15, 22, 85, 32, 87, 34, cascade: true, false, true, false, false, false, true, true, true, false, The exact answer as a fraction is 5247/80
1

{}

{}

""

368938

65563

451083

1073741824

Returns: 300352
2

{}

{}

""

580534

475709

598518

1073741824

Returns: 500327660
3

{}

{}

""

360155

269933

537337

1073741824

Returns: 334180380
4

{}

{}

""

405335

411478

645463

1073741824

Returns: 500331005
5

{}

{}

""

42896

833705

438864

1073741824

Returns: 400271999
6

{}

{}

""

690621

24810

107433

1073741824

Returns: 347305058
7

{}

{}

""

657

276622

988440

1073741824

Returns: 657679681
8

{}

{}

""

830729

504945

759020

1073741824

Returns: 354801658
9

{}

{}

""

573244

9580

961968

1073741824

Returns: 838735545
10

{}

{}

""

855336

942396

330908

1073741824

Returns: 481155261
99299

{}

{}

""

988044144

56300

6

2507971

Returns: 26398708
95944

{}

{}

""

1085916001

93

94494

2114419151

Returns: 955407480
94147

{536068, 852131, 652752, 573429, 499657, 820338, 840822, 456773, 383336, 963096, 796056, 34793, 637314, 277886, 942872, 675588, 638199, 542078, 989430, 706855, 953674, 494728, 958841, 742586}

{669331, 837262, 998004, 330294, 869824, 23313, 604945, 254824, 221631, 362769, 452604, 908921, 725393, 192954, 185259, 492613, 965701, 208327, 134088, 103198, 143298, 765900, 823240, 597291}

"NNYNNYYNYNYNYYYNYNNYYYYN"

200513682

133

51

2147440970

Returns: 11356625
99010

{}

{}

""

346617440

6

19

55885287

Returns: 767564239
98830

{}

{}

""

467288229

13

93141

15810

Returns: 820587011
94907

{}

{}

""

1891726748

1003

1

102

Returns: 0
92029

{779350}

{76321}

"N"

3240676

58

129166

2143039924

Returns: 181872278
96464

{638638}

{246679}

"N"

458337118

1240

44775

2147482963

Returns: 211262991
92710

{617727, 412913, 904152, 365232, 127711, 434809, 309198, 575934, 671651, 230209, 712076, 962404, 363768, 805969, 94476, 672581, 329415, 106865, 37524, 211626, 850454, 586244, 142052, 346247, 981945, 95308, 874214, 334840, 806084, 750149, 695619, 984106, 990987, 960512, 449804, 530809, 572481, 600392, 789475, 807200}

{713092, 944458, 369259, 836234, 546647, 544714, 446168, 668835, 460452, 457221, 709039, 433181, 763124, 514494, 23776, 204277, 342291, 51455, 628797, 983951, 449342, 945021, 106023, 460423, 810916, 611112, 130057, 100970, 887740, 350921, 458390, 774664, 955519, 61878, 349914, 826045, 791280, 196581, 958305, 852729}

"NNNYYYYNNYYNYYNYYNNYYNNYYNYNNNYNNNNNYNYN"

1741737939

8

21

2147453432

Returns: 951401529
97743

{263303, 559312, 223345, 558160, 390772, 493890, 960974, 224666, 348571, 419917, 955572, 40197, 705701, 677871, 614964, 434865, 341259, 850335, 843437, 563714, 361470, 938607, 7845, 114596, 21555, 326077, 830212, 50948, 638554, 229296, 862915, 861087, 885506, 549703, 906440, 641637, 3523, 36609, 914223, 581598, 616711, 51650, 402072, 936445, 800139, 486578, 200245, 94133, 290723, 986754, 707910, 975551, 666704, 930246, 414638, 534998, 364761, 39646, 929735, 68437, 318811, 630652, 749012, 326305, 54558, 639849, 961335, 463207, 485921, 426527, 763911, 755322, 348771, 754434, 94300, 265509, 894369, 934934, 993606, 440844, 391642, 983865, 102995, 742712, 395724, 395807, 184990, 310055, 31239, 31959, 603048, 709001, 604808, 851512, 929429, 200684, 132102, 588415, 233626, 90495, 7986, 443484, 448406, 436483, 741435, 443585, 606404, 769180, 133777, 161469, 810712, 756706, 775819, 996595, 777566, 893516, 393961, 565067, 672543, 950667, 482428, 275398, 671466, 865266, 672539, 154731, 78730, 41546, 618505, 253203, 852631}

{766500, 616320, 134497, 73929, 951811, 18383, 143628, 128597, 543688, 817744, 133465, 641878, 895755, 976578, 991042, 306305, 597634, 631962, 923196, 438637, 573955, 781652, 511776, 642217, 895341, 609164, 912898, 24599, 175536, 819874, 843990, 626828, 568291, 606352, 863723, 664094, 759365, 152944, 975147, 242460, 889782, 122980, 158873, 939380, 952300, 298990, 646692, 507855, 941077, 846110, 681992, 513856, 482999, 864129, 895412, 634411, 324234, 429622, 790457, 970915, 471554, 634983, 192394, 13414, 448734, 847868, 826341, 979682, 914565, 511028, 513420, 767606, 427859, 360167, 393153, 582719, 316554, 838564, 940930, 322227, 413634, 872614, 867974, 394757, 37283, 654037, 800070, 551913, 281777, 148523, 490069, 411441, 106265, 876444, 924840, 808554, 691544, 112873, 621610, 35596, 385634, 983417, 669519, 860590, 934170, 356726, 696090, 710649, 599490, 787888, 154657, 1149, 273031, 368304, 167765, 650951, 900982, 41707, 835602, 844274, 432346, 504288, 752035, 339192, 154683, 278571, 988888, 268598, 346832, 428601, 689135}

"YYYYNYNNYNYYYYNYYYNNYNYYNYNNYNYYYNNYNNYNNYNNNYYNNNYYYNNNYNYYNYYNNYNYYYNNYNYYYYYNNNNYYNNYYYNNYYNNNNYYNNYNNNNYNYYYYYYNNYNNYNNYYNYYNNN"

1263893249

24

1519

2135232430

Returns: 754393268
95062

{9678, 660968, 298201}

{287144, 579746, 435995}

"YNN"

227225975

35776

1512

109708

Returns: 597670193
98603

{256417, 722435, 772715, 923417, 970582}

{747249, 980590, 469657, 771614, 748930}

"YNYNY"

1117747418

284148

60

102

Returns: 867504780
93200

{}

{}

""

618455383

258713

7770

2134945016

Returns: 488937296
96577

{261744, 247127, 3706, 269512, 568359, 857660, 26616, 840559, 353435, 415887, 901797, 557240, 317591, 747604, 207634, 265915, 70958, 711627, 53085, 254704, 183101, 640039, 369711, 363083, 87656, 717660, 523430, 273568, 294237, 806199, 626555, 385883, 214299, 852968, 50279, 864558, 273096, 510913, 244087, 696792, 114672, 553804, 879575, 320510, 193547, 416061, 294832, 776575, 620476, 958066, 747449, 211413, 553698, 293878, 796806, 168238, 169289, 335652, 160677}

{291743, 505497, 103507, 299572, 727836, 274102, 158343, 410037, 707220, 230001, 232578, 840672, 789640, 828258, 186766, 90420, 964511, 304156, 541936, 152825, 855705, 487726, 815324, 309539, 33107, 990608, 111766, 930571, 712708, 581868, 231601, 217399, 111464, 206508, 523652, 401872, 317121, 751414, 267744, 12761, 898161, 351711, 377880, 440373, 101389, 92214, 345598, 972517, 272692, 559217, 875209, 242995, 609248, 987420, 754325, 723612, 946210, 144428, 257893}

"NYYYYNYNYYNNYNYNYYNNYNYNYNYNYYYNYNNNNNYYYYNNNNNYNNYNYNNNYYY"

226763001

20751

39721

2138233078

Returns: 70193910
92377

{800421, 269022, 9917, 661951, 579996, 292674, 559407, 280618, 487517, 550019, 643104, 489666, 922463, 157871, 381149, 141499, 703657, 900003, 218021, 20664, 102996, 56776, 403088, 517885, 216039, 688788, 707366, 554514, 704522, 603893, 165490, 663006, 734615, 385581, 60867, 584835, 779723, 190588, 921568, 576639, 249946, 504913, 812398, 502739, 447649, 59805, 736575, 521268, 727141, 737000, 913794, 722147, 812376, 912206, 245668, 537478, 604020, 340427, 534555, 230697, 407208, 777615, 478251, 142319, 671081, 178054, 180154, 921125, 207735, 843455, 348678, 1963, 620762, 548756, 771650, 209708, 575067, 890534, 469580, 171527, 305765, 547063, 673245, 455601, 686481, 495293, 581314, 457235, 905074, 719916, 22504, 174906, 610791, 449018, 418245, 998632, 33840, 584621, 51815, 63528, 635329, 723356, 106794, 217629, 505519, 197436, 837533, 578299}

{936219, 33611, 827822, 559561, 940585, 807054, 125993, 17326, 347887, 271359, 502903, 291760, 103347, 955237, 794486, 774601, 691241, 122687, 376230, 506777, 9488, 291980, 599203, 482468, 918753, 964525, 467672, 194651, 129258, 981651, 271289, 386574, 488474, 56523, 515901, 725888, 34363, 446546, 672692, 85888, 722419, 939764, 797177, 733092, 220247, 388710, 205698, 241661, 759215, 613786, 150163, 215938, 519535, 539015, 780879, 111847, 304719, 807907, 635352, 668741, 774974, 718683, 566640, 796665, 902646, 104268, 831857, 881765, 513811, 203599, 39629, 157507, 772010, 530793, 792841, 271043, 155354, 294122, 391136, 153999, 890207, 348867, 957595, 903388, 833619, 696671, 875517, 955968, 557657, 388295, 942584, 133254, 948454, 150345, 449051, 426489, 598522, 848584, 333041, 711141, 188542, 634295, 856241, 814929, 393316, 19867, 956490, 109689}

"NYYYYYYYYYNYYNYYYNYYNYYYNYNYYYNYNYNNYYNYYYNNNNYNNYYYYNYNNNYYNNYYNYNNYYNNNYNNNYNYNNYYNYYYYNYNNYYYNNYNNNNYYNYN"

2005272623

48562

6

166013

Returns: 8566077
96819

{556069, 951915, 188013, 730794, 761519, 640139, 788635, 190332, 632159, 116712, 410436, 339562, 281328, 7341, 992199, 937569, 722768, 835796, 925573, 975034, 725578, 524697, 560992, 286251, 755289, 185429, 535020, 900682, 8966, 660567, 540167, 616883, 322275, 910405, 601827, 311957, 703953, 429606, 603862, 612117, 392781, 346684, 256239, 295297, 224370, 713832, 962303, 723705, 353239, 422981, 861896, 829343, 864619, 732773, 389980, 718288, 775224, 870305, 221889, 143374, 799437, 372102, 538879, 30395, 486813, 155334, 572464, 368900, 934094, 414878, 93799, 90236, 77294, 582094, 440057, 903019, 820377, 829188, 528780, 898199, 161597, 701981, 194202, 854996, 176530, 475061, 72682, 223942, 384248, 707473, 401458, 201909, 521836, 734240, 73906, 658490, 584626, 520642, 208157, 58924, 21002, 338832, 589457, 204082, 399086, 13300, 145293, 583091, 702920, 412127, 988868, 385596, 243176, 114078, 261989, 209249, 405473, 270194, 617700, 483354, 850946, 765719, 819269, 900137, 415503, 441419, 507181, 36187, 173837, 162712, 203194, 372622, 986764, 958914, 624744, 817048, 757720, 558125, 919228, 367876, 900171, 154686, 727065, 49453, 899334, 677234, 870110, 38148, 133593, 664516, 192893, 188297, 52865, 12470, 733637, 374650, 955006, 221116, 925880, 24391, 530825, 916623, 139746, 31946, 766458, 360173, 782779, 265221, 316609, 434523, 888945, 851067, 779196, 865973, 150144, 469465, 836668, 758908, 465218, 169050, 696044, 167631, 556161, 911180, 447116, 13783}

{134725, 967766, 190372, 515977, 939808, 851694, 132850, 938126, 437310, 388183, 26284, 8979, 610273, 481088, 213724, 317384, 869704, 175983, 292726, 541480, 759530, 808032, 320841, 688892, 640457, 435556, 192838, 893710, 336793, 949393, 106080, 613513, 386034, 920723, 846571, 580361, 690602, 805258, 233605, 757828, 955925, 220889, 646099, 479733, 465453, 916211, 196283, 236599, 831040, 684690, 288275, 25202, 864986, 796517, 662033, 100388, 414222, 50293, 382028, 595470, 663781, 64336, 459236, 40842, 111463, 922692, 268163, 357974, 690896, 221196, 385358, 895744, 10580, 363138, 232450, 221512, 205334, 194409, 938691, 354032, 246018, 407035, 917413, 62846, 696402, 121618, 135478, 834260, 639638, 532961, 650244, 991491, 439504, 342227, 381256, 470456, 509619, 483993, 834126, 520121, 621690, 177404, 932448, 794699, 38121, 437268, 621638, 920339, 532290, 855305, 572322, 487207, 338195, 388586, 454233, 178743, 545131, 680271, 954310, 580800, 560541, 240424, 520577, 431275, 813717, 783256, 48681, 368531, 909246, 319100, 654603, 258099, 843966, 492105, 256494, 842383, 213954, 96380, 522840, 996849, 694728, 395475, 608848, 227669, 522077, 24746, 336221, 260645, 203039, 346542, 765865, 614996, 542304, 870314, 891179, 234939, 18252, 413977, 742793, 892443, 42564, 534984, 611177, 350575, 582307, 568793, 343040, 362357, 664031, 535708, 481827, 828662, 654577, 36665, 606027, 624375, 193620, 791058, 99097, 217055, 66250, 971821, 262596, 604778, 279054, 401006}

"YYNNNNNYNYYNNYNNNNYNNNNNYYNNNYNNYNNYYYYYNNNYYNYNYYNYYNYYYNYNYYNYYYYYYYYYNNNYYYYNYNNNNYNYNYNNYYNYYYYYNYYYYNNYYYNNNNNNYNNNNYNNNNYYYYNNNNNYYYNYNNNNNYYYYYYNNNYNNNYYNYYYNYNYYYYYYNNYYYNNYYNYNN"

1237799168

735

75671

2147430827

Returns: 556815619
96015

{}

{}

""

704908780

1105

999

3792

Returns: 793741066
99886

{395187, 198043, 234358, 417948, 727886, 858744, 826376, 840011, 43678, 156006, 68923, 874756, 807105, 638801, 188829, 985936, 962508, 387100, 896032, 370200, 682598, 451429, 295050, 899718, 751281, 631297, 62215, 475085, 455708, 917149, 751255, 24142, 922760, 749315, 755485, 810756, 579620, 38158, 16514, 732853, 53479, 635629, 123666, 42611, 109069, 572289, 933297, 117334, 932066, 907409, 562594, 936014, 255552, 15048, 568840, 996404, 150379, 316299, 917216, 530438, 502381, 2948, 86388, 873172, 525105, 627784, 570891, 649404, 838215, 601455, 278413, 973219, 899155, 985747, 811950, 497512, 195047, 950761, 225815, 229052, 846258, 945637, 349260, 888149, 729727, 807231, 88738, 916866, 703903, 624584, 611227, 522308, 116096, 21289, 489060, 717055, 466447, 29327, 44101, 523745, 481774, 217080, 786394, 806886, 122888, 608026, 420695, 339527, 445112, 378205, 835825, 953481, 772699, 907913, 815655, 166892, 914288, 308062, 434360, 809113, 703705, 506604, 596230, 260105, 310377, 962683, 476820, 351171, 847575, 404068, 553092, 977585, 327442, 857807, 455021, 642299, 791110, 345407, 464488, 3232, 156961, 767902, 258984, 926491, 643418, 375810, 232894, 896619, 124454, 321021, 828536, 84669, 793233, 728324, 506999, 342074, 104217, 340897, 3646, 416587, 210140, 805241, 552795, 286231, 566171, 258887, 146091, 770781, 833169, 671681, 33843, 61363, 322970, 132880, 638047, 523653, 828482, 547788, 314268, 104404, 520848, 452228, 204274, 769866, 439147, 118230, 381420, 656626, 410623, 486109, 836016, 193580, 291352, 817688, 299838, 35402, 618481, 608929, 718467, 301092, 254051, 33824, 925543, 305451, 356442, 25359, 514228, 597328}

{402797, 728398, 966876, 699401, 290112, 674204, 440966, 632466, 184742, 700584, 116311, 621057, 5943, 404564, 930881, 680459, 562640, 801821, 584521, 391617, 767765, 94387, 583478, 694570, 723340, 210613, 594120, 461703, 533826, 566043, 807087, 554257, 889714, 741021, 777351, 696570, 162184, 254006, 983870, 632040, 369412, 836603, 572015, 501645, 669967, 814290, 418136, 390229, 442419, 992844, 935680, 302188, 413709, 176478, 189593, 215859, 522043, 999019, 374473, 567332, 649037, 268583, 441013, 886028, 798119, 376097, 999318, 866705, 398494, 276238, 864417, 175959, 413717, 839670, 56704, 624224, 801260, 46560, 405354, 565086, 462191, 340605, 37898, 288952, 927835, 751446, 701529, 818858, 402171, 407214, 237237, 406376, 236585, 388133, 25890, 130899, 307692, 129959, 561425, 646800, 742337, 120476, 750161, 879692, 433088, 657291, 678294, 416032, 270028, 387269, 400387, 381473, 54656, 983453, 360177, 847911, 811327, 975653, 984765, 718230, 448243, 176714, 684067, 525481, 170721, 438373, 742415, 738658, 808538, 28754, 264642, 270895, 362904, 723553, 61524, 749543, 591772, 763048, 509389, 246743, 887941, 645948, 106313, 902731, 327092, 703041, 587694, 792791, 75158, 448700, 510091, 577572, 553289, 966871, 398397, 370425, 534991, 863355, 203104, 666305, 602419, 483370, 216809, 398367, 503967, 358027, 944433, 259679, 407712, 292972, 573706, 751472, 415937, 398200, 104156, 387158, 2336, 739609, 7853, 245515, 288082, 46032, 847018, 120368, 469945, 348892, 486886, 764486, 250695, 450651, 838875, 934658, 893282, 874351, 873850, 594815, 7990, 294812, 465775, 409277, 341145, 926523, 164609, 983658, 998630, 380488, 337737, 883194}

"NNYNNNYYNYYNYNNYYYYNYNNYYNNNYYNNYYNYYNNNYNNYNNNYYNNYYNNYYYNYYNNNYNNNNYYYYNYYNYNNNNNNNYNYNYYNYYYYYNYNNNNNYNNNYNYNNNYYNYYYNYNNYNNNYNNYYYNYNYNNYNNNYYYNYYNYYNYYYNNNNYYYYYYYNYYYYNNNNNNYYNNNYNYNYYNYYYYYYNYNNNYYNNYY"

1344594894

229863

1

2147482855

Returns: 539761239
91512

{}

{}

""

1819960627

433

79

2091884192

Returns: 921969002
93033

{}

{}

""

878930647

32949

19692

21179648

Returns: 718364010
99980

{}

{}

""

1310530754

1

537

2147084031

Returns: 746609595
98807

{655153, 975778, 914477, 78906, 129320, 55735, 616661, 936216, 881961, 667794, 565850, 105869, 325019, 119518}

{467005, 831852, 501811, 617543, 656135, 336042, 220872, 476903, 350671, 785519, 250762, 178730, 361957, 63878}

"YYYYNNYNNNYNNN"

1108435379

13

2

2147425559

Returns: 765771453
96886

{}

{}

""

1503440498

105997

88855

1

Returns: 647970869
94739

{837125, 352798, 187993, 537404, 543170, 688480, 287759, 906545, 171776, 945386, 280308, 438301, 89991, 413333, 888255, 440620, 785250, 308474, 111961, 79187, 26344, 209787, 579720, 638773, 189283, 907398, 533071, 512043, 376022, 589523, 370334, 339752, 454411, 1908, 268824, 64359, 966363, 355857, 637867, 928796, 34703, 947378, 42546, 108114, 431167, 317801, 887885, 524231, 428290, 414494, 825338, 406075, 266983, 708184, 579163, 768245, 295953, 855510, 651444, 162107, 308567, 239098, 252176, 782888, 413663, 727295, 379672, 980647, 483249, 485105, 987066, 472835, 849104, 484425, 335564, 603815, 829899, 209848, 336808, 18638, 989847, 835077, 927326, 329834, 47786, 824700, 526975, 288736, 864311, 95171, 101445, 774286, 805737, 622477, 403903, 587657, 494452, 497888, 527187, 570218, 267469, 393376, 471138, 370552, 692685, 576236, 579027, 76917, 656569, 385320, 418110, 902339, 901602, 283648, 100297, 589336, 788390, 571137, 650252, 467685, 141332, 618725, 493449, 163063, 728274, 680438, 814151, 583474, 369222, 52568, 307022, 516369, 913543, 515770, 168789, 795237, 608967, 140674, 492970, 763852, 798389, 985758, 37392, 254244, 557145, 779376, 411597, 628646, 802678}

{298022, 284151, 46187, 469396, 54145, 996177, 292985, 875903, 107657, 824873, 569378, 167449, 705455, 643985, 580717, 23532, 359790, 478661, 965829, 479777, 214823, 468672, 41443, 432114, 450764, 936471, 22011, 282813, 241485, 356545, 329260, 165259, 632354, 512239, 939715, 552259, 442783, 608448, 710471, 313310, 336895, 636019, 364772, 953940, 853482, 548127, 614889, 46792, 506149, 518191, 296908, 76660, 902710, 672693, 466977, 169872, 212835, 271710, 59899, 530781, 539991, 364270, 365313, 319209, 183496, 128293, 219326, 328638, 807253, 871673, 143966, 613293, 420763, 169855, 401731, 848092, 447781, 566742, 509276, 234257, 321948, 102234, 166994, 332128, 117059, 466889, 275979, 160644, 728227, 277682, 268258, 634479, 967220, 754175, 788298, 106294, 451417, 336132, 192966, 963547, 852499, 944907, 78847, 243087, 131784, 946834, 166784, 767611, 240797, 33368, 549909, 787470, 4812, 346047, 603994, 807350, 58461, 879942, 135737, 91988, 286785, 32492, 662391, 56379, 383072, 6815, 763494, 605660, 280203, 307592, 984789, 992323, 3911, 930815, 181903, 481545, 219685, 251594, 331079, 917647, 403303, 981509, 798590, 324304, 793977, 127483, 802467, 856962, 108944}

"YNYYNYYNYNNYNNNNYYNNYYYYNNYYYYNNYNYNYNYYNYNNNNYNYYYNNYYYNNYNNYNYYNNYYYNYYNNYYNNNNYNNYYNNYNYNNNNNNYNYNYYNNNNNYYNYNNYNYNYYYYYYNYNYYYNYNYNYYYYYYYNYNYYYY"

1184499888

322

7041

106

Returns: 845378787
94653

{370612, 218918, 465803, 572752, 215670, 196722, 697838, 632994, 647594, 701523, 736119, 857648, 531251, 164114, 534970, 270934, 549754, 785696, 608771, 127225, 646037, 344762, 226937, 300576, 323695, 962933, 624523, 79743, 744889, 30508}

{333157, 847704, 397987, 773731, 25159, 140524, 950616, 447190, 957068, 692495, 185535, 92584, 472478, 387833, 111604, 741672, 534288, 634123, 795795, 840330, 648004, 289435, 250245, 735650, 368462, 772008, 19872, 630277, 942401, 695810}

"YNNYYYYNYNYYYYNNYNYYNYNYNNYNNY"

688930000

28882

403919

2128285081

Returns: 586779988
94392

{604861, 149591, 274591, 302174, 230489, 28324, 608057, 347588, 492226, 276497, 914166}

{16071, 817376, 382248, 520802, 571481, 686312, 570255, 258732, 730074, 290193, 804892}

"YNYYNYYNYNN"

2043679914

59

150143

3750

Returns: 265092040
91593

{621486, 206734, 275557, 405829, 844903, 387434, 343029, 288012, 271312, 848398, 562774, 274726, 819594, 406259, 962297, 104579, 510221, 221684, 951032, 486651, 267912, 248174, 810741, 842602, 383175, 481147, 214331, 59865, 397241}

{76129, 522685, 886606, 405952, 927487, 221846, 650691, 49250, 632019, 889736, 693074, 809013, 318125, 119967, 234371, 27770, 448135, 227228, 230381, 908176, 213970, 962389, 534407, 948469, 579168, 223308, 720871, 87653, 85694}

"YYYNNNNYNNNNYNNNYNNNNNNNYNNNY"

1764847786

4120

9

2147483613

Returns: 22971199
91121

{}

{}

""

890619382

12556

63041

11502

Returns: 629754587
98638

{651652, 679703, 970151, 865654, 265654, 995146, 448624, 9483, 815828, 928605, 350174, 145136, 674880, 203575, 84320, 942881, 942714}

{309315, 644478, 817062, 407300, 474036, 443602, 340679, 779297, 245159, 801759, 985045, 517988, 311163, 914450, 245394, 80905, 362960}

"NYNNNYYNNNNNYNYNN"

1748202609

11

772409

2147483630

Returns: 761782343
94926

{}

{}

""

509224083

10673

619

2147429167

Returns: 454673066
93796

{695072, 357391, 276471, 528341, 503684, 792636, 977252, 458935, 648812, 444633, 459759, 481098, 535214, 274359, 595599, 902350, 176171, 778757, 806610, 234434, 143462, 657390, 861022, 410998, 646983, 922996, 881327, 527093, 138828, 135410, 622508, 318754, 80172, 651924, 187975, 866134, 128523, 558550, 707643, 799366, 817685, 85276, 49351, 500984, 473931, 342297, 943332, 940244, 401981, 136948, 479634, 18724, 913057, 503482, 361128, 417064, 531282, 812738, 829688, 650759, 849546, 5602, 530882, 651717, 644798, 400708, 435309, 907078, 792978, 933637, 429408, 48317, 236661, 323061, 978214, 69595, 424759, 783867, 71995, 698737, 407513, 237748, 72769, 18810, 215759, 986450, 606935, 952338, 301705, 599379, 988774, 971354, 722335, 496268, 628831, 587835, 208155, 102586, 786742, 880349, 141829, 463548, 982040, 784797, 318029, 734920, 257287, 394078, 115207, 599147, 21407, 199358, 594862, 352038, 212832, 15106, 362515, 150183, 297347, 778476, 797254, 496957, 747895, 789173, 49880, 622687, 836056, 232034, 643310, 221881, 593721, 659993, 456545, 822513, 181690, 217239, 337157, 490970, 21290, 526596, 192274, 632962, 419889, 964759, 141484, 307966, 475822, 827619, 254075, 864974, 170599, 258781, 434969, 803147, 508007, 575599, 939126, 882980, 856810, 895439, 134293, 179584, 773376, 939937, 407371, 156555, 837262, 210469, 326014, 255701, 796162, 761871, 335207, 780080, 701746, 199757, 264585, 411716, 929904, 260038, 784499, 259105, 489061, 968633, 417042, 141523, 82390, 152222, 393630, 423179, 489877, 416113, 131804, 481790, 869102, 199884, 542677, 398545, 701916, 778841, 424147, 808841, 710639, 345864, 462346, 173577, 137222, 869187, 576555, 214092, 135457, 245674, 850925, 38742, 395489, 101060, 207885, 520942, 557815, 605816, 383422, 643792, 85504, 442452, 187685, 108968, 778719, 712229, 863240, 429809, 768696, 784956, 190070, 570417, 599796, 603200, 355522, 417692, 331069, 425750, 609101, 535878, 871467, 903765, 398119, 150544, 872796, 673817, 480912, 881281, 128053, 913774, 575881, 238668, 787622, 972121, 660325, 179516, 801621, 491675, 881156, 841919, 366613, 73024, 685763, 975944, 264134, 348236, 936867, 631751, 612989, 829550, 348167, 475857, 716700, 266454, 252315, 70981, 186528, 972377, 820380, 97311, 21663, 986572, 472322, 33754, 775048, 941698, 300949, 794733, 171015, 992020, 408403, 528414, 133746, 592098, 888936, 831292, 813236, 699531, 580625, 391317, 631401, 353818, 355351, 150897, 331019, 664247, 649841, 362943, 820470, 27277, 819770, 395954, 363237, 351070, 360765, 758132, 705580, 774422, 355354, 344716, 134007, 290386, 553561, 139390, 551064, 803604, 599737, 977495, 531140, 433102, 352680, 288273, 30731, 348468, 728642, 168795, 101465, 52986, 181740, 305256, 343695, 932417, 72192, 62403, 430229, 857992, 595780, 552826, 943113, 780976, 66002, 836808, 335456, 816516, 776481, 104233, 169968, 492393, 823591, 634283, 30447, 870150, 463637, 900639, 256951, 430901, 570762, 715233, 278153, 798487, 432941, 20501, 581080, 73578, 551849, 186517, 258326, 777491, 895750, 735399, 776218, 709869, 682344, 784689, 960912, 629950, 828095, 267369, 142825, 129216, 656137, 696324, 998513, 536604, 305180, 132511, 573185, 881199, 381305, 774800, 936958, 556140, 668722, 612159, 604428, 684483, 234909, 420552, 224832, 244369, 159981, 460093, 145416, 282499, 39681, 522278, 193990, 781148, 933407, 492208, 742299, 656797, 759266, 612080, 900341, 521948, 797410, 610524, 889472, 290546, 577316, 830791, 825895, 47088, 366197, 912737, 344335, 429053, 905360, 173531, 379771, 186064, 892433, 602646, 423710, 691597, 247933, 290762, 655274, 474718, 861977, 684705, 416398, 135886, 641453, 566334, 183380, 951281, 170206, 493609, 432313, 915184, 319694, 803244, 169115, 189014, 652202, 460638, 907520, 355061, 259534, 657739, 939064}

{533712, 80620, 723846, 296022, 1890, 349986, 251205, 165995, 5207, 407310, 441302, 254150, 18742, 206111, 148663, 234696, 829018, 820072, 631781, 765725, 41115, 63748, 510148, 557216, 73841, 995297, 867258, 346460, 434428, 235348, 599165, 127756, 950578, 714144, 39438, 999318, 708026, 149194, 877034, 75507, 272654, 136405, 843088, 300396, 398204, 446598, 341472, 435247, 619127, 160649, 997933, 547564, 749425, 545577, 886021, 870710, 375330, 827113, 749117, 16331, 734594, 383001, 700716, 23637, 886720, 753117, 364103, 467421, 291986, 691714, 340177, 830767, 479644, 217157, 359156, 945777, 578204, 142607, 440402, 769566, 149514, 691272, 749163, 798859, 626011, 730870, 448948, 646697, 467143, 594181, 524266, 693997, 287633, 53992, 105225, 9535, 524903, 825300, 645493, 389572, 38931, 889819, 327472, 702315, 859541, 694439, 212588, 129422, 916694, 610668, 620746, 503537, 495000, 782432, 539319, 191734, 851161, 380092, 206724, 379177, 773714, 270871, 167123, 72546, 828241, 23180, 270204, 437371, 469964, 70184, 46935, 993796, 721675, 302761, 18791, 20002, 544443, 648517, 322962, 889058, 2882, 794528, 30010, 123551, 565372, 313645, 938315, 329392, 846912, 383303, 657103, 686865, 762667, 634965, 774977, 133000, 687214, 267840, 848495, 948071, 53644, 770814, 222436, 454720, 975544, 63289, 646747, 285224, 326327, 26600, 176887, 563399, 271106, 140412, 155246, 666776, 417852, 879022, 999823, 199867, 485257, 961866, 345635, 60805, 335624, 593548, 663818, 62771, 690192, 984460, 613252, 656374, 873868, 241617, 962165, 843094, 681744, 320427, 783737, 799225, 903908, 39027, 607672, 711475, 226099, 514281, 901115, 341398, 384241, 385483, 170771, 41521, 190128, 877726, 614014, 258101, 537570, 720336, 669209, 765522, 159233, 119736, 686833, 430385, 644282, 729378, 919729, 691846, 135659, 455101, 714182, 562939, 806274, 612612, 572716, 294551, 305819, 399832, 580612, 938361, 87049, 264136, 576999, 781499, 548159, 304378, 996425, 388914, 123711, 154678, 405095, 896757, 895802, 529074, 97667, 957579, 884524, 581647, 704742, 679766, 547733, 175051, 174015, 825689, 318069, 652267, 315397, 197119, 330279, 574761, 644506, 661346, 380113, 986103, 654552, 349593, 601283, 281665, 872376, 419317, 705025, 339823, 698659, 419460, 640046, 352594, 454934, 942396, 237307, 32113, 332098, 656905, 739551, 414269, 833912, 814939, 529874, 679783, 296906, 791332, 896000, 659645, 245369, 671903, 387463, 990254, 369505, 3204, 454508, 548609, 875620, 783018, 333531, 482512, 340653, 820215, 48463, 333526, 766434, 900581, 799017, 647976, 210871, 272986, 772997, 93458, 910699, 119517, 105644, 754080, 254313, 245994, 407364, 234757, 112597, 607550, 975696, 629477, 221570, 863641, 567143, 167304, 576421, 24947, 40638, 423599, 931060, 621755, 216159, 24951, 748146, 880364, 234812, 548424, 886381, 246195, 308994, 68022, 902626, 979050, 791675, 199703, 510898, 616685, 421398, 659910, 862493, 224749, 844319, 592544, 550790, 418207, 8129, 796713, 684527, 924333, 961391, 547065, 208560, 960647, 532993, 622746, 968075, 619867, 233091, 115320, 449903, 493479, 797193, 323826, 246608, 894893, 85358, 604726, 401454, 418389, 177187, 181455, 280585, 372477, 202876, 414042, 495146, 50751, 591874, 730160, 217263, 708752, 628904, 456146, 97024, 278865, 840072, 507524, 722328, 995389, 38116, 645959, 950422, 501297, 958539, 469538, 81876, 698032, 507510, 877351, 155527, 836176, 433967, 201625, 547636, 925931, 490852, 307341, 704748, 326481, 786457, 540514, 25895, 290060, 676947, 546380, 153254, 580121, 932663, 272894, 858075, 804482, 161950, 1727, 752239, 707129, 605737, 627169, 146572, 650321, 922989, 929580, 667934, 557446, 66362, 597391, 237877, 770230, 353114, 773511, 585110, 823829, 621524, 658347, 526183, 162689, 673260, 325888, 653457}

"YNNNNNYYNNYNYYYYNNYNYNNNYNYYYNYYNYYYNNYYNNYYNYNNYYYYYYNYNNYYYYNNNNNYYYNYNYNYYNNNYNNNNYYNNYYYYYYNYYYYNNNYNNNYNYYYNNNNNYNNNYYYYYNYNYYNYNYNNYNNYYNYYNYNYYNYNNYYYNNNNNNNYYYNNYYYNNYNYYNNNNNNYYYYYNNNYNYYNNYNNYYYNYNYYYYYYNNYYYNYNNNNNNNYYYNYNNNYNNNNNYNNNYNNYNYYNNNYNYNYYNYNYYNNYNYYNYNYNNYNYNYNYYYNNYNNNNYNYNNYNYYYYNYNNNNNYYYYYYYYNYYNNNYYYNNYYYNYNNNYYYNYNNNNNYYYNNNNNYNYNNNYNNNYNYYNYYYNNNYYNYNNYYYYYYYYYNYNNNYYYNYNYYYNNYYYNYYYNYYNYNYYYYNNYNNNYYYYNNNNNYNYNNYNNYYNNNNNYYNYYYYNNNYYYNYYNYY"

1020960249

3666

126

1399

Returns: 522400371
99756

{680828, 742235, 623439, 376295, 141040, 236545, 16118, 452919, 981457, 670726, 957339, 817430, 169265, 891582, 803732, 118547, 397799, 68211, 199058, 201576, 389600, 543296, 966683, 920975, 809798, 442364, 390679, 946568, 527050, 402359, 88912, 467276, 349566, 194278, 780257, 446718, 974135, 394860, 197747, 21867, 120286, 287062, 891341, 982091, 446849, 170503, 53749, 347138, 900497, 677504, 616445, 636490, 76121, 857427, 869771, 400892, 26689, 359312, 308277, 354254, 518629, 637711, 495883, 288165, 547238, 730079, 84860, 358357, 222750, 369606, 7695, 80506, 864187, 57607, 940925, 907718, 469929, 548947, 565297, 238691, 372443, 152215, 233693, 401140, 780501, 489205, 690202, 387158, 795135, 323445, 403747, 695175, 129634, 954568, 498834, 660927, 235657, 998676, 76940, 342974, 647317, 196147}

{280501, 195555, 392910, 802780, 435184, 78486, 75806, 745499, 307235, 273091, 991191, 767916, 1963, 686903, 673841, 235090, 503920, 608137, 527795, 104783, 956921, 874010, 879536, 654127, 905546, 520301, 251761, 284336, 674349, 208546, 855993, 851793, 787824, 82342, 854674, 579732, 98219, 9819, 236519, 391586, 358154, 767403, 752342, 372654, 619356, 560143, 605898, 30103, 819016, 783357, 441387, 560307, 606571, 94367, 871514, 584339, 547185, 355610, 957693, 515184, 632597, 491039, 283763, 700016, 50853, 988852, 812586, 205115, 787772, 54689, 59768, 865308, 189403, 401157, 427253, 456923, 787160, 688906, 911672, 596386, 798968, 862168, 163569, 986978, 239332, 919190, 272551, 53738, 78556, 302173, 858656, 4142, 913457, 723350, 965635, 507845, 782798, 382527, 572698, 285684, 410328, 888899}

"YYNNNYYYNYYNNNNYYYYNNNYYNYNNYYYYYYYYYNYNYYYNNNNYNYNNYYNYYNNYYNYNNNNYYYNNNYYNNYNYYYNNNYNYNYYYYYYYYNYNNN"

1727405454

282

60

2147068506

Returns: 628696150
91595

{427692, 923326, 563703, 935026, 944549, 709524, 543080, 108353, 220125}

{551407, 522717, 825916, 467927, 657091, 794349, 881956, 116952, 489214}

"YNYYYYNYN"

1585698843

13375

28960

42981

Returns: 543127893
98903

{}

{}

""

1661021601

3

55820

3

Returns: 177959822
90872

{742272, 213113, 988672, 921167, 112988, 936271, 407475, 698735, 583289, 63599, 274756, 128123, 589156, 15252, 715571, 821494, 405213, 80011, 792236, 580106, 195876, 156184, 300716, 632190, 821916, 482380, 796517, 145627, 807449, 234104, 908737, 860427, 645336, 92262, 420347, 650989, 408411, 817815, 306154, 224230, 892920, 311585, 182582, 180005, 600667, 73096, 483557, 661815, 849967, 185814, 965473, 19956, 696055, 511918, 283362, 139598, 883212, 740746, 584226, 398865, 29168, 4609, 218659, 349645, 277561, 5274, 424979, 1663, 804287, 774770, 829177, 383162, 598838, 292549, 353797, 596095, 541912, 266123, 53985, 71996, 97910, 983891, 81670, 224225, 738383, 518169, 885522, 466363, 879742, 678099, 901432, 574175, 109504, 880581, 610557, 492090, 884025, 472459, 910017, 995231, 761690, 289185, 611930, 523242, 405368, 288327, 261816, 36227, 220510, 94677, 750477, 243477, 767801, 162937, 562622, 483448, 555697, 25241, 581807, 981804, 966735, 37009, 657467, 427206, 248979, 758746, 15768, 644095, 527937, 579669, 404142, 462981, 94792, 414843, 392411, 145523, 216396, 808380, 928889, 82203, 803768, 753534, 696582, 283014, 238693, 713656, 3430, 996774, 577584, 175723, 136386, 284317, 468226, 632757, 993660, 570643, 166263, 357198, 852104, 863332, 356244, 710188, 73065}

{518022, 541719, 797408, 68620, 675781, 735344, 555261, 575807, 823630, 700427, 588615, 247458, 771887, 29817, 647939, 1939, 494202, 46406, 8891, 518272, 359466, 301607, 766009, 570264, 158279, 905789, 33703, 999338, 863550, 760105, 770309, 998312, 289700, 242312, 942914, 491191, 860471, 902601, 203194, 315943, 939483, 959608, 902094, 119356, 862978, 461382, 785029, 160817, 979002, 795356, 821396, 951861, 845797, 175006, 464076, 123889, 489955, 261249, 710404, 806736, 199860, 653748, 669386, 584528, 952176, 710021, 910499, 367676, 147860, 563043, 853999, 437716, 71832, 607999, 577405, 156631, 420983, 400275, 191140, 853949, 630302, 959932, 646007, 138063, 946797, 152042, 950651, 688705, 948303, 702092, 353958, 438492, 338980, 28747, 858698, 570680, 848979, 218672, 357696, 251397, 850808, 405799, 220281, 314913, 529244, 915444, 201900, 262621, 614869, 672566, 488114, 566535, 92610, 866072, 893566, 345977, 928697, 360556, 503625, 975703, 274640, 824097, 139518, 74544, 95896, 626556, 975420, 804654, 568704, 978109, 885762, 533443, 192704, 697413, 276372, 873471, 875292, 545042, 45680, 972411, 236879, 348405, 656511, 754538, 625437, 634454, 385833, 151222, 952592, 370124, 621191, 483322, 613009, 457220, 991892, 539982, 69113, 548785, 358939, 725106, 951601, 536977, 448222}

"YNYYNYYYYNNYYYYYYNNYYNNYYNYNYNYYNNYNYYNYYYYYNYNNNNNNYNNNNNNYNNYYYYNNYNNNNYYYNYYYYYNNYNYYNYYYYNNYYYYNYYYNYNNNYNYYYYNNYNNYNNNNNNYNYYNYNYYNNYYYNNYNNNNYYYNNYYYNYNYNYNY"

1149483079

828

8073

599992516

Returns: 252465818
96506

{}

{}

""

1664184446

929

10029

1867332334

Returns: 985386561
93027

{}

{}

""

1944490415

1

2

2147483588

Returns: 102862611
93851

{309730, 864477, 939443, 92202, 102575, 408869, 737820, 989424, 238171, 221204, 905173, 80263, 415520, 378083, 289588, 415422, 171777, 461128, 570892, 67264, 745658, 168717, 274625, 450553, 728654, 893355, 664165, 442550, 716553, 596860, 242904, 32461, 829916, 716717, 104193, 906885, 462806, 309892, 725818, 532971, 210892, 998415, 702245, 941798, 316582, 247217, 795352, 721088, 10395, 184628, 895236, 556190, 322016, 947363, 667922, 724503, 895027, 50436, 957694, 315152, 378973, 738005, 648322, 184737, 240277, 386905, 348908, 393186, 886650, 718876, 481935, 781639, 95709, 701180, 199076, 593608, 537568, 785482}

{298984, 983251, 768046, 861196, 450156, 861673, 53350, 97113, 875175, 908703, 321892, 694338, 981162, 708695, 963087, 114990, 60514, 885722, 525078, 231067, 799162, 692596, 819305, 281129, 971721, 162511, 847183, 488545, 314006, 456319, 64366, 506287, 6546, 494310, 540945, 762596, 19613, 857700, 32414, 758176, 860787, 671954, 102279, 633672, 127747, 407703, 943890, 129338, 851401, 163192, 335940, 752869, 667101, 192097, 536978, 827202, 876620, 329135, 90135, 372005, 17816, 365029, 632481, 993035, 160225, 698440, 914791, 145232, 427839, 319268, 565408, 189089, 233308, 249793, 945157, 79717, 570720, 871696}

"NNYYNNNYYNNYYYNNNNNYNNYYNYNYNYYYYYNNYYNNNNYYNYYNYNNNNNYYNNNYYYYNNNNYYYYYNYNYYY"

549857318

13

31394

16

Returns: 807371881
93732

{}

{}

""

744293682

550

6

34533648

Returns: 728999313
97570

{860316, 735731, 546005, 698396, 244843, 270938, 567665, 549474, 178708, 922027, 19148, 344545, 529006, 820600, 957517, 299805, 768819, 463603, 977934, 781366, 366417, 377898, 19669, 335170, 409716, 162397, 192721, 466087, 536857, 335638, 119689, 47217, 753322, 910941, 539999, 361377, 41635, 110575, 72553, 486966, 485735, 542850, 581190, 646245, 172552, 942379, 167983, 992530, 262887, 640512, 569281, 707655, 582058, 551850, 762293, 446168, 861545, 836415, 803406, 725197, 244869, 719247, 131140, 512484, 564889, 377293, 357039, 61978, 389453, 505071, 387228, 363599, 928120, 381116, 170973, 832535, 708184, 867242, 469548, 472758, 73179, 630340, 56075, 536614, 645726, 156103, 779759, 193416, 483346, 848975, 259642, 590683, 171357, 344208, 831878, 197022, 916540, 714975, 395041, 418595, 720518, 174829, 697793, 83507, 483772, 812262, 655195, 104634, 562027, 642887, 543000, 173686, 594082, 115312, 684773, 586693, 566706, 229530, 376209, 178316, 555427, 503551, 441311, 660558, 142131, 186130, 920798, 938780, 762067, 567441, 761676, 814119, 202455, 789214, 567745, 21263, 395508, 432423, 613040, 696257, 205598, 604002, 412042, 870730, 36581, 90276, 945601, 218186, 226576, 472255, 609905, 736332, 348009, 615186, 680539, 664973, 373739, 131264, 642674}

{747199, 722091, 422179, 899204, 723187, 722351, 870893, 883624, 618706, 365011, 414935, 179517, 472345, 274224, 349154, 117415, 632422, 533261, 389382, 333659, 292370, 656941, 384546, 520864, 352998, 273699, 519119, 771935, 46852, 311629, 700255, 905079, 263680, 821488, 364165, 319640, 690210, 173205, 521597, 357984, 99856, 604959, 133052, 697541, 581384, 45463, 59844, 196442, 235264, 835545, 687075, 961885, 669849, 637894, 269820, 555254, 627566, 638450, 983113, 177953, 618974, 749994, 204844, 639629, 996884, 528929, 276576, 146358, 850155, 422773, 844707, 908400, 781704, 167704, 331629, 549849, 129258, 680363, 436318, 816873, 67700, 440460, 837058, 897770, 377343, 42938, 814937, 185326, 165223, 854, 702343, 14622, 215529, 170581, 566399, 30115, 213022, 521219, 146872, 373776, 458546, 399556, 520000, 80016, 171687, 312971, 472093, 538316, 623571, 901778, 787384, 345143, 441530, 231874, 618915, 828208, 635139, 285135, 761574, 752560, 350005, 984947, 605095, 112, 65730, 846023, 145780, 890836, 283048, 62899, 992366, 590420, 934769, 537422, 462015, 564872, 116806, 464292, 95167, 52205, 756090, 706125, 723938, 849406, 586624, 71892, 847575, 955240, 815601, 662152, 425075, 858164, 614708, 891067, 638430, 823723, 82750, 739522, 325249}

"NYYYNNYNYYYYNYYNNNNNYYYNYYNYNYYNYNYNNNYYYNYNNYNYYNNYNNNYYNNYYNNNNNNYNYYYNYYNNNYNNNYYYYNYYYYYNNYNNNYYNYYYYYYYYNYYYNYYYNNYYYYNYNNYNNNYYYNNNNYYNYYYYNNYNNYYNNNNNYN"

876780221

3363

587

823

Returns: 641161389
98417

{}

{}

""

927571257

212

439

6

Returns: 45510650
96926

{}

{}

""

243986028

233628

962

2594580

Returns: 111098309
90425

{}

{}

""

1124266847

32

1

1018

Returns: 0
99854

{572967, 384083}

{939090, 577258}

"NN"

2039906394

1

1070

1023226

Returns: 676327992
98038

{141601, 140349, 246636}

{601995, 422023, 853662}

"NNN"

1636796054

1710

505

2144699572

Returns: 690697961
91716

{720125, 515279, 609055, 267243, 546309, 201943, 118103, 528678, 935738, 363858, 225038, 4486, 55265, 387187, 823842, 268180, 80883, 836994, 901691, 423748, 7569, 203048, 711626, 618944, 154599, 633627, 464409, 750899, 480799, 265342, 453997, 420973, 593208, 758923, 202070, 725272, 817624, 650529, 647158, 480682, 956155, 343113, 191022, 540081, 169123, 99793, 255859, 89779, 753066, 113638, 655166, 715028, 250653, 697161, 657504, 670207, 121610, 526039, 518369, 158388, 800124, 232885, 199336, 661864, 968565, 171581, 532782, 977151, 468630, 688194, 366651, 793413, 70307, 916519, 564420, 261483, 960833, 963710, 971747, 299184, 199895, 251257, 918922, 89857, 524042, 447675, 28454, 384255}

{415224, 499866, 47291, 871441, 705715, 197921, 607667, 884098, 808527, 530488, 48097, 608825, 786753, 126359, 140866, 313924, 95832, 669605, 691544, 610864, 37384, 824380, 583525, 498419, 69425, 597713, 901586, 567653, 818757, 940455, 277968, 286867, 346791, 250174, 397592, 365701, 963732, 211146, 718772, 625601, 145359, 712513, 652289, 831789, 332565, 226405, 116398, 925889, 562333, 210498, 869379, 744267, 155398, 227479, 686369, 447614, 267576, 418646, 158405, 394226, 716476, 665116, 337974, 397917, 696555, 493351, 182034, 525488, 805182, 73907, 25402, 680101, 396662, 989788, 744943, 336954, 998318, 647912, 4038, 590281, 91226, 294693, 326988, 158670, 728258, 495811, 945622, 58619}

"YYNYNNNNNNYNNYYNNNNYNNNNNYNYNNYYYNYYYNNYNYYNNYYYYYNYNNNNNYNNNYYNNNNYNYNYYYNNYYNNYNYNYYYN"

259215348

108

842824

2371389

Returns: 594381107
95093

{186864, 100142, 894295, 793354, 870666, 286586, 497198, 835556, 39090, 108795, 671565, 34500, 933666, 368400, 105014, 221186, 166379, 205752, 394095, 842206, 818435, 563264, 699127, 201989, 228967, 156692, 170897, 692289, 41243, 47808, 725810, 946966, 378238, 819076, 776921, 779646, 907816, 924513, 137430, 320727, 419766, 931629, 832975, 557634, 1569, 577943, 616885, 756977, 796402, 26507, 120786, 718543, 49290, 892373, 479140, 130574, 274813, 505495, 797501, 927456, 228256, 447122, 214928, 1176, 906049, 13132, 435501, 634956, 14179, 994700, 126100, 531210, 124558, 998046, 601518, 96914, 149814, 316961, 375341, 498380, 172665, 973195, 499858, 878570, 915218, 678870, 857677, 89478, 312296, 810786, 367056, 604666, 769628, 403874, 945650, 52317, 656934, 803837, 842519, 145333, 764712, 413038, 502847, 148304, 806697, 608165, 201149, 126028, 108833, 214956, 585074, 443211, 484740, 705631, 622239, 540615, 962825, 746351, 201527, 485937, 834669, 577130, 36614, 649308, 904167, 119958, 328071, 838236, 745119, 96212, 475165, 172984, 561248, 243894, 829905, 752524, 410866, 618639, 181702, 604715, 588731, 324026, 956930, 274758, 29786, 697593, 464088, 915967, 156071, 303858, 419697, 68793, 249426, 590646, 417555, 666053, 385964, 775617, 813825, 835037, 881889, 187914, 673027, 466225, 502149, 931489, 116341, 142453, 350696, 632801, 730002, 867311, 598350, 561601, 913991, 316492, 32643, 157561, 18735, 320678, 728342, 959726, 964718, 433455, 165732, 114284, 989407, 909898, 870055, 290271, 996232, 925753, 635590, 751192, 106140, 4884, 573899, 894990, 381260, 702854, 557446, 858337, 152318, 355669, 841139, 633475, 408440, 668347, 51693, 362430, 760890, 665715, 693824, 925195, 284584, 746239, 887321, 17800, 486774, 401400, 517578, 905081, 681210, 63860, 979022, 461345, 587638, 762815, 560480, 187579, 998970, 58647, 318952, 954862, 319307, 258928, 217937, 600614, 1146, 188676, 411657, 88667, 633950, 443245, 398556, 595813, 937342, 107965, 760487, 105359, 310996, 20921, 313426, 78869, 767945, 350908, 258028, 770989, 880310, 513539, 299446, 517614, 538649, 394703, 446344, 699915, 454765, 985419, 576369, 546557, 785983, 35592, 811000, 728815, 904837, 687641, 67884, 933914, 834134, 27908, 782187, 428433, 6769, 551072, 585217, 437374, 500294, 974315, 495497, 610138, 21091, 257211, 695743, 157715, 639945, 751218, 446640, 594212, 546663, 13556, 264950, 878528, 131379, 41153, 596961, 304705, 997991, 214232, 96573, 512884, 906102, 952553, 158516, 330885, 164312, 950374, 770819, 200279, 751594, 380356, 602805, 676619, 63983, 266366, 348891, 300437, 442364, 795898, 110321, 529685, 833892, 501223, 360108, 373903, 35419, 563833, 562831, 732388, 83989, 32947, 485668, 778599, 348840, 793657, 406340, 676852, 820735, 694866, 724057, 851341, 661764, 172352, 390006, 252599, 409055, 660837, 797944, 785050, 9709, 401004, 478273, 718105, 874487, 862610, 378301, 221405, 747125, 998054, 808589, 60503, 20629, 491630, 960518, 516646, 803129, 271809, 977893, 750711, 588346, 837911, 176271, 415512, 930448, 760468, 68445, 33448, 334870, 327175, 903745, 949674, 491775, 641352, 575073, 540217, 939454, 479275, 64301, 930348, 274331, 376618, 210927, 837052, 968056, 944563, 188541, 47281, 875725, 419286, 612913, 217777, 945756, 352706, 821951, 732736, 91338, 940263, 821261, 378738, 563856, 339824, 338296, 912342, 152467, 590541, 237641, 917535, 610617, 803973, 394239, 421018, 206731, 796463, 923143, 245346, 442146, 344757, 57194, 546630, 249426, 231141, 758739, 115372, 131666, 168716, 396071, 481064, 895082, 502749, 352300, 711047, 35181, 639371, 629166, 61844, 205143, 395174, 978118, 774645, 906032, 568992, 291534, 32041, 667489, 562628, 703984, 634490, 706518, 875238, 468244, 367058, 608092, 335115, 447387, 7314, 813884, 393614, 331824, 85371, 948691, 755142, 14921, 328060, 746556}

{678725, 604693, 404772, 842064, 622831, 927644, 302395, 270262, 429295, 927230, 254512, 706428, 603245, 344314, 851315, 825158, 497592, 104670, 671950, 215, 129584, 180141, 571622, 774242, 743919, 613895, 917330, 18523, 199152, 101982, 967176, 466864, 474931, 682411, 750137, 876166, 293237, 122400, 999836, 836015, 47775, 258016, 984234, 613589, 439828, 138602, 984421, 547587, 85435, 241644, 992778, 657181, 530220, 814050, 457548, 678374, 213788, 804352, 564043, 479337, 257563, 249064, 35441, 71229, 708658, 923425, 918592, 195486, 333213, 916302, 4932, 13810, 414986, 275710, 782249, 935329, 114659, 209319, 372769, 163288, 799512, 121057, 202528, 950770, 825050, 964419, 792123, 260320, 360084, 731802, 536916, 99120, 627280, 997918, 172465, 903230, 292336, 76311, 839088, 988617, 114514, 597087, 994074, 750444, 293787, 77021, 617127, 808353, 231549, 935567, 599831, 404374, 498356, 573245, 952977, 60296, 866775, 805607, 259919, 31881, 764549, 843051, 584652, 314301, 787146, 685341, 731799, 789715, 109969, 159098, 440779, 979855, 373272, 922681, 571480, 927698, 543760, 442713, 398385, 290878, 550163, 88750, 10960, 375305, 527769, 911007, 903803, 826132, 673252, 181740, 973851, 519076, 119530, 989767, 460845, 823434, 452053, 90006, 737604, 668, 782407, 76045, 413601, 774143, 386070, 332662, 282134, 156774, 499749, 561795, 393847, 537862, 322662, 868650, 77921, 598142, 961318, 481835, 785607, 244364, 199119, 315783, 886754, 847537, 348849, 183791, 542849, 35543, 365779, 275251, 775966, 328230, 7203, 39054, 656713, 500182, 21108, 32065, 769028, 431670, 472599, 526278, 308857, 134018, 400025, 363038, 97848, 754910, 22098, 942765, 39866, 869225, 705607, 662250, 461638, 569691, 684212, 646650, 61567, 27534, 651431, 187891, 73980, 885759, 634721, 81619, 824995, 685294, 797883, 599434, 854562, 269820, 286933, 370243, 879634, 82018, 36780, 439048, 909902, 848805, 202261, 777865, 134416, 319314, 212052, 209160, 352843, 638185, 223051, 721509, 754020, 553544, 911445, 549538, 398889, 743731, 328230, 509645, 330016, 680883, 674511, 266282, 76272, 516809, 72123, 76281, 948795, 126157, 923904, 701867, 68916, 338631, 704735, 745005, 781754, 724260, 770336, 22391, 118706, 698521, 305606, 210177, 184287, 63128, 164406, 851638, 779681, 499831, 866144, 289406, 320892, 840872, 628656, 624154, 155599, 185152, 707287, 856596, 962001, 323794, 459669, 257154, 823285, 494709, 479728, 81509, 940132, 205863, 744280, 971454, 234764, 359926, 127007, 486189, 484789, 23263, 213234, 118403, 520846, 735414, 601989, 519617, 166650, 351954, 396273, 740753, 171968, 221726, 728615, 133452, 633790, 284040, 908635, 339973, 408242, 680159, 206114, 106483, 517417, 103604, 326195, 327657, 35201, 449055, 998532, 343732, 114186, 278051, 338160, 106151, 238634, 907689, 898671, 757274, 143059, 734624, 661755, 60418, 820380, 557732, 869808, 360845, 636654, 293252, 258557, 858748, 937683, 992320, 721242, 336578, 70277, 261121, 544056, 932023, 639985, 453134, 407362, 995957, 510561, 567042, 948002, 628164, 326252, 758673, 260576, 677689, 654013, 175932, 882626, 47182, 994533, 723020, 762812, 648834, 206857, 753403, 100273, 278049, 99550, 464492, 341336, 96849, 164216, 795263, 430371, 66534, 848847, 845176, 783701, 457058, 562474, 347931, 855224, 665572, 883411, 575015, 809832, 418110, 853930, 767853, 885641, 525623, 977352, 492987, 1817, 451069, 799184, 394505, 155133, 497048, 273276, 566046, 494978, 81647, 243953, 716587, 262735, 869405, 246989, 196242, 31694, 172880, 680853, 744847, 412632, 553001, 803625, 627177, 908969, 399590, 946410, 655678, 746512, 305950, 252877, 872556, 482940, 314686, 691412, 680386, 315963, 547848, 663266, 735945, 173198, 502031, 541523, 637188, 969149, 601306, 132511, 890315, 196005, 678568, 400855, 484959, 534434, 56983, 444148, 673617, 600491, 236557, 739895}

"YNNNYNYYYNYNYNNYYNYNNNNNYYYNYNYNYNYNYYYNYYNYYYYYYYYYNNYNYYNNYYYNYYYNYNYNYNYYYNNNNYYYNNNNYNNNNNYYNYYYNYYYNNNYYNNYNNNNYYNYNYNYNNYYYNNNYNYYYYYNYYNNYNNYYNYYNYYYNNYYNYYNNYYYNNNNNYYNNYNNYNYYNNNYYNYNNYNNYNYYNNYNNYNYNYNNNNNNNNNNNYNYYYYNNYYYNNNNYYYYYNNNYNYYNNNYNNYYNYNNNYYYYNYNYYNYNNYNNNNYNNYYYNNYNYNYNNNNNYYNNNYYNYYNNYNYNYNYNNYYNYYYYYYNNYYYNYYYYYYYYYNNNYYNYNYNYNNYNYYNNNNNNNYNYYYYYNYYYYYYNYNYNYNYNNNNNNYYYYYNYYYNNYNYNYNYYNNNYNNYYNNNNNNYYNNYYNNYYNNYYNNNNNYYYNYNYYYNYNYNNNNYNNNYNNNYYNNYYYNYNYN"

409029897

23

1

2147483598

Returns: 429917461
96886

{722866, 641259, 499741, 485499, 401705, 957479, 412934, 714211}

{670033, 656786, 606700, 122604, 536235, 230146, 455948, 633490}

"YNNNYYYY"

1526119363

292961

775

1037962807

Returns: 630606029
91108

{67262, 806226, 826659, 139082, 991064, 203334, 374724, 115852, 864011, 935951, 530356}

{272615, 310473, 473522, 512688, 799584, 550458, 408581, 73158, 396325, 866052, 793302}

"YYYNYYNNYYN"

1225257871

187

466557

2807

Returns: 884102999
94477

{727952, 613669, 32936, 809032, 383376, 577539, 456243, 384851, 640883, 600691, 592827, 142770, 511837, 483833, 228860}

{999521, 844461, 263413, 614723, 450752, 426193, 953327, 980743, 599328, 950972, 852612, 624508, 482275, 368129, 908787}

"NYYNYYYNYYNNNNN"

1676286587

9

1

2147483560

Returns: 141448216
92720

{}

{}

""

108486811

494

9

12

Returns: 646182062
94744

{}

{}

""

860391553

6160

9

904991852

Returns: 578364864
93455

{}

{}

""

398863777

11744

29

3390462

Returns: 90617666
99267

{}

{}

""

339872502

13

613

2135983990

Returns: 911976435
97660

{702983, 247523, 376423, 950809, 394243, 397345, 352333, 518706, 101931, 655602, 28039, 136913, 187702, 919064, 699138, 849255, 174744, 476619, 283462, 70422}

{479, 546346, 286633, 934799, 96061, 870532, 708191, 317746, 911334, 889204, 455881, 90638, 405565, 98283, 646631, 477106, 277147, 307372, 966921, 769913}

"NYNYYYNNNYNNNYYNYYYY"

1349411407

273763

4

2146487348

Returns: 670836197
94414

{}

{}

""

1085755068

2

323335

1815482724

Returns: 479898024
97260

{204494, 44574, 465069, 217635, 20984, 691343, 99469, 506687, 84810, 886085, 807274, 463774, 224914, 637324, 596113, 184396, 842458, 407761, 20406, 256566, 725063, 925239, 749593, 928034, 886685, 330035, 542565, 249412, 590394, 636609}

{235976, 861328, 123157, 687835, 565468, 18787, 910747, 985401, 179506, 152012, 109528, 522337, 105341, 42394, 359196, 221463, 297286, 824979, 859228, 492689, 608838, 253368, 835425, 478113, 506188, 752802, 611773, 174977, 448457, 583186}

"YYYNNYNNYYYYYYYNNYYYNYYYNYYYNN"

959892172

287

405

1818915466

Returns: 509661010
94091

{}

{}

""

2019459036

9

55286

2147481840

Returns: 765499781
97207

{}

{}

""

725733710

9

175805

1884399370

Returns: 666652454
99305

{}

{}

""

1951844757

217

1750

2147483642

Returns: 24484238
94262

{182183, 209845, 994097, 353316, 383416, 172423, 414232, 446266, 63227, 646447, 751982, 906339, 681851, 228958, 882652, 603360, 454797, 981037, 59231, 417208, 357137, 416405, 511792, 933035, 48378, 675000, 848200, 538728, 340899, 961919, 590216, 998220, 932699, 609818, 396360, 76237, 739557, 183250}

{324572, 386759, 132813, 274731, 139734, 51325, 274812, 340264, 26012, 481449, 711296, 478656, 31243, 413437, 81689, 292396, 168006, 211941, 834797, 60227, 121053, 127518, 640498, 970895, 221022, 43890, 426096, 12987, 964099, 649444, 847790, 349143, 976135, 437540, 817953, 398797, 12546, 217975}

"NYYNYYYNNYNNNNNYNYYNYNYYYYYYNYYYYNNYNY"

998843752

10

1022

26451741

Returns: 91688172
98275

{}

{}

""

38723574

4

643342

2133214993

Returns: 291519739
95941

{}

{}

""

1618507555

7

332959

2147113320

Returns: 892011958
91110

{}

{}

""

1554688136

140

7

2147483260

Returns: 607143579
95500

{}

{}

""

1805629465

814

218064

2043822124

Returns: 98411749
95794

{744905, 129934, 783371, 704619, 235090, 801305, 711534, 423910, 298025, 934043, 579621, 690874, 966292, 119996, 411171, 239992, 263625, 220319, 495731, 355099, 929997, 390978, 758148, 280239, 444137, 191479, 862113, 851622, 962317, 747573, 834908, 433736, 372896, 712258, 373631, 702819, 695104, 313884, 296770, 488416, 10511, 847697, 936602, 643158, 493280, 720981, 896081, 569164, 560221, 799117, 880149, 153330, 751758, 141429, 15325, 355757, 505996, 558775, 944010, 358649, 718966, 341384, 177851, 467697, 1555, 996249, 263250, 566945, 849397, 812708, 206347, 754282, 818684, 45646, 354628, 992766, 700035, 402915, 686598, 882457, 461277, 258080, 531459, 16296, 220118, 25918, 55030, 924302, 697748, 897921, 415894, 542935, 71938, 577853, 655035, 184429, 305229, 372683, 806047, 633653, 373660, 333662, 24363, 765662, 901249, 792270, 614596, 905420, 276800, 859593, 388149, 292528, 840178, 515143, 264306, 249302, 798020, 223303, 510052, 377435, 44908, 384580, 316859, 805722, 782939, 588603, 704759, 347207, 120121, 238155, 414008, 981595, 440102, 238911, 231495, 668081, 541219, 20755, 373387, 529238, 464612, 211525, 64417, 101461, 349129, 9305, 279634, 390712, 915792, 209946, 125082, 733103, 799938, 277995, 456219, 441869, 470124, 945100, 9802, 413300, 909907, 975409, 499157, 629901, 359236, 848331, 691377, 24821, 418022, 325661, 497680, 448487, 951968, 691520, 846404, 889454, 441521, 156617, 302852, 735236, 729743, 313257, 622991, 679177, 179678, 793627, 568931, 160449, 17672, 867700, 42706, 605509, 624290, 858301, 116921, 915290, 487351, 860585, 856610, 269548, 327783, 348319, 521595, 938348, 283001, 925419, 376806, 234504, 43519, 229486, 42411, 358674, 972997, 806620, 409442, 900269, 237259, 506244, 172161, 982366, 648214, 55930, 788259, 529091, 542900, 846336, 146662, 437039, 831802, 507490, 880006, 618553, 673533, 471351, 60890, 463334, 625364, 622722, 340129, 15590, 556821, 571218, 941307, 23702, 60342, 631362, 323677, 317976, 261706, 810084, 552835, 681845, 891023, 546272, 721993, 178102, 107608, 286268, 453017, 30215, 691583, 621696, 784214, 134043, 382793, 475650, 845606, 451731, 952339, 900951, 335080, 100608, 398708, 134018, 729831, 820255, 42462, 451211, 936397, 12067, 54694, 320059, 309609, 203448, 219940, 764201, 588744, 839502, 707056, 176532, 539687, 99855, 269777, 848045, 414124, 538052, 579727, 317572, 981750, 852610, 678391, 390535, 833817, 118471, 574635, 212125, 600268, 444694, 653624, 532541, 63004, 965076, 277466, 498326, 301351, 49132, 437392, 785620, 330683, 589796, 16647, 173811, 988408, 151262, 876782, 903819, 859845, 301947, 718006, 88197, 45730, 639428, 781025, 270443, 722503, 884904, 398142, 247385, 157651, 172542, 927864, 86033, 412331, 275835, 913364, 750386, 558471, 346601, 616525, 543734, 641249, 904520, 462174, 405692, 676734, 763002, 781011, 118347, 938417, 208848, 121412, 907402, 658527, 33139, 433880, 131295, 214118, 580506, 776911, 631801, 839988, 948122, 830952, 879196, 12100, 303949, 222169, 362420, 401559, 555907, 453329, 822712, 134530, 159036, 815509, 843201, 71950, 693963, 844380, 259746, 106168, 964328, 185306, 421562, 347103, 87198, 53517, 557210, 451940, 960796, 304392, 90489, 470815, 837509, 791211, 498170, 861764, 97125, 173317, 898573, 280167, 227684, 245492, 219660, 739825, 467659, 228575, 427030, 633853, 642583, 509953, 536738, 197454, 186361, 419832, 579558, 241253, 856655, 516560, 771280, 719394, 249727, 17738, 92833, 976583, 183351, 900431, 679078, 453592, 61972, 468132, 57953, 361150, 680700, 342239, 893619, 283155, 908860, 532809, 467095, 994331, 33131, 89248, 819570, 785502, 155748, 890124, 473642, 949542, 70581, 866081, 935372, 979720, 81639, 96485, 33921, 598650, 612168, 661136, 781162, 781813, 908665, 378897, 859294, 464340, 341260, 543522, 95689, 401489, 489706, 423872, 736718, 261807, 22788, 843079, 789715, 760611, 921692, 15601, 898444, 63119, 639785, 155551}

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"YNYNNNYYYNYNYNNNNYNYNNNYYNYNYYNNYNNNNNYNNNNNYNYNNNNYYNYNNNYYYYYNYYYYYNYNYYYNYYYNNYNNYYYNNYYYNYYYNYYNYYYNNYNYNNNYNYNYNYYYNYNYNYNNNNNYYYNYYYYYNNYNNNYYYYYNNYNYNYNNNYNYNYYNYNNYNYNNNNNYNNYNYYYYNNYYYNNYNYYYNNYYYYNYYNNYYYNYNYNNYNNNYYNYYNNNNNYNNNNYYNYYYYNNNNNYYNYYNNYYYNNNNYNYNYYYYYNNNYYNNNYYYNNYYNYNYNNYNNYYYYNNNNNYYYNYYYNNNYYYNNNNNNYYNNYYNYNYYNYYNYYNYYNYYYNNYNNNNYYNYNNYYNNNYNNYYNYYNNYNNNNYYNNNYYNNNYYNYYYYNYYNYYYYNNNNNYNNNNYYYYYNNNNYYYYYNNYNNYYNYYNYYYYNNYYYYYNNYYNYNNYNYYYYNNYNYYYNNNNNNNYYYNYYYYYNN"

111769111

33161

158095

2146408022

Returns: 299757543
90502

{}

{}

""

2069914077

30

1

2040231109

Returns: 0
94854

{592692, 883483, 647065}

{65058, 681196, 454495}

"NYN"

1899220026

499

1934

2147482857

Returns: 734971352
90232

{}

{}

""

1097511144

332

55

7322

Returns: 230550166
91998

{363889, 323716, 583355, 65908, 82364, 358369, 842120, 292314, 248523, 590607, 387151, 609367, 384279, 249719, 859599, 448134, 933023, 242850, 742416, 512416, 60217, 440999, 111859, 927438, 323096, 66199, 34503, 211497, 669931, 171106, 806697, 180056, 207571, 901869, 957740, 464803, 130460, 473543, 140696, 909560, 216451, 654111, 2330, 574019, 575057, 318975, 45036, 419150, 898588, 886638, 78051, 807945, 755503, 987036, 148397, 39826, 949855, 402992, 557924, 223606, 429245, 903950, 641134, 216949, 55610, 657399, 792166, 990423, 39757, 416941, 122059, 133703, 331765, 967679, 929153, 958583, 805361, 414790, 656026, 363820, 729581, 297121, 127854, 824549, 664965, 487374, 98421, 634068, 692470, 623985, 945072, 615179, 538070, 736913, 88187, 430512, 662618, 998850, 671912, 63601, 433646, 447722, 87878, 368352, 314357, 247490, 828291, 458657, 993213, 358110, 452909, 913007, 899118, 913597, 863805, 717260, 715225, 502598, 77314, 735134, 933269, 534751, 252012, 635101, 734079, 549185, 827461, 41956, 159094, 232847, 368595, 799681, 928705, 899204, 101940, 302608, 433199, 61937, 450730, 150686, 205555, 489007, 637711, 66144, 192918, 687987, 995012, 133573, 493159, 397316, 164636, 888224, 515732, 721950, 219219, 372474, 18167, 596918, 342445, 220582, 196989, 845884, 366209, 486827, 516492, 607668, 511651, 67800, 993426, 353728, 968845, 294346, 150833, 342936, 61816, 698373, 417820, 2326, 785999, 654565, 345420, 168595, 745906, 750527, 614893, 593053, 564686, 592468, 305903, 981632, 750873, 299954, 612683, 561046, 828258, 862835, 470474, 695289, 664428, 328122, 243495, 709215, 398066, 644706, 447692, 785756, 791452, 710213, 424092, 705900, 104793, 323715, 599129, 127095, 820900, 537209, 421747, 129309, 78787, 890714, 37035, 696350, 987496, 492746, 417858, 504111, 72716, 843807, 416399, 607155, 405147, 249380, 405348, 443307, 779467, 502177, 44615, 28122, 724310, 636265, 778040, 962873, 292359, 225950, 387605, 696487, 730526, 682277, 986392, 46773, 266359, 24815, 644032, 363301, 976190, 871035, 437642, 489627, 919055, 307477, 316665, 956389, 211209, 666479, 587117, 55477, 499430, 595298, 168659, 815493, 11063, 475375, 945782, 39845, 432003, 51739, 720160, 136553}

{65469, 243604, 804326, 69474, 33674, 477549, 843071, 27317, 455255, 226422, 547353, 602571, 169399, 334935, 308432, 245574, 522471, 68874, 619772, 646835, 598731, 907713, 825875, 588524, 763478, 201752, 836012, 483266, 535886, 338553, 669512, 444902, 103048, 613113, 72374, 141000, 713782, 456350, 424134, 671640, 291727, 627895, 318736, 219053, 254073, 216181, 3430, 440201, 987191, 424539, 194799, 649168, 198972, 571297, 65830, 523005, 218555, 655909, 897342, 69114, 788688, 751557, 489569, 866205, 609896, 3784, 655893, 961282, 559298, 595198, 385311, 931390, 689267, 955526, 529358, 680331, 371464, 932342, 338967, 128825, 920777, 206032, 203683, 71075, 510489, 620862, 585538, 62825, 163767, 412887, 264691, 966919, 572617, 513755, 95274, 817823, 869638, 803731, 325861, 553010, 623991, 540523, 45104, 293436, 372535, 22972, 283811, 501884, 465457, 293374, 686529, 693330, 382416, 280030, 869886, 30344, 821367, 442147, 183661, 246156, 835313, 15480, 2390, 342457, 117706, 92962, 285643, 205484, 373101, 629992, 140876, 710298, 465485, 194036, 165371, 783111, 29876, 40062, 717461, 791863, 326928, 660533, 491818, 202650, 86830, 388476, 482937, 938241, 389846, 112566, 322574, 70062, 898543, 582754, 338575, 574611, 923166, 554293, 435238, 551560, 305425, 597410, 879475, 51549, 106085, 682862, 352161, 542847, 535435, 558512, 72756, 635481, 731205, 936807, 612190, 244924, 83294, 41390, 297107, 490555, 194745, 347320, 373734, 699279, 778418, 468528, 492854, 105195, 684577, 368520, 16406, 209926, 187363, 635472, 463827, 832831, 910265, 715131, 692217, 871635, 274242, 656414, 478118, 508244, 344753, 724847, 289319, 691007, 712468, 800119, 178956, 965325, 395596, 790251, 212656, 283653, 488099, 725681, 426217, 482768, 301395, 888626, 401712, 837651, 544858, 433812, 202879, 88823, 340615, 817355, 479963, 639162, 650222, 457908, 367962, 301031, 999244, 12296, 406827, 749659, 469069, 251970, 112369, 380145, 622617, 106584, 725758, 660368, 934243, 905847, 636584, 288419, 930836, 585442, 248354, 643296, 156341, 921287, 933016, 42634, 978657, 517672, 41355, 439206, 267845, 384597, 753905, 943397, 155804, 383423, 621819, 709627, 382099, 968765, 272245, 347250, 928929, 545179}

"NNYYNYNYYNYNNYNNYYYYYNNNNNNYNNYNNNNNNYYYNYYNYNYYNYYYNNNYYNNYYYYNNYYNYYNNNNYYNYNYYYNYYNNNNYYYYYNNYYNYNYYYNYNNYNNYNNYYNNNYYNYYYYYYNYYYYYYNNYYNYYNNNNYNNYYNYYYYYNNYYNYNNNYYNNNYYYNYYYYNYNNYNNNYYYNYYNYNYNYYYYYNYYYYYNNNNYNNNYYNYNNYYNYYYYYNNNNNNYNNYYNYNNYNYYNNNNNNNYYNNNYNNNNYNNYYNYNNYY"

353536898

2257

680928

295941956

Returns: 784079139
99466

{}

{}

""

465702355

2

13

2147467474

Returns: 117597983
92218

{564568, 47003, 882263}

{371531, 94687, 814011}

"YYN"

2055228188

2602

52

59391204

Returns: 179852869
94504

{127911, 610296, 562329}

{960347, 432554, 562561}

"YYY"

205155261

90

17129

2144686728

Returns: 728904675
91297

{}

{}

""

430772514

29457

8374

2147304694

Returns: 694374722
95675

{}

{}

""

1143726347

26955

30446

2147483606

Returns: 175311731
95963

{}

{}

""

377228716

1

1

2146090384

Returns: 0
95437

{550869, 827183, 690683, 946620, 542363, 379062, 229054, 68302, 206248, 493997, 172166, 478637, 941440, 565425, 784090, 853533, 810752, 968548, 961697, 598650, 720877, 917818, 608187, 395967, 95312, 96571, 361539, 514820, 512606, 968315, 495595, 56518, 577835, 613496, 440528, 558347, 155325, 416447, 888835, 467324, 719541, 168831, 430867, 231310, 788119, 991782, 906075, 32032, 636799, 215747, 233628, 819722, 952392, 820959, 704493, 630912, 991011, 900170, 784877, 915227, 927552, 713933, 393313, 13560, 711969, 451253, 473539, 108617, 245863, 756836, 448243, 341469, 844093, 69661, 364252, 425575, 857604, 61486, 477850, 480850, 280492, 819201, 55376, 512757, 112633, 953858, 941229, 847849, 546635, 965180, 613990, 265263, 238499, 799275, 319158, 65885, 379270, 733083, 645883, 261016, 859959, 968154, 419758, 552181, 387175, 757978, 897999, 20294, 354141, 932222, 52105, 742439, 985210, 59223, 505794, 958960, 568457, 426671, 439913, 584701, 29340, 233013, 941623, 943072, 750207, 903349, 182648, 103706, 75493, 413663, 799544, 123815, 45376, 482147, 283751, 72551, 471126, 665387, 858859, 187310, 231686, 910666, 747014, 325040, 675700, 163522, 191983, 58602, 64219}

{229123, 954766, 558796, 490587, 213615, 402254, 697537, 531830, 17331, 640545, 570872, 171370, 448012, 4988, 291014, 404430, 218853, 1007, 38325, 26373, 584853, 920055, 75168, 708907, 664949, 297675, 886141, 800324, 277824, 939222, 57346, 261459, 832715, 365534, 274768, 623335, 883941, 656322, 540414, 382397, 387882, 745389, 692514, 761622, 882572, 563716, 742860, 991520, 246381, 993966, 856983, 70629, 960423, 990321, 131256, 804697, 444266, 664090, 964724, 801963, 343775, 184205, 743416, 433803, 675365, 534013, 891258, 627548, 716820, 608396, 151961, 190350, 420639, 277857, 892743, 546003, 467837, 369699, 817525, 127748, 568559, 841903, 373222, 553615, 935950, 942195, 635530, 61933, 740670, 146044, 900251, 328486, 551967, 501441, 409182, 157759, 515939, 81161, 215882, 96875, 643577, 522083, 438757, 661230, 543206, 730647, 851761, 676952, 300843, 937180, 554938, 500681, 991697, 152040, 776715, 732294, 275614, 500473, 557172, 715757, 75991, 545345, 856822, 464101, 365239, 20298, 842366, 394390, 83585, 793176, 568515, 163634, 339016, 446023, 807613, 825372, 224705, 27249, 813012, 842185, 346717, 780353, 244159, 956472, 719617, 246437, 678331, 580570, 126787}

"YYYNNYNNYYNYYYNNYYYYNNYNNYNNYNNNYYNNYYNNYNYNNNYYNNNNNNYNNYNYYYYNNNYNNYYYNYYNYNYYYYYNYNYYYYYNYYYYNNNNNNNNNYYNNNYNNNNNYYYYYNNYYYYYYNNNNYYYYNNYNNNYYNNYY"

94119130

26

13

2114906959

Returns: 295955678
90754

{394013, 86312, 691274, 239214, 378979, 404004, 197542, 106979, 455525, 669580, 857728, 491939, 691357, 414648, 755919, 244185, 27281, 948057, 340401, 331427, 785756, 369479, 190180, 687422, 643589, 325735, 799947, 446877, 193215, 103716, 15041, 921802, 653093, 619854, 802833, 707466, 793564, 702348, 74689, 715233, 453094, 816972, 559528, 723506, 845704, 423635, 202557, 867597, 598593, 203151, 51194, 85094, 88046, 520163, 152380, 629788, 710760, 377107, 524099, 299224, 793115, 879954, 415536, 231116, 913372, 979389, 458027, 208891, 873725, 294948, 601679, 653934, 752197, 416652, 545321, 346884, 367178, 623586, 430697, 76876, 256651, 608338, 852789, 819489, 369390, 637102, 326362, 315315, 628119, 82996, 145152, 796144, 148426, 246327, 638361, 353468, 283228, 523703, 541562, 98898, 7929, 326698, 295413, 482083, 445317, 452333, 732873, 801778, 367542, 162271, 240396, 734299, 194640, 565381, 656729, 473172, 358004, 137469, 981761, 869885, 867049, 435590, 274845, 878746, 927076, 587404, 271334, 818438, 675531, 811328, 703640, 314453, 153413, 5855, 354291, 120730, 848454, 719374, 701933, 388799, 862682, 856024, 627944, 943693, 20633, 311842, 714906, 396284, 81506, 656152, 626483, 882117, 28596, 74141, 164886, 28420}

{701489, 978043, 9620, 164105, 99995, 725616, 465650, 728114, 222044, 144839, 990611, 946006, 941461, 393454, 566260, 480116, 77715, 105497, 685506, 752077, 983724, 92698, 862499, 733261, 240817, 395162, 969317, 576636, 414371, 1106, 711923, 215613, 911631, 158850, 449057, 694400, 630875, 438868, 213314, 808087, 316849, 665146, 885636, 740665, 33936, 989944, 952110, 427936, 500770, 576029, 894155, 198693, 895820, 500143, 529846, 73310, 736831, 284443, 460192, 550652, 601901, 733072, 732922, 254766, 258847, 406561, 496131, 524155, 145900, 707768, 729963, 861855, 604952, 766722, 393621, 238050, 595650, 272270, 452792, 542681, 15420, 421368, 709360, 974943, 83740, 573781, 299913, 149813, 651414, 178993, 531937, 468754, 942605, 696794, 333337, 564028, 563395, 968380, 423237, 288213, 92783, 473659, 290095, 209146, 729603, 141615, 893796, 79917, 377966, 587246, 58368, 524104, 348465, 638126, 346173, 119597, 460386, 430249, 139496, 848861, 10433, 607003, 573798, 609915, 53614, 477978, 165573, 85224, 342011, 216830, 27401, 748885, 23560, 633368, 448532, 933868, 706847, 901115, 14838, 869953, 398067, 910415, 301357, 97686, 279820, 776679, 203568, 386242, 129994, 930069, 921564, 684102, 592718, 590940, 713950, 631270}

"YYNYNYNNYYNNNYYNNYYNYYYNYNNYYYNYNYNYYNYYNNNNYNNYYNNNNYNNYYNNYNYYYNNNYNYNNYNYYNNYYYNNNYNYNYNYYYNNYYYNNNNNYYNNYNNNYNYNYYYNYNNYNNYNNNNYNYYYNNYYYNNYYNNNNNYYYNNY"

1856078577

359147

1385

29100

Returns: 310809137
94608

{}

{}

""

1989345746

6192

154

2139830567

Returns: 577813092
90164

{}

{}

""

347967853

344

1

1232579

Returns: 0
90443

{636817, 660900, 491349, 409174, 393812, 506584, 383599, 530601, 11358, 822753, 117102, 211679, 706965, 569484, 981408, 255169, 980390, 690472, 513243, 476822}

{903849, 945514, 62745, 388082, 821228, 54194, 956233, 729699, 853200, 191302, 916986, 597203, 635892, 109055, 613700, 692074, 8173, 593360, 370038, 655612}

"NNNYNYNNNNYNYNYNNYYN"

1430969996

35997

435

9452

Returns: 155035742
97950

{}

{}

""

1920094295

107

524068

2147482945

Returns: 996408180
92734

{899214, 815437}

{236790, 546035}

"NY"

947070920

1

1330

1723103361

Returns: 677244876
99788

{383256, 119149, 752769, 607477, 726887, 115755, 843421, 55239, 552526, 106432, 787597, 311296, 552899, 234130, 121401, 468365, 848276, 296428, 12121, 238947, 754380, 257516, 642361, 759618, 386169, 463864, 843911, 452708, 365500, 55762, 690691, 533709, 279314, 214434, 754550, 645294, 64434, 532277, 252534, 768549, 856356, 921701, 239266, 303440, 538776, 623190, 642720, 903087, 25308, 461545, 853609, 145527, 575549, 801779, 39295, 519462, 542257, 696500, 936397, 163078, 181908, 458740, 510235, 402297, 717547, 774748, 977953, 74974, 350367, 298532, 754201, 920562, 82948, 496804, 622193, 861680, 957074, 376682, 102931, 80549, 120819, 705352, 940366, 117760, 671684, 107842, 570625, 841102, 18444, 666523, 406498, 864315, 991808, 30093, 517983, 816857, 72314, 416749, 553124, 788731, 745425, 788272, 851042, 179097, 78223, 762174, 30786, 393298, 564694, 260246, 976608, 946263, 237182, 698218, 812020, 445035, 513016, 916089, 201300, 830689, 38130, 916909, 890182, 674479, 411714, 322249, 81428, 283309, 480225, 922507, 490840, 563071, 24682, 963062, 257313, 240431, 873401, 438408, 16559, 630656, 594074, 761119, 692951, 985832, 814588, 116498, 138879, 103718, 997182, 300729, 354492, 125181, 193831, 453738, 673264, 208519, 553092, 905902, 307937, 279817, 778334, 448897, 486216, 440164, 73696, 161723, 569605, 546444, 194073, 938565, 579163, 943915, 546740, 95384, 791058, 667611, 418384, 934983, 181412, 249096, 151121, 254189, 380745, 44094, 512070, 908043, 540406, 75598, 951181, 780811, 533104, 325671, 5139, 290952, 795895, 23288, 625603, 908512, 534853, 663114, 106380, 59443, 384770, 484846, 519011, 286263, 285718, 295084, 427976, 689979, 774005, 810753, 670951, 946958, 299163, 783318, 368489, 744372, 14344, 738485, 468638, 811252, 180603, 857269, 259955, 344482, 78416, 845267, 131168, 350054, 620183, 445027}

{962927, 25256, 615818, 749648, 325865, 546042, 826816, 196608, 715129, 572741, 397292, 639220, 730130, 297755, 163176, 943640, 7913, 216832, 445635, 938705, 856801, 722062, 920214, 232444, 234204, 2935, 349474, 827163, 748064, 187804, 485792, 481938, 468173, 651280, 634884, 320553, 761434, 665595, 540503, 977830, 506176, 517019, 707929, 233561, 275749, 742113, 932416, 571629, 579458, 701564, 728377, 210155, 530701, 12506, 492853, 693406, 249979, 955608, 129924, 737749, 290921, 107897, 655108, 391036, 380754, 175821, 165472, 898421, 183772, 625077, 419188, 779524, 548129, 212199, 384444, 605105, 541074, 919563, 767673, 627852, 158285, 637193, 33263, 836923, 417455, 763259, 448460, 200018, 293007, 175596, 292750, 264304, 302198, 929395, 675748, 57352, 138602, 714463, 451699, 996850, 434094, 99562, 489689, 710583, 318597, 639602, 30557, 536124, 415548, 417743, 198923, 745221, 330164, 455324, 17898, 387466, 442691, 68165, 406279, 485985, 885920, 706273, 486730, 775538, 265190, 339236, 554019, 876421, 661826, 259997, 909401, 624420, 129753, 514917, 771887, 16454, 871185, 202512, 952614, 230221, 746023, 94080, 863280, 556525, 511964, 136527, 11746, 541756, 468997, 459786, 206290, 797042, 773389, 132241, 441665, 70582, 6499, 870616, 246074, 262449, 740578, 7221, 417098, 254880, 243482, 711505, 71235, 531428, 533216, 939554, 513248, 237796, 246599, 67571, 457461, 289694, 228348, 862576, 314049, 798048, 491729, 337164, 724243, 198691, 709192, 756176, 465134, 801141, 653089, 88099, 157887, 982790, 537047, 491552, 860903, 115205, 77833, 926082, 231759, 890760, 645762, 140844, 218297, 291476, 750706, 121313, 879710, 394822, 883395, 20816, 558519, 332795, 511709, 337341, 55700, 906075, 665273, 287996, 575223, 862728, 611057, 838467, 212246, 988785, 29451, 254360, 543746, 116734, 465904, 86539, 361321, 706398}

"NNNYNNYNNYNNNNNYNYNNNYNYNNYNNYNNNYYYYYNNNNNNNYNYNYNNNNNNYYYYYYNYYYYNNYYNYNNYYYNYYNYYNNNYYYNNYYNYYNNYYYYNYYYNNNNNYYNNNNNYNNYYNYNNNNYNNNNYYYNNNNYYYYNYYYYNNYNYYYNNYNYNYNYNYYNNNYNNYYNYNYYYYYNYYNYNYYNYNNYYNNYYNYYNNYNYYYNNNYNNNNYYNNYNYYYN"

1449505560

29

364077

2145193975

Returns: 268336926
92466

{141234, 594522, 807786, 915285, 657867, 772759, 998164, 457253, 984618, 818133, 679464, 427961, 240443, 47764, 677168, 530667, 749328, 402605, 285930, 301202, 860840, 505344, 289400, 98593, 413748, 6589, 971465, 463896, 136989, 222038, 584883, 39049, 580540, 508834, 527271, 581246, 237206, 362733, 389794, 128025, 441803, 415399, 129766, 922136, 159512, 557403, 850053, 593760, 476901, 665549, 440687, 456803, 205696, 828816, 918780, 885137, 189556, 740178, 584598, 615958, 385719, 148849, 684398, 37514, 570097, 740868, 796384, 952446, 856792, 480509, 407938, 459169, 2634, 742628, 836074, 315015, 354080, 607555, 143777, 896230, 269034, 482386, 996039, 325371, 978783, 210949, 298189, 779794, 773845, 207395, 932231, 979369, 473699, 721127, 909244, 804043, 467034, 281615, 246048, 965994, 599750, 802184, 122232, 661044, 379291, 267715, 615928, 615562, 101635, 730207, 969564, 630582, 309766, 740657, 229557, 890812, 725641, 539347, 572799}

{728798, 855203, 179880, 86640, 227121, 318566, 646071, 623327, 200724, 431434, 801880, 261552, 107405, 954883, 148030, 106819, 848446, 81821, 240519, 306048, 548198, 591099, 647489, 617692, 354560, 188969, 771802, 218687, 424893, 50625, 903905, 30186, 591725, 139102, 433837, 431884, 70616, 124895, 939114, 577533, 246657, 689342, 855196, 7849, 471673, 776853, 400114, 349659, 929078, 332969, 183448, 937314, 882414, 566180, 46026, 999565, 952433, 184845, 858536, 304699, 385391, 124662, 522767, 86908, 166879, 801366, 289289, 943568, 828631, 332366, 198491, 501599, 539735, 906162, 590172, 255416, 980492, 66970, 75163, 749510, 708435, 857853, 175392, 624396, 117693, 952284, 577902, 938170, 191322, 705397, 13710, 786285, 10674, 944503, 368064, 433420, 571044, 525878, 522829, 975227, 38747, 830546, 667199, 687313, 107686, 901619, 943759, 929336, 506051, 942397, 258987, 39394, 44745, 539818, 673071, 817248, 428019, 814454, 455082}

"YNYYYYYNYNNYYYNNNYYYNNNNNYNNNYYYNNNNYNYYNYNYYYNYYYYNYNYNNNNYYNNYYNNYYNNYYNYYYYNNYYNYYNYNYNNNYYYYNNNNYYYYYNNNNNNYNYNNNNN"

1872193993

1403

543

2143729021

Returns: 966766728
99038

{638672, 438585, 169956, 623582, 119339, 495060, 727584, 344305, 203238, 280338, 608101, 229169, 400791, 729968, 870721, 308324, 550454, 574108}

{787046, 573036, 511945, 261465, 656280, 235725, 162956, 244989, 429295, 65463, 425611, 349523, 114796, 697652, 870008, 36661, 673176, 864668}

"YYNNYNNNYNNNNNYNNN"

435009671

332

29575

12041964

Returns: 970395800
94871

{}

{}

""

501366853

804

1136

1

Returns: 473938867
99551

{234697, 900935, 392195, 969524, 290806, 897211, 761802, 159658, 426481, 179102, 55536, 619277, 299119, 17816, 452140, 804459, 815533, 154536, 348783, 713621, 742120, 605449, 615650, 252147, 864935, 374977, 506195, 843073, 239316, 370086, 659743, 981691, 818680, 254473, 369274, 487567, 691925, 861149, 868886, 398033, 735394, 221472, 9278, 435818, 583585, 248915, 300351, 865945, 60601, 981428, 186483, 883901, 470441, 528567, 380209, 323486, 400326, 459057, 376580, 28717, 375180, 203727, 694123, 744675, 956585, 952788, 363551, 584333, 308975, 110511, 63094, 949768, 869033, 919461, 193175, 171293, 741051, 2550, 999135, 6799, 545938, 727095, 705730, 307654, 704537, 614243, 969479, 407466, 802669, 767633, 983167, 237387, 918358, 449376, 330145, 530066, 94334, 269797, 836997, 812498, 251307, 609454, 125919, 597932, 287432, 662947, 317814, 3454, 317848, 171272, 841181, 740723, 792754, 618657, 487670, 618, 889645, 507724, 503521, 724198, 272270, 804998, 245807, 633965, 982394, 986762, 90575, 523036, 793760, 548197, 366950, 485901, 538593, 757619, 912092, 655854, 37493, 853600, 61249, 583168, 62927, 717177, 673820, 175298, 182857, 862660, 700857, 914235, 45132, 628545, 376357, 113868, 988473, 191754, 348298, 320188, 858189, 725718}

{147478, 484579, 371875, 210317, 311466, 340694, 848587, 25760, 877367, 466298, 307020, 965047, 779497, 661951, 156505, 45615, 770895, 973984, 209706, 144797, 20610, 866167, 32165, 332904, 112586, 397412, 947636, 53236, 937755, 643333, 629023, 937190, 151874, 429901, 347364, 924799, 291455, 135701, 206945, 520261, 116865, 55593, 889677, 742091, 831355, 699960, 338285, 618455, 889548, 721533, 27941, 614096, 779805, 126647, 229902, 20166, 130237, 820707, 800542, 386590, 814656, 886044, 902020, 605345, 150393, 815655, 15424, 595349, 807205, 610341, 239624, 108189, 440990, 829800, 49642, 769985, 403102, 947313, 908771, 219219, 869205, 381010, 889983, 479041, 187613, 418332, 318265, 120515, 21312, 115835, 686072, 103211, 228434, 948083, 161242, 546866, 548975, 819132, 20496, 956125, 403774, 876487, 746268, 847075, 49224, 8195, 784334, 612373, 951449, 14111, 496278, 646161, 222460, 437966, 543990, 219512, 951314, 625442, 367310, 440120, 126318, 560540, 973885, 543147, 43106, 805404, 825098, 431215, 52803, 519857, 485897, 807476, 103016, 797354, 644392, 594251, 798322, 63971, 181989, 643932, 124685, 805215, 192217, 92018, 667517, 164967, 600674, 972616, 866741, 783172, 770289, 631551, 254966, 595500, 380110, 612222, 331082, 727929}

"NNYNNNNNNYNNNNYYNNYNNNNYNNYYYNYYNYNNNYNNNYNYYNNYNNNNNYNNNNYYYNYYYNYNNYNNNYYYYYNYNYYNYYYYNNNYYYYYYNYYYNNYNNYYNYNYNYNYYYYNNYYNNYNYNNYYNNYNNNNYYYNYYNNYNNNNNYNYYY"

1568973913

6061

32

131646898

Returns: 24644893
96344

{713813, 793494, 556357, 876627, 482733, 883781, 131854}

{400759, 176286, 372748, 417210, 150549, 50990, 414698}

"YNNNNNN"

1493435669

61780

14467

2091900536

Returns: 960237294
95341

{14164, 199589, 246070, 322482, 668051, 511994, 601028, 14781, 839444, 60003, 672439}

{736864, 862458, 978996, 414294, 985051, 537434, 160964, 448523, 850440, 334220, 608031}

"YNYNYYYNNNY"

1533892259

195

40515

1097032

Returns: 361821821

Statistics

Problem Statement for "Cascade"

Problem Statement

Definition

Notes

Constraints

Examples