bin1 := (1,2452)(2,4060)(3,1912)(4,1292)(5,3117)(6,1698)(7,3388)(8,2003)(9,755)
     (10,3183)(11,3501)(12,2162)(13,3936)(14,3597)(15,1614)(16,994)(17,3337)
     (18,3006)(19,697)(20,2245)(21,3643)(22,3258)(23,3352)(24,3635)(25,599)
     (26,1932)(27,1678)(28,386)(29,302)(30,3393)(31,1411)(32,2240)(33,1314)
     (34,3442)(35,3143)(36,239)(37,121)(38,3800)(39,2097)(40,55)(41,3178)(42,
     909)(43,2102)(44,2128)(45,1136)(46,1012)(47,1453)(48,829)(49,3964)(50,
     2146)(51,361)(52,1728)(53,3617)(54,3620)(56,1226)(57,2064)(58,3941)(59,
     2991)(60,2059)(61,2858)(62,542)(63,2687)(64,1037)(65,3354)(66,3128)(67,
     1580)(68,2969)(69,3110)(70,3606)(71,984)(72,1066)(73,447)(74,2109)(75,
     3452)(76,296)(77,3925)(78,3056)(79,3371)(80,3838)(81,3888)(82,3609)(83,
     2562)(84,1054)(85,1634)(86,1814)(87,3627)(88,3511)(89,508)(90,385)(91,
     3714)(92,3289)(93,3286)(94,3881)(95,3088)(96,1079)(97,147)(98,3236)(99,
     1124)(100,669)(101,1181)(102,1023)(103,2899)(104,2610)(105,3312)(106,
     3917)(107,367)(108,1252)(109,1417)(110,1320)(111,161)(112,4045)(113,3931)
     (114,3795)(115,1926)(116,744)(117,4023)(118,3711)(119,136)(120,422)(122,
     611)(123,1885)(124,3114)(125,3717)(126,1568)(127,1899)(128,3098)(129,890)
     (130,236)(131,477)(132,2906)(133,1193)(134,462)(135,1956)(137,2706)(138,
     4049)(139,1717)(140,3791)(141,3053)(142,3949)(143,526)(144,1036)(145,
     2598)(146,1953)(148,1848)(149,2330)(150,978)(151,3723)(152,1336)(153,
     1816)(154,2840)(155,3902)(156,2634)(157,1260)(158,1168)(159,705)(160,
     1399)(162,2143)(163,2301)(164,3581)(165,2265)(166,1647)(167,3355)(168,
     3153)(169,1942)(170,2096)(171,2338)(172,2364)(173,2171)(174,1879)(175,
     1447)(176,986)(177,3237)(178,3288)(179,1087)(180,3688)(181,2021)(182,344)
     (183,1043)(184,3379)(185,3081)(186,1843)(187,459)(188,2762)(189,2746)
     (190,2031)(191,1450)(192,761)(193,2144)(194,2098)(195,3580)(196,240)(197,
     2785)(198,2200)(199,843)(200,2275)(201,2539)(202,2645)(203,3983)(204,
     3024)(205,2654)(206,3805)(207,1475)(208,457)(209,1619)(210,2053)(211,
     1584)(212,3663)(213,3604)(214,961)(215,2633)(216,2595)(217,2142)(218,282)
     (219,3219)(220,2536)(221,1264)(222,3846)(223,2555)(224,2506)(225,989)
     (226,289)(227,2719)(228,2151)(229,2720)(230,1078)(231,2174)(232,1308)
     (233,1697)(234,2304)(235,1190)(237,2083)(238,1487)(241,3058)(242,1361)
     (243,3768)(244,396)(245,3293)(246,2212)(247,1134)(248,3659)(249,1666)
     (250,2549)(251,1689)(252,3526)(253,2513)(254,2358)(255,3910)(256,3883)
     (257,2827)(258,2581)(259,2415)(260,2586)(261,1295)(262,4020)(263,3326)
     (264,3064)(265,1957)(266,1049)(267,1979)(268,2522)(269,1626)(270,2417)
     (271,1946)(272,3587)(273,2412)(274,3455)(275,904)(276,3362)(277,1234)
     (278,2477)(279,3898)(280,1591)(281,2614)(283,1881)(284,347)(285,2745)
     (286,2416)(287,690)(288,763)(290,3400)(291,3001)(292,957)(293,2490)(294,
     2198)(295,2166)(297,825)(298,2885)(299,889)(300,1585)(301,1009)(303,1243)
     (304,1438)(305,1581)(306,3257)(307,3187)(308,2441)(309,1630)(310,3875)
     (311,1364)(312,3077)(313,3720)(314,3428)(315,4044)(316,4010)(317,2254)
     (318,1179)(319,2592)(320,3852)(321,837)(322,3535)(323,507)(324,2727)(325,
     2252)(326,467)(327,3071)(328,919)(329,1103)(330,3134)(331,3965)(332,2241)
     (333,2913)(334,481)(335,1976)(336,2108)(337,475)(338,1739)(339,3105)(340,
     3408)(341,2339)(342,3667)(343,1221)(345,381)(346,2900)(348,3483)(349,
     1527)(350,1033)(351,3952)(352,2177)(353,3382)(354,3092)(355,3231)(356,
     884)(357,2711)(358,3432)(359,2281)(360,4004)(362,3247)(363,646)(364,2317)
     (365,857)(366,3493)(368,1996)(369,2189)(370,812)(371,2353)(372,842)(373,
     3558)(374,565)(375,1163)(376,3514)(377,2955)(378,769)(379,1970)(380,3640)
     (382,2837)(383,707)(384,2487)(387,2849)(388,2699)(389,2761)(390,3536)
     (391,1149)(392,1994)(393,2692)(394,1316)(395,1060)(397,2266)(398,1233)
     (399,4051)(400,2118)(401,2183)(402,1636)(403,1904)(404,2106)(405,681)
     (406,547)(407,3741)(408,1240)(409,2671)(410,3652)(411,2408)(412,2664)
     (413,1072)(414,1440)(415,2676)(416,3280)(417,3778)(418,1873)(419,1350)
     (420,3542)(421,3007)(423,496)(424,3449)(425,930)(426,3657)(427,3932)(428,
     1024)(429,2161)(430,1200)(431,3797)(432,1008)(433,1255)(434,3654)(435,
     1484)(436,1948)(437,1392)(438,2639)(439,1209)(440,3614)(441,1609)(442,
     1779)(443,2220)(444,3431)(445,3623)(446,2421)(448,3969)(449,2861)(450,
     2632)(451,1368)(452,3758)(453,2208)(454,2860)(455,2395)(456,1462)(458,
     2036)(460,1949)(461,928)(463,923)(464,3340)(465,765)(466,3598)(468,2878)
     (469,819)(470,1674)(471,1268)(472,1474)(473,2430)(474,2120)(476,525)(478,
     1631)(479,2045)(480,1093)(482,3045)(483,2226)(484,1294)(485,561)(486,
     1189)(487,3631)(488,3448)(489,3848)(490,3490)(491,1763)(492,3023)(493,
     1927)(494,2775)(495,2306)(497,2296)(498,1973)(499,2908)(500,3815)(501,
     1205)(502,1480)(503,1653)(504,920)(505,2377)(506,2232)(509,3664)(510,
     2185)(511,545)(512,2643)(513,3106)(514,3423)(515,3042)(516,1950)(517,
     2156)(518,2192)(519,2077)(520,3140)(521,2238)(522,2315)(523,3961)(524,
     3853)(527,2538)(528,1838)(529,832)(530,2033)(531,2612)(532,3890)(533,
     2786)(534,3619)(535,3374)(536,576)(537,3253)(538,1724)(539,2764)(540,
     2402)(541,1559)(543,2696)(544,4014)(546,2076)(548,1583)(549,1520)(550,
     1002)(551,594)(552,2769)(553,2049)(554,1963)(555,2823)(556,1270)(557,732)
     (558,787)(559,1472)(560,1731)(562,1740)(563,3135)(564,2741)(566,1518)
     (567,759)(568,3425)(569,3836)(570,1257)(571,2333)(572,2032)(573,3674)
     (574,629)(575,3478)(577,2381)(578,3166)(579,3333)(580,4052)(581,3863)
     (582,3136)(583,1512)(584,2356)(585,4059)(586,2560)(587,2921)(588,1395)
     (589,3073)(590,1077)(591,2666)(592,749)(593,3461)(595,2345)(596,2710)
     (597,1802)(598,1605)(600,3319)(601,2037)(602,2190)(603,840)(604,610)(605,
     1035)(606,3816)(607,3471)(608,1720)(609,3145)(612,2567)(613,641)(614,
     3666)(615,3655)(616,1385)(617,2392)(618,2399)(619,2042)(620,2351)(621,
     3986)(622,3539)(623,897)(624,3746)(625,3482)(626,2100)(627,3496)(628,
     1039)(630,2750)(631,738)(632,3302)(633,3734)(634,3429)(635,1381)(636,
     3860)(637,3012)(638,3561)(639,1884)(640,3226)(642,2157)(643,2534)(644,
     1827)(645,648)(647,4017)(649,2379)(650,805)(651,1597)(652,2912)(653,835)
     (654,2018)(655,2247)(656,3874)(657,3633)(658,3068)(659,664)(660,2802)
     (661,2715)(662,1752)(663,1590)(665,3608)(666,1404)(667,1878)(668,969)
     (670,869)(671,1247)(672,2277)(673,3718)(674,2282)(675,1075)(676,1657)
     (677,3274)(678,1745)(679,1513)(680,1870)(682,3713)(683,1110)(684,3975)
     (685,3104)(686,2631)(687,2066)(688,2286)(689,3893)(691,3696)(692,3332)
     (693,3154)(694,2225)(695,3049)(696,2705)(698,2547)(699,3002)(700,2730)
     (701,3347)(702,858)(703,1458)(704,2478)(706,1090)(708,2651)(709,3862)
     (710,2615)(711,1594)(712,2920)(713,1310)(714,3576)(715,1482)(716,3447)
     (717,1006)(718,1759)(719,3441)(720,1812)(721,3271)(722,998)(723,1001)
     (724,3880)(725,3463)(726,2023)(727,2260)(728,2939)(729,1639)(730,2442)
     (731,1940)(733,2132)(734,1546)(735,1934)(736,1549)(737,2824)(739,3208)
     (740,3072)(741,2523)(742,3335)(743,1650)(745,2357)(746,1588)(747,1042)
     (748,2863)(750,1592)(751,3859)(752,2160)(753,987)(754,3705)(756,2114)
     (757,2814)(758,3991)(760,3763)(762,3099)(764,2050)(766,2929)(767,1025)
     (768,3987)(770,3040)(771,1572)(772,2959)(773,3894)(774,1326)(775,3806)
     (776,1596)(777,1443)(778,4034)(779,2694)(780,836)(781,1733)(782,2280)
     (783,1108)(784,908)(785,2502)(786,3817)(788,1567)(789,3405)(790,2668)
     (791,2426)(792,3022)(793,3698)(794,2078)(795,962)(796,1105)(797,1683)
     (798,1538)(799,1494)(800,3703)(801,981)(802,3926)(803,2000)(804,2259)
     (806,1999)(807,3554)(808,1571)(809,3239)(810,4015)(811,3196)(813,3549)
     (814,3928)(815,1670)(816,3523)(817,2788)(818,995)(820,3798)(821,1074)
     (822,1182)(823,824)(826,2930)(827,979)(828,1691)(830,4037)(831,2773)(833,
     3108)(834,1289)(838,1275)(839,2060)(841,2688)(844,2540)(845,2332)(846,
     2835)(847,1923)(848,1896)(849,3923)(850,3793)(851,1204)(852,1014)(853,
     3701)(854,2718)(855,1237)(856,2450)(859,3472)(860,3994)(861,1716)(862,
     1680)(863,2607)(864,3507)(865,3672)(866,2006)(867,1380)(868,3344)(870,
     1529)(871,1818)(872,2289)(873,3708)(874,2877)(875,952)(876,2997)(877,
     1600)(878,2072)(879,1830)(880,1068)(881,1485)(882,2116)(883,3078)(885,
     1915)(886,1821)(887,2757)(888,3440)(891,1764)(892,2945)(893,2205)(894,
     1433)(895,2790)(896,3695)(898,1265)(899,1050)(900,1137)(901,3090)(902,
     3026)(903,1073)(905,1338)(906,4028)(907,3821)(910,1057)(911,1914)(912,
     2230)(913,2552)(914,2807)(915,3966)(916,3582)(917,3094)(918,1229)(921,
     3728)(922,3403)(924,3066)(925,3469)(926,2239)(927,1031)(929,1578)(931,
     1126)(932,2987)(933,3177)(934,3378)(935,1564)(936,3884)(937,2390)(938,
     3559)(939,3858)(940,2257)(941,3673)(942,3995)(943,2898)(944,1442)(945,
     1997)(946,2497)(947,1888)(948,1027)(949,3325)(950,3510)(951,3430)(953,
     2207)(954,3277)(955,1758)(956,3160)(958,3849)(959,1750)(960,2312)(963,
     3651)(964,1537)(965,2950)(966,2382)(967,2660)(968,2227)(970,1477)(971,
     2940)(972,3186)(973,3227)(974,3350)(975,2799)(976,2153)(977,1515)(980,
     2130)(982,1261)(983,1889)(985,3119)(988,2496)(990,3275)(991,3359)(992,
     1566)(993,3315)(996,1158)(997,3809)(999,2367)(1000,2754)(1003,3039)(1004,
     1725)(1005,2659)(1007,2055)(1010,3314)(1011,1971)(1013,3824)(1015,3591)
     (1016,2573)(1017,3021)(1018,3126)(1019,1694)(1020,1815)(1021,2101)(1022,
     2086)(1026,1242)(1028,1374)(1029,2819)(1030,3156)(1032,2110)(1034,2789)
     (1038,1161)(1040,2811)(1041,3057)(1044,2604)(1045,1560)(1046,1089)(1047,
     2022)(1048,3527)(1051,1754)(1052,3915)(1053,3234)(1055,1448)(1056,1304)
     (1058,1235)(1059,1224)(1061,3515)(1062,2419)(1063,3417)(1064,1299)(1065,
     1514)(1067,3484)(1069,1401)(1070,3803)(1071,1786)(1076,2891)(1080,1671)
     (1081,3644)(1082,1133)(1083,1819)(1084,1854)(1085,2460)(1086,3905)(1088,
     3410)(1091,2088)(1092,3935)(1094,3568)(1095,2359)(1096,1685)(1097,2466)
     (1098,2976)(1099,3458)(1100,3794)(1101,1347)(1102,2862)(1104,1496)(1106,
     2973)(1107,2635)(1109,2515)(1111,2830)(1112,1449)(1113,3990)(1114,2685)
     (1115,3684)(1116,2593)(1117,1894)(1118,2299)(1119,3004)(1120,2925)(1121,
     1892)(1122,3610)(1123,2934)(1125,3292)(1127,2894)(1128,1606)(1129,1283)
     (1130,1623)(1131,1575)(1132,2473)(1135,3168)(1138,3000)(1139,3180)(1140,
     3207)(1141,1574)(1142,2796)(1143,2554)(1144,2145)(1145,1944)(1146,2867)
     (1147,3089)(1148,2147)(1150,2892)(1151,1792)(1152,1313)(1153,3398)(1154,
     1599)(1155,3704)(1156,2485)(1157,2781)(1159,3313)(1160,2678)(1162,1212)
     (1164,3616)(1165,1624)(1166,2058)(1167,2551)(1169,3035)(1170,2405)(1171,
     2047)(1172,2489)(1173,3725)(1174,2444)(1175,2724)(1176,1783)(1177,2708)
     (1178,3782)(1180,3533)(1183,1753)(1184,3259)(1185,2665)(1186,1312)(1187,
     2453)(1188,2797)(1191,2602)(1192,2601)(1194,4058)(1195,1236)(1196,1965)
     (1197,2755)(1198,1269)(1199,2956)(1201,3075)(1202,2404)(1203,1528)(1206,
     1603)(1207,3074)(1208,1808)(1210,1217)(1211,2043)(1213,3827)(1214,2324)
     (1215,1305)(1216,1704)(1218,2649)(1219,3722)(1220,1895)(1222,2020)(1223,
     2481)(1225,3381)(1227,3184)(1228,3787)(1230,3534)(1231,2256)(1232,2287)
     (1238,3199)(1239,2557)(1241,1820)(1244,2134)(1245,3131)(1246,3937)(1248,
     2349)(1249,1250)(1251,2767)(1253,1569)(1254,2864)(1256,2766)(1258,3215)
     (1259,2152)(1262,1406)(1263,1613)(1266,1551)(1267,1388)(1271,3169)(1272,
     3475)(1273,1303)(1274,1918)(1276,2545)(1277,2828)(1278,2770)(1279,2590)
     (1280,2575)(1281,2307)(1282,3945)(1284,3901)(1285,2825)(1286,2420)(1287,
     1787)(1288,3406)(1290,3656)(1291,3310)(1293,2831)(1296,3790)(1297,2768)
     (1298,1519)(1300,2155)(1301,2251)(1302,1517)(1306,2479)(1307,3016)(1309,
     1506)(1311,1793)(1315,3889)(1317,2670)(1318,1913)(1319,2697)(1321,2368)
     (1322,2558)(1323,3390)(1324,3086)(1325,3553)(1327,3683)(1328,2095)(1329,
     3147)(1330,3551)(1331,1495)(1332,2363)(1333,2890)(1334,1984)(1335,1780)
     (1337,1563)(1339,1722)(1340,2902)(1341,2107)(1342,2121)(1343,2111)(1344,
     3082)(1345,1654)(1346,1550)(1348,2321)(1349,3980)(1351,2164)(1352,1920)
     (1353,1675)(1354,3174)(1355,4011)(1356,2270)(1357,3857)(1358,2526)(1359,
     2806)(1360,2792)(1362,3336)(1363,1928)(1365,1714)(1366,3216)(1367,2815)
     (1369,2080)(1370,3691)(1371,1824)(1372,2140)(1373,3220)(1375,1993)(1376,
     2448)(1377,1955)(1378,3649)(1379,3198)(1382,3464)(1383,2401)(1384,3658)
     (1386,3228)(1387,1504)(1389,1954)(1390,2213)(1391,2516)(1393,2423)(1394,
     3921)(1396,1826)(1397,1788)(1398,2486)(1400,3702)(1402,3422)(1403,3978)
     (1405,2519)(1407,1429)(1408,2311)(1409,2285)(1410,2029)(1412,1859)(1413,
     3459)(1414,2268)(1415,2290)(1416,2591)(1418,3096)(1419,2985)(1420,1557)
     (1421,3747)(1422,3944)(1423,3444)(1424,3517)(1425,3569)(1426,2652)(1427,
     2838)(1428,2054)(1430,3766)(1431,3692)(1432,2258)(1434,2065)(1435,1553)
     (1436,3291)(1437,1890)(1439,1509)(1441,3735)(1444,1705)(1445,1805)(1446,
     3956)(1451,1855)(1452,3929)(1454,3356)(1455,1876)(1456,2630)(1457,3601)
     (1459,3742)(1460,3594)(1461,2576)(1463,2011)(1464,1499)(1465,2932)(1466,
     1511)(1467,1987)(1468,2780)(1469,2087)(1470,2759)(1471,3530)(1473,2071)
     (1476,3148)(1478,1737)(1479,3297)(1481,1893)(1483,1690)(1486,3218)(1488,
     1703)(1489,2074)(1490,4032)(1491,3887)(1492,3027)(1493,2217)(1497,2139)
     (1498,2933)(1500,1945)(1501,2173)(1502,3229)(1503,2079)(1505,3334)(1507,
     3175)(1508,2454)(1510,2809)(1516,1834)(1521,3013)(1522,3767)(1523,3891)
     (1524,3011)(1525,1986)(1526,2800)(1530,3395)(1531,2249)(1532,2625)(1533,
     2772)(1534,2569)(1535,3513)(1536,2771)(1539,2674)(1540,1960)(1541,3327)
     (1542,2787)(1543,3139)(1544,1757)(1545,1782)(1547,1981)(1548,1785)(1552,
     3532)(1554,4003)(1555,2500)(1556,1729)(1558,3865)(1561,3416)(1562,2378)
     (1565,3102)(1570,2701)(1573,3951)(1576,3955)(1577,2729)(1579,1645)(1582,
     1861)(1586,3421)(1587,3163)(1589,3570)(1593,1840)(1595,2237)(1598,2744)
     (1601,3034)(1602,3222)(1604,3372)(1607,3976)(1608,3618)(1610,3564)(1611,
     2995)(1612,1627)(1615,2004)(1616,4006)(1617,2075)(1618,1770)(1620,3645)
     (1621,2488)(1622,2763)(1625,3101)(1628,3164)(1629,2910)(1632,2122)(1633,
     2084)(1635,2089)(1637,2008)(1638,2585)(1640,3129)(1641,2440)(1642,2971)
     (1643,2150)(1644,4039)(1646,2510)(1648,3843)(1649,1991)(1651,2201)(1652,
     2627)(1655,3677)(1656,1903)(1658,2833)(1659,3248)(1660,1790)(1661,3361)
     (1662,3984)(1663,2082)(1664,2331)(1665,2895)(1667,2667)(1668,1941)(1669,
     3909)(1672,2458)(1673,2655)(1676,2115)(1677,3968)(1679,3730)(1681,3290)
     (1682,1748)(1684,2418)(1686,2484)(1687,2491)(1688,2319)(1692,2090)(1693,
     2914)(1695,2638)(1696,1868)(1699,1742)(1700,3384)(1701,2947)(1702,2857)
     (1706,2411)(1707,2389)(1708,3051)(1709,3529)(1710,3825)(1711,3870)(1712,
     1836)(1713,3041)(1715,3224)(1718,4000)(1719,4038)(1721,3161)(1723,3294)
     (1726,3697)(1727,2264)(1730,2873)(1732,2774)(1734,3506)(1735,3963)(1736,
     1929)(1738,3709)(1741,3615)(1743,2495)(1744,1860)(1746,3933)(1747,2657)
     (1749,2246)(1751,4040)(1755,3841)(1756,3397)(1760,2621)(1761,2016)(1762,
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