doublings:= [ <1, [ <1, 1> ]>, <2, [ <1, 4>, <2, 1>, <3, 9> ]>, <3, [ <1, 6>, <2, 3>, <3, 2>, <4, 7>, <5, 13>, <6, 24>, <7, 20>, <8, 30>, <9, 32>, <10, 25> ]>, <4, [ <1, 4>, <2, 6>, <3, 9>, <4, 7>, <5, 3>, <6, 11>, <7, 12>, <8, 22>, <9, 28>, <10, 37>, <11, 34>, <12, 39>, <13, 38>, <14, 118>, <15, 81>, <16, 119>, <17, 59>, <18, 72>, <19, 49>, <20, 120>, <21, 94>, <22, 51>, <23, 121>, <24, 122>, <25, 97>, <26, 79>, <27, 102>, <28, 105>, <29, 96>, <30, 104>, <31, 98>, <32, 123>, <33, 124>, <34, 90>, <35, 114> ]>, <5, [ <1, 4>, <2, 7>, <6, 9>, <7, 10>, <8, 8>, <11, 89>, <13, 72>, <14, 73>, <15, 74>, <16, 75>, <17, 76>, <18, 45>, <19, 77>, <20, 53>, <21, 37>, <22, 78>, <23, 79>, <24, 80>, <25, 81>, <26, 82>, <27, 62>, <28, 83>, <29, 84>, <30, 67>, <31, 61>, <32, 85>, <33, 86>, <34, 70>, <35, 69>, <36, 87>, <37, 88>, <38, 71>, <40, 318>, <41, 319>, <42, 170>, <43, 320>, <44, 321>, <45, 154>, <46, 322>, <47, 323>, <48, 106>, <49, 324>, <50, 325>, <51, 326>, <52, 327>, <53, 328>, <54, 216>, <55, 329>, <56, 330>, <57, 331>, <58, 171>, <59, 332>, <60, 198>, <61, 228>, <62, 232>, <63, 233>, <64, 231>, <65, 209>, <66, 122>, <67, 333>, <68, 334>, <69, 335>, <70, 210>, <71, 336>, <72, 337>, <73, 338>, <74, 339>, <75, 340>, <76, 341>, <77, 342>, <78, 343>, <79, 344>, <80, 345>, <81, 346>, <82, 347>, <83, 348>, <84, 349>, <85, 219>, <86, 193>, <87, 350>, <88, 140>, <89, 142>, <90, 257>, <91, 351>, <92, 202>, <93, 277>, <94, 352>, <95, 278>, <96, 279>, <97, 353>, <98, 354>, <99, 355>, <100, 226>, <101, 281>, <102, 285>, <103, 236>, <104, 356>, <105, 357>, <106, 252>, <107, 358>, <108, 260>, <109, 282>, <110, 273>, <111, 359>, <112, 293>, <113, 298>, <114, 360>, <115, 300>, <116, 305>, <117, 317>, <136, 456> ]>, <6, [ <2, 5>, <8, 143>, <11, 88>, <12, 89>, <13, 90>, <14, 91>, <15, 92>, <16, 93>, <17, 94>, <18, 95>, <19, 96>, <20, 97>, <21, 98>, <22, 99>, <23, 100>, <24, 101>, <25, 102>, <26, 103>, <27, 104>, <28, 105>, <29, 106>, <30, 107>, <31, 108>, <32, 109>, <33, 110>, <34, 111>, <35, 79>, <36, 80>, <37, 112>, <38, 113>, <39, 114>, <40, 115>, <41, 116>, <42, 117>, <43, 118>, <44, 119>, <45, 120>, <46, 121>, <47, 122>, <48, 123>, <49, 124>, <50, 125>, <51, 126>, <52, 127>, <53, 128>, <54, 129>, <55, 130>, <56, 131>, <57, 132>, <58, 133>, <59, 134>, <60, 84>, <61, 135>, <62, 136>, <63, 85>, <64, 137>, <65, 138>, <66, 139>, <67, 140>, <68, 141>, <69, 87>, <70, 142>, <71, 144>, <90, 613>, <91, 614>, <92, 615>, <93, 616>, <94, 617>, <95, 618>, <96, 239>, <97, 619>, <98, 620>, <99, 621>, <100, 243>, <101, 622>, <102, 623>, <103, 624>, <104, 625>, <105, 626>, <106, 627>, <107, 628>, <108, 629>, <109, 630>, <110, 631>, <111, 632>, <112, 633>, <113, 634>, <114, 635>, <115, 636>, <116, 637>, <117, 638>, <118, 639>, <119, 640>, <120, 641>, <121, 642>, <122, 643>, <123, 644>, <124, 645>, <125, 646>, <126, 647>, <127, 648>, <128, 649>, <129, 650>, <130, 651>, <131, 299>, <132, 652>, <133, 653>, <134, 654>, <135, 655>, <136, 656>, <137, 657>, <138, 658>, <139, 189>, <140, 659>, <141, 660>, <142, 661>, <143, 662>, <144, 663>, <145, 664>, <146, 665>, <147, 666>, <148, 667>, <149, 668>, <150, 669>, <151, 404>, <152, 670>, <153, 671>, <154, 672>, <155, 673>, <156, 674>, <157, 675>, <158, 676>, <159, 677>, <160, 678>, <161, 679>, <162, 680>, <163, 681>, <164, 682>, <165, 683>, <166, 684>, <167, 685>, <168, 686>, <169, 687>, <170, 688>, <171, 689>, <172, 690>, <173, 691>, <174, 692>, <175, 693>, <176, 694>, <177, 257>, <178, 695>, <179, 696>, <180, 697>, <181, 698>, <182, 217>, <183, 699>, <184, 700>, <185, 460>, <186, 701>, <187, 456>, <188, 702>, <189, 430>, <190, 703>, <191, 704>, <192, 461>, <193, 705>, <194, 706>, <195, 707>, <196, 708>, <197, 709>, <198, 710>, <199, 711>, <200, 712>, <201, 713>, <202, 714>, <203, 333>, <204, 715>, <205, 716>, <206, 717>, <207, 718>, <208, 719>, <209, 720>, <210, 721>, <211, 414>, <212, 722>, <213, 723>, <214, 479>, <215, 724>, <216, 725>, <217, 726>, <218, 727>, <219, 728>, <220, 483>, <221, 729>, <222, 730>, <223, 731>, <224, 732>, <225, 733>, <226, 734>, <227, 735>, <228, 736>, <229, 737>, <230, 738>, <231, 739>, <232, 740>, <233, 741>, <234, 742>, <235, 743>, <236, 744>, <237, 745>, <238, 746>, <239, 481>, <240, 364>, <241, 747>, <242, 748>, <243, 749>, <244, 750>, <245, 751>, <246, 752>, <247, 753>, <248, 539>, <249, 754>, <250, 755>, <251, 756>, <252, 757>, <253, 758>, <254, 759>, <255, 321>, <256, 760>, <257, 761>, <258, 762>, <259, 763>, <260, 764>, <261, 765>, <262, 356>, <263, 766>, <264, 363>, <265, 767>, <266, 431>, <267, 768>, <268, 463>, <269, 545>, <270, 769>, <271, 392>, <272, 389>, <273, 540>, <274, 454>, <275, 473>, <276, 770>, <277, 771>, <278, 772>, <279, 773>, <280, 596>, <281, 774>, <282, 597>, <283, 775>, <284, 475>, <285, 776>, <286, 777>, <287, 778>, <288, 495>, <289, 779>, <290, 780>, <291, 781>, <292, 505>, <293, 782>, <294, 783>, <295, 506>, <296, 784>, <297, 510>, <298, 785>, <299, 512>, <300, 786>, <301, 571>, <302, 787>, <303, 532>, <304, 533>, <305, 788>, <306, 789>, <307, 565>, <308, 790>, <309, 791>, <310, 792>, <311, 583>, <312, 586>, <313, 595>, <314, 793>, <315, 606>, <316, 608>, <317, 794>, <361, 807>, <362, 808>, <363, 806>, <364, 809>, <451, 1113>, <452, 1131> ]>, <7, [ <7, 54>, <8, 55>, <9, 56>, <10, 57>, <11, 58>, <12, 59>, <13, 60>, <14, 61>, <15, 62>, <16, 63>, <17, 64>, <18, 65>, <19, 66>, <20, 67>, <21, 68>, <22, 69>, <23, 70>, <24, 71>, <25, 72>, <26, 73>, <27, 74>, <28, 75>, <29, 76>, <30, 77>, <31, 78>, <32, 79>, <33, 80>, <34, 81>, <35, 82>, <36, 83>, <37, 84>, <38, 85>, <39, 86>, <40, 87>, <41, 88>, <42, 89>, <43, 90>, <44, 91>, <45, 92>, <46, 93>, <47, 94>, <48, 95>, <49, 96>, <50, 97>, <51, 98>, <52, 99>, <53, 100>, <54, 101>, <55, 102>, <56, 103>, <57, 104>, <58, 105>, <59, 106>, <60, 107>, <61, 108>, <62, 109>, <63, 110>, <64, 111>, <65, 53>, <66, 112>, <67, 113>, <68, 114>, <69, 115>, <70, 116>, <71, 117>, <72, 118>, <73, 119>, <74, 120>, <75, 121>, <76, 122>, <77, 123>, <78, 124>, <79, 125>, <80, 126>, <81, 127>, <82, 128>, <83, 129>, <84, 130>, <85, 131>, <86, 132>, <87, 133>, <145, 652>, <146, 653>, <147, 654>, <148, 655>, <149, 656>, <150, 657>, <151, 658>, <152, 659>, <153, 660>, <154, 661>, <155, 662>, <156, 663>, <157, 664>, <158, 665>, <159, 666>, <160, 667>, <161, 668>, <162, 669>, <163, 670>, <164, 671>, <165, 672>, <166, 673>, <167, 674>, <168, 675>, <169, 676>, <170, 677>, <171, 678>, <172, 679>, <173, 680>, <174, 681>, <175, 682>, <176, 683>, <177, 684>, <178, 685>, <179, 686>, <180, 687>, <181, 688>, <182, 288>, <183, 689>, <184, 690>, <185, 691>, <186, 692>, <187, 693>, <188, 694>, <189, 695>, <190, 696>, <191, 697>, <192, 698>, <193, 699>, <194, 700>, <195, 701>, <196, 702>, <197, 703>, <198, 704>, <199, 705>, <200, 706>, <201, 707>, <202, 708>, <203, 709>, <204, 710>, <205, 711>, <206, 712>, <207, 713>, <208, 714>, <209, 715>, <210, 716>, <211, 717>, <212, 718>, <213, 719>, <214, 720>, <215, 721>, <216, 722>, <217, 723>, <218, 724>, <219, 725>, <220, 726>, <221, 727>, <222, 728>, <223, 729>, <224, 730>, <225, 731>, <226, 732>, <227, 733>, <228, 734>, <229, 342>, <230, 735>, <231, 736>, <232, 737>, <233, 738>, <234, 739>, <235, 740>, <236, 741>, <237, 742>, <238, 743>, <239, 744>, <240, 745>, <241, 746>, <242, 747>, <243, 748>, <244, 749>, <245, 750>, <246, 751>, <247, 752>, <248, 753>, <249, 754>, <250, 755>, <251, 756>, <252, 757>, <253, 758>, <254, 759>, <255, 760>, <256, 761>, <257, 762>, <258, 763>, <259, 764>, <260, 765>, <261, 766>, <262, 767>, <263, 768>, <264, 769>, <265, 770>, <266, 206>, <267, 771>, <268, 772>, <269, 773>, <270, 774>, <271, 775>, <272, 776>, <273, 777>, <274, 778>, <275, 779>, <276, 780>, <277, 781>, <278, 782>, <279, 783>, <280, 784>, <281, 785>, <282, 786>, <283, 787>, <284, 788>, <285, 789>, <286, 790>, <287, 791>, <288, 792>, <289, 793>, <290, 794>, <291, 795>, <292, 796>, <293, 797>, <294, 798>, <295, 799>, <296, 800>, <297, 801>, <298, 802>, <299, 803>, <300, 804>, <301, 805>, <302, 806>, <303, 807>, <304, 808>, <305, 809>, <306, 810>, <307, 811>, <308, 812>, <309, 813>, <310, 814>, <311, 815>, <312, 816>, <313, 817>, <314, 818>, <315, 819>, <316, 820>, <317, 821>, <318, 822>, <319, 823>, <320, 824>, <321, 825>, <322, 826>, <323, 827>, <324, 828>, <325, 829>, <326, 830>, <327, 831>, <328, 832>, <329, 833>, <330, 834>, <331, 835>, <332, 836>, <333, 837>, <334, 838>, <335, 839>, <336, 840>, <337, 841>, <338, 842>, <339, 843>, <340, 844>, <341, 845>, <342, 230>, <343, 846>, <344, 847>, <345, 848>, <346, 849>, <347, 850>, <348, 851>, <349, 852>, <350, 853>, <351, 854>, <352, 855>, <353, 856>, <354, 857>, <355, 858>, <356, 859>, <357, 860>, <358, 861>, <359, 862>, <360, 863>, <361, 864>, <362, 865>, <363, 866>, <364, 867>, <365, 868>, <366, 869>, <367, 870>, <368, 871>, <369, 872>, <370, 873>, <371, 515>, <372, 874>, <373, 875>, <374, 876>, <375, 877>, <376, 878>, <377, 879>, <378, 880>, <379, 881>, <380, 882>, <381, 883>, <382, 884>, <383, 885>, <384, 886>, <385, 420>, <386, 887>, <387, 888>, <388, 293>, <389, 889>, <390, 890>, <391, 891>, <392, 892>, <393, 893>, <394, 894>, <395, 895>, <396, 896>, <397, 897>, <398, 898>, <399, 899>, <400, 900>, <401, 901>, <402, 902>, <403, 903>, <404, 904>, <405, 905>, <406, 906>, <407, 907>, <408, 908>, <409, 909>, <410, 910>, <411, 911>, <412, 912>, <413, 913>, <414, 914>, <415, 915>, <416, 916>, <417, 917>, <418, 587>, <419, 918>, <420, 919>, <421, 920>, <422, 921>, <423, 922>, <424, 923>, <425, 924>, <426, 925>, <427, 926>, <428, 927>, <429, 928>, <430, 929>, <431, 930>, <432, 931>, <433, 932>, <434, 933>, <435, 934>, <436, 331>, <437, 935>, <438, 936>, <439, 937>, <440, 938>, <441, 939>, <442, 940>, <443, 941>, <444, 942>, <445, 447>, <446, 593>, <447, 943>, <448, 944>, <449, 601>, <450, 945>, <451, 946>, <452, 947>, <453, 602>, <454, 948>, <455, 949>, <456, 950>, <457, 951>, <458, 952>, <459, 953>, <460, 954>, <461, 955>, <462, 956>, <463, 957>, <464, 958>, <465, 959>, <466, 960>, <467, 961>, <468, 962>, <469, 963>, <470, 964>, <471, 965>, <472, 966>, <473, 967>, <474, 968>, <475, 969>, <476, 970>, <477, 971>, <478, 972>, <479, 973>, <480, 974>, <481, 975>, <482, 976>, <483, 977>, <484, 978>, <485, 979>, <486, 980>, <487, 981>, <488, 982>, <489, 983>, <490, 984>, <491, 985>, <492, 986>, <493, 987>, <494, 366>, <495, 988>, <496, 989>, <497, 990>, <498, 991>, <499, 992>, <500, 371>, <501, 993>, <502, 994>, <503, 995>, <504, 996>, <505, 997>, <506, 998>, <507, 999>, <508, 1000>, <509, 1001>, <510, 1002>, <511, 497>, <512, 1003>, <513, 536>, <514, 1004>, <515, 1005>, <516, 1006>, <517, 1007>, <518, 1008>, <519, 1009>, <520, 1010>, <521, 1011>, <522, 1012>, <523, 1013>, <524, 1014>, <525, 1015>, <526, 1016>, <527, 1017>, <528, 1018>, <529, 1019>, <530, 405>, <531, 1020>, <532, 1021>, <533, 1022>, <534, 1023>, <535, 1024>, <536, 1025>, <537, 1026>, <538, 1027>, <539, 1028>, <540, 1029>, <541, 1030>, <542, 1031>, <543, 1032>, <544, 1033>, <545, 1034>, <546, 1035>, <547, 1036>, <548, 1037>, <549, 1038>, <550, 1039>, <551, 1040>, <552, 1041>, <553, 491>, <554, 1042>, <555, 1043>, <556, 1044>, <557, 1045>, <558, 1046>, <559, 512>, <560, 1047>, <561, 519>, <562, 529>, <563, 1048>, <564, 535>, <565, 1049>, <566, 1050>, <567, 1051>, <568, 1052>, <569, 1053>, <570, 1054>, <571, 1055>, <572, 1056>, <573, 1057>, <574, 1058>, <575, 1059>, <576, 1060>, <577, 1061>, <578, 1062>, <579, 1063>, <580, 1064>, <581, 1065>, <582, 1066>, <583, 1067>, <584, 1068>, <585, 1069>, <586, 1070>, <587, 1071>, <588, 580>, <589, 581>, <590, 1072>, <591, 1073>, <592, 1074>, <593, 1075>, <594, 1076>, <595, 1077>, <596, 1078>, <597, 1079>, <598, 1080>, <599, 608>, <600, 1081>, <601, 618>, <602, 1082>, <603, 1083>, <604, 1084>, <605, 626>, <606, 1085>, <607, 627>, <608, 1086>, <609, 632>, <610, 647>, <611, 648>, <612, 1087>, <795, 1102>, <796, 1103>, <797, 1104>, <798, 1105>, <799, 1106>, <800, 1107>, <801, 1108>, <802, 1109>, <803, 1110>, <804, 1111>, <805, 1112>, <806, 1113>, <807, 1114>, <808, 1115>, <809, 1116>, <810, 1166>, <811, 1167>, <812, 1168>, <813, 1169>, <814, 1170>, <815, 1171>, <816, 1172>, <817, 1173>, <818, 1174>, <819, 1175>, <820, 1176>, <821, 1177>, <822, 1178>, <823, 1179>, <824, 1234>, <825, 1235>, <826, 1236>, <827, 1237>, <828, 1238>, <829, 1239>, <830, 1240>, <831, 1255>, <1099, 1758>, <1100, 1713>, <1101, 1759>, <1102, 1757> ]>, <8, [ <3, 19>, <4, 20>, <5, 21>, <6, 22>, <7, 23>, <8, 24>, <9, 25>, <10, 26>, <11, 27>, <12, 28>, <13, 29>, <14, 30>, <15, 31>, <16, 32>, <17, 33>, <18, 34>, <19, 35>, <20, 36>, <21, 37>, <22, 38>, <23, 39>, <24, 40>, <25, 41>, <26, 42>, <27, 43>, <28, 44>, <29, 45>, <30, 46>, <31, 47>, <32, 48>, <33, 49>, <34, 50>, <35, 51>, <36, 52>, <37, 53>, <38, 54>, <39, 55>, <40, 56>, <41, 57>, <42, 58>, <43, 59>, <44, 60>, <45, 61>, <46, 62>, <47, 63>, <48, 64>, <49, 65>, <50, 66>, <51, 67>, <52, 68>, <53, 69>, <134, 336>, <135, 337>, <136, 338>, <137, 339>, <138, 340>, <139, 341>, <140, 342>, <141, 343>, <142, 344>, <143, 345>, <144, 346>, <145, 347>, <146, 348>, <147, 349>, <148, 350>, <149, 351>, <150, 352>, <151, 353>, <152, 354>, <153, 355>, <154, 356>, <155, 357>, <156, 358>, <157, 359>, <158, 360>, <159, 361>, <160, 362>, <161, 363>, <162, 364>, <163, 365>, <164, 366>, <165, 367>, <166, 368>, <167, 369>, <168, 370>, <169, 371>, <170, 372>, <171, 373>, <172, 374>, <173, 375>, <174, 376>, <175, 377>, <176, 378>, <177, 379>, <178, 380>, <179, 381>, <180, 382>, <181, 383>, <182, 384>, <183, 385>, <184, 386>, <185, 387>, <186, 388>, <187, 389>, <188, 390>, <189, 391>, <190, 392>, <191, 393>, <192, 394>, <193, 395>, <194, 396>, <195, 397>, <196, 398>, <197, 399>, <198, 400>, <199, 401>, <200, 402>, <201, 403>, <202, 404>, <203, 405>, <204, 406>, <205, 407>, <206, 408>, <207, 409>, <208, 410>, <209, 411>, <210, 412>, <211, 413>, <212, 414>, <213, 415>, <214, 416>, <215, 417>, <216, 418>, <217, 419>, <218, 420>, <219, 421>, <220, 422>, <221, 423>, <222, 424>, <223, 425>, <224, 426>, <225, 427>, <226, 428>, <227, 429>, <228, 430>, <229, 431>, <230, 432>, <231, 433>, <232, 434>, <233, 435>, <234, 436>, <235, 437>, <236, 438>, <237, 439>, <238, 440>, <239, 441>, <240, 442>, <241, 443>, <242, 444>, <243, 445>, <244, 446>, <245, 447>, <246, 448>, <247, 449>, <248, 450>, <249, 451>, <250, 452>, <251, 453>, <252, 454>, <253, 455>, <254, 456>, <255, 457>, <256, 458>, <257, 459>, <258, 460>, <259, 461>, <260, 462>, <261, 463>, <262, 464>, <263, 465>, <264, 466>, <265, 467>, <266, 468>, <267, 469>, <268, 470>, <269, 471>, <270, 472>, <271, 473>, <272, 474>, <273, 475>, <274, 476>, <275, 477>, <276, 478>, <277, 479>, <278, 266>, <279, 480>, <280, 481>, <281, 482>, <282, 483>, <283, 484>, <284, 485>, <285, 486>, <286, 487>, <287, 488>, <288, 489>, <289, 490>, <290, 491>, <291, 492>, <292, 493>, <293, 494>, <294, 495>, <295, 496>, <296, 497>, <297, 498>, <298, 499>, <299, 500>, <300, 501>, <301, 502>, <302, 503>, <303, 504>, <304, 505>, <305, 506>, <306, 507>, <307, 508>, <308, 509>, <309, 510>, <310, 511>, <311, 512>, <312, 513>, 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