bin1 := (1,3,6)(2,4,8)(5,9,14)(7,11,17)(10,15,22)(12,18,26)(13,19,28)(16,23,33)
     (20,29,39)(21,30,41)(24,34,46)(25,35,48)(31,42,56)(32,43,58)(36,49,65)
     (37,50,67)(38,51,69)(40,53,72)(44,59,79)(45,60,81)(47,62,84)(52,70,93)
     (54,73,97)(55,74,99)(57,76,102)(61,82,109)(63,85,113)(64,86,115)(66,88,
     118)(68,90,121)(71,94,126)(75,100,133)(77,103,137)(78,104,139)(80,106,
     142)(83,110,147)(87,116,154)(89,119,158)(91,122,162)(92,123,164)(95,127,
     169)(96,128,171)(98,130,174)(101,134,179)(105,140,186)(107,143,190)(108,
     144,192)(111,148,197)(112,149,199)(114,151,202)(117,155,207)(120,159,212)
     (124,165,219)(125,166,221)(129,172,228)(131,175,232)(132,176,234)(135,
     180,239)(136,181,241)(138,183,244)(141,187,249)(145,193,256)(146,194,258)
     (150,200,265)(152,203,269)(153,204,271)(156,208,276)(157,209,278)(160,
     213,283)(161,214,285)(163,216,288)(167,222,295)(168,223,297)(170,225,300)
     (173,229,305)(177,235,312)(178,236,314)(182,242,321)(184,245,325)(185,
     246,327)(188,250,332)(189,251,334)(191,253,337)(195,259,344)(196,260,346)
     (198,262,349)(201,266,354)(205,272,361)(206,273,363)(210,279,370)(211,
     280,372)(215,286,379)(217,289,383)(218,290,385)(220,292,388)(224,298,395)
     (226,301,399)(227,302,401)(230,306,406)(231,307,408)(233,309,411)(237,
     315,417)(238,316,419)(240,318,422)(243,322,427)(247,328,434)(248,329,436)
     (252,335,443)(254,338,447)(255,339,449)(257,341,452)(261,347,459)(263,
     350,463)(264,351,465)(267,355,470)(268,356,472)(270,358,475)(274,364,482)
     (275,365,484)(277,367,487)(281,373,494)(282,374,496)(284,376,499)(287,
     380,504)(291,386,511)(293,389,515)(294,390,517)(296,392,520)(299,396,525)
     (303,402,532)(304,403,534)(308,409,541)(310,412,545)(311,413,547)(313,
     414,549)(317,420,556)(319,423,560)(320,424,562)(323,428,567)(324,429,569)
     (326,431,572)(330,437,579)(331,438,581)(333,440,584)(336,444,589)(340,
     450,596)(342,453,600)(343,454,602)(345,456,605)(348,460,610)(352,466,617)
     (353,467,619)(357,473,626)(359,476,630)(360,477,632)(362,479,635)(366,
     485,642)(368,488,646)(369,489,648)(371,491,651)(375,497,658)(377,500,661)
     (378,501,663)(381,505,668)(382,506,670)(384,508,673)(387,512,678)(391,
     518,685)(393,521,689)(394,522,691)(397,526,696)(398,527,698)(400,529,701)
     (404,535,708)(405,536,710)(407,538,713)(410,542,718)(415,550,727)(416,
     551,729)(418,553,732)(421,557,737)(425,563,744)(426,564,746)(430,570,753)
     (432,573,757)(433,574,759)(435,576,762)(439,582,769)(441,585,772)(442,
     586,774)(445,590,779)(446,591,781)(448,593,784)(451,597,789)(455,603,796)
     (457,606,800)(458,607,802)(461,611,807)(462,612,809)(464,614,812)(468,
     620,819)(469,621,821)(471,623,824)(474,627,829)(478,633,836)(480,636,840)
     (481,637,842)(483,639,845)(486,643,850)(490,649,857)(492,652,861)(493,
     653,863)(495,655,866)(498,659,871)(502,664,877)(503,665,879)(507,671,886)
     (509,674,890)(510,675,892)(513,679,897)(514,680,899)(516,682,902)(519,
     686,907)(523,692,914)(524,693,916)(528,699,922)(530,702,926)(531,703,928)
     (533,705,931)(537,711,938)(539,714,941)(540,715,943)(543,719,948)(544,
     720,950)(546,722,953)(548,724,956)(552,730,963)(554,733,967)(555,734,969)
     (558,738,974)(559,739,976)(561,741,979)(565,747,986)(566,748,988)(568,
     750,991)(571,754,996)(575,760,1003)(577,763,1007)(578,764,1009)(580,766,
     1012)(583,770,1017)(587,775,1023)(588,776,1025)(592,782,1032)(594,785,
     1036)(595,786,1038)(598,790,1043)(599,791,1045)(601,793,1048)(604,797,
     1053)(608,803,1060)(609,804,1062)(613,810,1068)(615,813,1072)(616,814,
     1074)(618,816,1077)(622,822,1084)(624,825,1087)(625,826,1089)(628,830,
     1094)(629,831,1096)(631,833,1099)(634,837,1104)(638,843,1111)(640,846,
     1114)(641,847,1116)(644,851,1121)(645,852,884)(647,854,1125)(650,858,
     1130)(654,864,1137)(656,867,1141)(657,868,1143)(660,872,1148)(662,874,
     1151)(666,880,1158)(667,881,1160)(669,883,1163)(672,887,1167)(676,893,
     1174)(677,894,1176)(681,900,1183)(683,903,1187)(684,904,1189)(687,908,
     1194)(688,909,1196)(690,911,1199)(694,917,1206)(695,918,1208)(697,920,
     1211)(700,923,1215)(704,929,1222)(706,932,1226)(707,933,1228)(709,935,
     1231)(712,939,1236)(716,944,1242)(717,945,1244)(721,951,1251)(723,954,
     1255)(725,957,1259)(726,958,1261)(728,960,1264)(731,964,1269)(735,970,
     1276)(736,971,1278)(740,977,1285)(742,980,1289)(743,981,1291)(745,983,
     1294)(749,989,1301)(751,992,1304)(752,993,1306)(755,997,1311)(756,998,
     1313)(758,1000,1316)(761,1004,1321)(765,1010,1328)(767,1013,1332)(768,
     1014,1334)(771,1018,1339)(773,1020,1342)(777,1026,1349)(778,1027,1351)
     (780,1029,1354)(783,1033,1359)(787,1039,1366)(788,1040,1368)(792,1046,
     1375)(794,1049,1379)(795,1050,1381)(798,1054,1386)(799,1055,1388)(801,
     1057,1391)(805,1063,1398)(806,1064,1400)(808,1066,1403)(811,1069,1407)
     (815,1075,1414)(817,1078,1418)(818,1079,1420)(820,1081,1422)(823,1085,
     1427)(827,1090,1433)(828,1091,1435)(832,1097,1442)(834,1100,1446)(835,
     1101,1448)(838,1105,1453)(839,1106,1455)(841,1108,1458)(844,1112,1463)
     (848,1117,1469)(849,1118,1471)(853,1123,1477)(855,1126,1481)(856,1127,
     1483)(859,1131,1488)(860,1132,1490)(862,1134,1493)(865,1138,1498)(869,
     1144,1505)(870,1145,1507)(873,1149,1512)(875,1152,1516)(876,1153,1518)
     (878,1155,1521)(882,1161,1528)(885,1164,1532)(888,1168,1537)(889,1169,
     1539)(891,1171,1542)(895,1177,1549)(896,1178,1551)(898,1180,1554)(901,
     1184,1559)(905,1190,1565)(906,1191,1567)(910,1197,1574)(912,1200,1578)
     (913,1201,1580)(915,1203,1583)(919,1209,1590)(921,1212,1594)(924,1216,
     1599)(925,1217,1601)(927,1219,1604)(930,1223,1609)(934,1229,1616)(936,
     1232,1620)(937,1233,1622)(940,1237,1627)(942,1239,1630)(946,1245,1637)
     (947,1246,1639)(949,1248,1642)(952,1252,1080)(955,1256,1651)(959,1262,
     1658)(961,1265,1662)(962,1266,1664)(965,1270,1669)(966,1271,1671)(968,
     1273,1674)(972,1279,1681)(973,1280,1683)(975,1282,1686)(978,1286,1691)
     (982,1292,1698)(984,1295,1702)(985,1296,1704)(987,1298,1707)(990,1302,
     1712)(994,1307,1718)(995,1308,1720)(999,1314,1727)(1001,1317,1731)(1002,
     1318,1733)(1005,1322,1738)(1006,1323,1740)(1008,1325,1742)(1011,1329,
     1747)(1015,1335,1754)(1016,1336,1756)(1019,1340,1761)(1021,1343,1765)
     (1022,1344,1767)(1024,1346,1770)(1028,1352,1777)(1030,1355,1780)(1031,
     1356,1782)(1034,1360,1787)(1035,1361,1789)(1037,1363,1792)(1041,1369,
     1799)(1042,1370,1801)(1044,1372,1804)(1047,1376,1809)(1051,1382,1816)
     (1052,1383,1818)(1056,1389,1825)(1058,1392,1828)(1059,1393,1830)(1061,
     1395,1833)(1065,1401,1840)(1067,1404,1844)(1070,1408,1849)(1071,1409,
     1851)(1073,1411,1854)(1076,1415,1858)(1082,1423,1867)(1083,1424,1869)
     (1086,1428,1874)(1088,1430,1877)(1092,1436,1884)(1093,1437,1886)(1095,
     1439,1889)(1098,1443,1894)(1102,1449,1901)(1103,1450,1903)(1107,1456,
     1910)(1109,1459,1914)(1110,1460,1916)(1113,1464,1921)(1115,1466,1924)
     (1119,1472,1931)(1120,1473,1933)(1122,1475,1936)(1124,1478,1940)(1128,
     1484,1947)(1129,1485,1949)(1133,1491,1956)(1135,1494,1960)(1136,1495,
     1962)(1139,1499,1967)(1140,1500,1969)(1142,1502,1972)(1146,1508,1979)
     (1147,1509,1981)(1150,1513,1986)(1154,1519,1993)(1156,1522,1997)(1157,
     1523,1999)(1159,1525,2002)(1162,1529,2007)(1165,1533,2012)(1166,1534,
     2014)(1170,1540,2021)(1172,1543,2025)(1173,1544,2027)(1175,1546,2030)
     (1179,1552,2037)(1181,1555,2041)(1182,1556,2043)(1185,1560,2048)(1186,
     1561,2050)(1188,1562,2052)(1192,1568,2059)(1193,1569,2061)(1195,1571,
     2064)(1198,1575,2069)(1202,1581,2076)(1204,1584,2080)(1205,1585,2082)
     (1207,1587,2085)(1210,1591,2090)(1213,1595,2095)(1214,1596,2097)(1218,
     1602,2104)(1220,1605,2108)(1221,1606,2110)(1224,1610,2115)(1225,1611,
     2117)(1227,1613,2120)(1230,1617,2124)(1234,1623,2131)(1235,1624,2133)
     (1238,1628,2138)(1240,1631,2142)(1241,1632,2144)(1243,1634,2147)(1247,
     1640,2154)(1249,1643,2157)(1250,1644,2159)(1253,1647,2163)(1254,1648,
     2165)(1257,1652,2170)(1258,1653,2172)(1260,1655,2175)(1263,1659,2180)
     (1267,1665,2187)(1268,1666,2189)(1272,1672,2196)(1274,1675,2200)(1275,
     1676,2202)(1277,1678,2205)(1281,1684,2212)(1283,1687,2215)(1284,1688,
     2217)(1287,1692,2222)(1288,1693,2224)(1290,1695,2227)(1293,1699,2232)
     (1297,1705,2239)(1299,1708,2243)(1300,1709,2245)(1303,1713,2250)(1305,
     1715,2253)(1309,1721,2260)(1310,1722,2262)(1312,1724,2265)(1315,1728,
     2270)(1319,1734,2277)(1320,1735,2279)(1324,1441,1891)(1326,1743,2288)
     (1327,1744,2290)(1330,1748,2295)(1331,1749,2297)(1333,1751,2300)(1337,
     1757,2307)(1338,1758,2309)(1341,1762,2314)(1345,1768,2321)(1347,1771,
     2325)(1348,1772,2327)(1350,1774,2330)(1353,1778,2335)(1357,1783,2341)
     (1358,1784,2343)(1362,1790,2350)(1364,1793,2354)(1365,1794,2356)(1367,
     1796,2359)(1371,1802,2366)(1373,1805,2370)(1374,1806,2372)(1377,1810,
     2377)(1378,1811,2379)(1380,1813,2382)(1384,1819,2389)(1385,1820,2391)
     (1387,1822,2394)(1390,1826,2399)(1394,1831,2405)(1396,1834,2409)(1397,
     1835,2411)(1399,1837,2414)(1402,1841,2419)(1405,1845,2424)(1406,1846,
     2426)(1410,1852,2433)(1412,1855,2437)(1413,1856,2439)(1416,1859,2443)
     (1417,1860,2445)(1419,1862,2448)(1421,1864,2451)(1425,1870,2458)(1426,
     1871,2460)(1429,1875,2465)(1431,1878,2469)(1432,1879,2471)(1434,1881,
     2474)(1438,1887,2481)(1440,1890,2484)(1444,1895,2490)(1445,1896,2492)
     (1447,1898,2495)(1451,1904,2502)(1452,1905,2504)(1454,1907,2507)(1457,
     1911,2512)(1461,1917,2519)(1462,1918,2521)(1465,1922,2526)(1467,1925,
     2530)(1468,1926,2532)(1470,1928,2535)(1474,1934,2542)(1476,1937,2546)
     (1479,1941,2551)(1480,1942,2553)(1482,1944,2556)(1486,1950,2563)(1487,
     1951,2565)(1489,1953,2568)(1492,1957,2573)(1496,1963,2580)(1497,1964,
     2582)(1501,1970,2589)(1503,1973,2593)(1504,1974,2595)(1506,1976,2598)
     (1510,1982,2605)(1511,1983,2607)(1514,1987,2612)(1515,1988,2614)(1517,
     1990,2617)(1520,1994,2622)(1524,2000,2629)(1526,2003,2633)(1527,2004,
     2635)(1530,2008,2640)(1531,2009,2642)(1535,2015,2649)(1536,2016,2651)
     (1538,2018,2653)(1541,2022,2658)(1545,2028,2665)(1547,2031,2669)(1548,
     2032,2671)(1550,2034,2674)(1553,2038,2679)(1557,2044,2686)(1558,2045,
     2688)(1563,2053,2697)(1564,2054,2699)(1566,2056,2702)(1570,2062,2709)
     (1572,2065,2712)(1573,2066,2714)(1576,2070,2719)(1577,2071,2721)(1579,
     2073,2724)(1582,2077,2729)(1586,2083,2736)(1588,2086,2740)(1589,2087,
     2742)(1592,2091,2747)(1593,2092,2749)(1597,2098,2756)(1598,2099,2758)
     (1600,2101,2761)(1603,2105,2766)(1607,2111,2773)(1608,2112,2775)(1612,
     2118,2782)(1614,2121,2786)(1615,2122,2788)(1618,2125,2792)(1619,2126,
     2794)(1621,2128,2797)(1625,2134,2804)(1626,2135,2806)(1629,2139,2811)
     (1633,2145,2818)(1635,2148,2822)(1636,2149,2824)(1638,2151,2827)(1641,
     2155,2832)(1645,2160,2838)(1646,2161,2840)(1649,2166,2846)(1650,2167,
     2848)(1654,2173,2855)(1656,2176,2859)(1657,2177,2861)(1660,2181,2866)
     (1661,2182,2868)(1663,2184,2871)(1667,2190,2878)(1668,2191,2880)(1670,
     2193,2883)(1673,2197,2888)(1677,2203,2895)(1679,2206,2899)(1680,2207,
     2901)(1682,2209,2904)(1685,2213,2909)(1689,2218,2915)(1690,2219,2917)
     (1694,2225,2924)(1696,2228,2928)(1697,2229,2930)(1700,2233,2935)(1701,
     2234,2937)(1703,2236,2940)(1706,2240,2945)(1710,2246,2952)(1711,2247,
     2954)(1714,2251,2959)(1716,2254,2963)(1717,2255,2965)(1719,2257,2968)
     (1723,2263,2975)(1725,2266,2978)(1726,2267,2980)(1729,2271,2985)(1730,
     2272,2987)(1732,2274,2990)(1736,2280,2997)(1737,2281,2999)(1739,2283,
     3002)(1741,2285,3005)(1745,2291,3012)(1746,2292,3014)(1750,2298,3021)
     (1752,2301,3025)(1753,2302,3027)(1755,2304,3030)(1759,2310,3037)(1760,
     2311,3039)(1763,2315,3044)(1764,2316,3045)(1766,2318,3048)(1769,2322,
     3053)(1773,2328,3060)(1775,2331,2631)(1776,2332,3065)(1779,2336,3070)
     (1781,2338,3073)(1785,2344,3080)(1786,2345,3082)(1788,2347,3085)(1791,
     2351,3090)(1795,2357,3097)(1797,2360,3101)(1798,2361,3103)(1800,2363,
     3106)(1803,2367,3111)(1807,2373,3118)(1808,2374,3120)(1812,2380,3127)
     (1814,2383,3131)(1815,2384,3133)(1817,2386,3136)(1821,2392,3143)(1823,
     2395,3146)(1824,2396,3148)(1827,2400,3153)(1829,2402,3156)(1832,2406,
     3161)(1836,2412,3168)(1838,2415,3172)(1839,2416,3174)(1842,2420,3179)
     (1843,2421,3181)(1847,2427,3188)(1848,2428,3190)(1850,2430,3193)(1853,
     2434,3198)(1857,2440,3205)(1861,2446,3212)(1863,2449,3215)(1865,2452,
     3219)(1866,2453,3221)(1868,2455,3224)(1872,2461,3231)(1873,2462,3233)
     (1876,2466,3238)(1880,2472,3245)(1882,2475,3249)(1883,2476,3251)(1885,
     2478,3254)(1888,2482,3259)(1892,2486,3264)(1893,2487,3266)(1897,2493,
     3273)(1899,2496,3277)(1900,2497,3279)(1902,2499,3282)(1906,2505,3289)
     (1908,2508,3293)(1909,2509,3295)(1912,2513,3300)(1913,2514,3302)(1915,
     2516,3305)(1919,2522,3312)(1920,2523,3314)(1923,2527,3319)(1927,2533,
     3326)(1929,2536,3330)(1930,2537,3332)(1932,2539,3335)(1935,2543,3340)
     (1938,2547,3345)(1939,2548,3347)(1943,2554,3354)(1945,2557,3358)(1946,
     2558,3360)(1948,2560,3363)(1952,2566,3370)(1954,2569,3374)(1955,2570,
     3376)(1958,2574,3381)(1959,2575,3383)(1961,2577,3386)(1965,2583,3393)
     (1966,2584,3395)(1968,2586,3398)(1971,2590,3403)(1975,2596,3410)(1977,
     2599,3414)(1978,2600,3416)(1980,2602,3419)(1984,2608,3426)(1985,2609,
     3428)(1989,2615,3435)(1991,2618,3439)(1992,2619,3441)(1995,2623,3446)
     (1996,2624,3448)(1998,2626,3451)(2001,2630,3455)(2005,2636,3461)(2006,
     2637,3463)(2010,2643,3470)(2011,2644,3472)(2013,2646,3475)(2017,2652,
     3482)(2019,2654,3484)(2020,2655,3486)(2023,2659,3491)(2024,2660,3493)
     (2026,2662,3496)(2029,2666,3501)(2033,2672,3508)(2035,2675,3512)(2036,
     2676,3514)(2039,2680,3519)(2040,2681,3521)(2042,2683,3524)(2046,2689,
     3531)(2047,2690,3533)(2049,2692,3536)(2051,2694,3539)(2055,2700,3546)
     (2057,2703,3550)(2058,2704,3552)(2060,2706,3555)(2063,2710,3560)(2067,
     2715,3566)(2068,2716,3568)(2072,2722,3575)(2074,2725,3579)(2075,2726,
     3581)(2078,2730,3586)(2079,2731,3588)(2081,2733,3591)(2084,2737,3596)
     (2088,2743,3603)(2089,2744,3605)(2093,2750,3612)(2094,2751,3614)(2096,
     2753,3617)(2100,2759,3624)(2102,2762,3627)(2103,2763,3629)(2106,2767,
     3634)(2107,2768,3636)(2109,2770,3639)(2113,2776,3646)(2114,2777,3648)
     (2116,2779,3651)(2119,2783,3656)(2123,2789,3663)(2127,2795,3670)(2129,
     2798,3674)(2130,2799,3676)(2132,2801,3679)(2136,2807,3686)(2137,2808,
     3688)(2140,2812,3693)(2141,2813,3695)(2143,2815,3698)(2146,2819,3703)
     (2150,2825,3710)(2152,2828,3713)(2153,2829,3715)(2156,2833,3720)(2158,
     2835,3723)(2162,2841,3730)(2164,2843,3733)(2168,2849,3739)(2169,2850,
     3741)(2171,2852,3744)(2174,2856,3749)(2178,2862,3756)(2179,2863,3758)
     (2183,2869,3765)(2185,2872,3769)(2186,2873,3771)(2188,2875,3774)(2192,
     2881,3781)(2194,2884,3784)(2195,2885,3786)(2198,2889,3791)(2199,2890,
     3793)(2201,2892,3796)(2204,2896,3801)(2208,2902,3808)(2210,2905,3812)
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