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)
     (20,29,40)(21,30,42)(24,34,47)(25,35,49)(27,37,52)(31,43,59)(32,44,60)
     (36,50,51)(38,53,69)(39,54,71)(41,56,74)(45,61,79)(46,62,81)(48,64,84)
     (55,72,73)(57,75,95)(58,76,97)(63,82,83)(65,85,106)(66,86,108)(67,87,110)
     (68,88,112)(70,90,115)(77,98,124)(78,99,126)(80,101,129)(89,113,114)(91,
     116,143)(92,117,145)(93,118,147)(94,119,149)(96,121,152)(100,127,128)
     (102,130,161)(103,131,163)(104,132,165)(105,133,167)(107,135,170)(109,
     137,173)(111,139,176)(120,150,151)(122,153,190)(123,154,192)(125,156,195)
     (134,168,169)(136,171,210)(138,174,175)(140,177,216)(141,178,218)(142,
     179,220)(144,181,223)(146,183,226)(148,185,229)(155,193,194)(157,196,239)
     (158,197,241)(159,198,243)(160,199,245)(162,201,248)(164,203,251)(166,
     205,254)(172,211,258)(180,221,222)(182,224,271)(184,227,228)(186,230,277)
     (187,231,279)(188,232,281)(189,233,283)(191,234,284)(200,246,247)(202,
     249,299)(204,252,253)(206,238,288)(207,255,305)(208,256,307)(209,257,309)
     (212,259,312)(213,260,314)(214,261,316)(215,262,318)(217,264,321)(219,
     266,324)(225,272,328)(235,285,342)(236,286,344)(237,287,346)(240,290,350)
     (242,292,353)(244,294,356)(250,300,361)(263,319,320)(265,322,382)(267,
     325,268)(269,326,387)(270,327,389)(273,329,392)(274,330,394)(275,331,396)
     (276,332,398)(278,334,401)(280,336,404)(282,338,407)(289,348,349)(291,
     351,420)(293,354,355)(295,357,426)(296,358,428)(297,359,430)(298,360,432)
     (301,362,435)(302,363,437)(303,364,439)(304,365,441)(306,367,444)(308,
     369,447)(310,371,450)(311,372,452)(313,374,455)(315,375,456)(317,377,459)
     (323,383,464)(333,399,400)(335,402,483)(337,405,406)(339,408,489)(340,
     409,491)(341,410,493)(343,412,496)(345,414,499)(347,416,440)(352,421,505)
     (366,442,525)(368,445,446)(370,448,531)(373,453,454)(376,457,458)(378,
     460,541)(379,461,543)(380,462,545)(381,463,547)(384,465,550)(385,466,552)
     (386,467,554)(388,469,557)(390,471,560)(391,472,562)(393,474,565)(395,
     476,567)(397,478,570)(403,484,575)(411,494,495)(413,497,588)(415,500,501)
     (417,502,592)(418,503,594)(419,504,596)(422,506,599)(423,507,601)(424,
     508,603)(425,509,605)(427,511,608)(429,513,611)(431,515,614)(433,517,617)
     (434,518,619)(436,520,622)(438,522,625)(443,526,628)(449,532,635)(451,
     534,638)(468,555,556)(470,558,661)(473,563,564)(475,566,669)(477,568,569)
     (479,571,673)(480,572,675)(481,573,677)(482,574,679)(485,576,682)(486,
     577,684)(487,578,686)(488,579,688)(490,581,691)(492,583,694)(498,589,699)
     (510,606,607)(512,609,719)(514,612,613)(516,615,725)(519,620,621)(521,
     623,732)(523,626,736)(524,627,738)(527,629,741)(528,630,743)(529,631,745)
     (530,632,747)(533,636,637)(535,639,753)(536,640,755)(537,641,757)(538,
     642,759)(539,643,761)(540,644,763)(542,646,766)(544,648,769)(546,650,772)
     (548,652,775)(549,653,777)(551,655,780)(553,656,781)(559,662,788)(561,
     664,791)(580,689,690)(582,692,693)(584,695,819)(585,696,821)(586,697,823)
     (587,698,825)(590,700,827)(591,701,829)(593,703,832)(595,705,835)(597,
     707,838)(598,708,840)(600,710,843)(602,712,846)(604,714,849)(610,720,854)
     (616,726,861)(618,728,864)(624,733,868)(633,748,634)(645,764,765)(647,
     767,900)(649,770,771)(651,773,905)(654,778,779)(657,782,914)(658,783,916)
     (659,784,918)(660,785,808)(663,789,790)(665,792,924)(666,793,926)(667,
     794,817)(668,795,928)(670,796,930)(671,797,932)(672,798,934)(674,800,937)
     (676,802,940)(678,804,943)(680,806,946)(681,807,948)(683,809,949)(685,
     811,952)(687,813,955)(702,830,971)(704,833,834)(706,836,977)(709,841,842)
     (711,844,985)(713,847,848)(715,850,991)(716,851,993)(717,852,995)(718,
     853,997)(721,855,1000)(722,856,1002)(723,857,1003)(724,858,1005)(727,862,
     863)(729,865,1011)(730,866,1013)(731,867,1014)(734,869,1017)(735,870,
     1019)(737,872,904)(739,874,1024)(740,875,1026)(742,877,1029)(744,879,
     1032)(746,881,1035)(749,884,1039)(750,885,1041)(751,886,1043)(752,887,
     1045)(754,889,1048)(756,891,1051)(758,893,1054)(760,895,1057)(762,897,
     1060)(768,901,1063)(774,906,1068)(776,908,1071)(786,919,787)(799,935,936)
     (801,938,1097)(803,941,942)(805,944,1103)(810,950,1110)(812,953,954)(814,
     956,1116)(815,957,1118)(816,958,1119)(818,959,1121)(820,961,1124)(822,
     963,1127)(824,965,1130)(826,966,1131)(828,968,1134)(831,972,1136)(837,
     978,1143)(839,980,1146)(845,986,1151)(859,1006,860)(871,1020,1021)(873,
     1022,1184)(876,1027,1028)(878,1030,1192)(880,1033,1034)(882,1036,1198)
     (883,1037,1200)(888,1046,1047)(890,1049,1050)(892,1052,1053)(894,1055,
     1216)(896,1058,1059)(898,1061,1221)(899,1062,1222)(902,1064,1225)(903,
     1065,1183)(907,1069,1070)(909,1072,1232)(910,1073,1234)(911,1074,1236)
     (912,1075,1238)(913,1076,1240)(917,1077,1241)(920,1080,1245)(921,1081,
     1246)(922,1082,1248)(923,1083,1250)(925,1085,1253)(927,1087,1256)(929,
     1088,1257)(931,1090,1260)(933,1092,1263)(939,1098,1267)(945,1104,1273)
     (947,1106,1276)(951,1111,1279)(960,1122,1123)(962,1125,1291)(964,1128,
     1129)(967,1132,1133)(969,1115,1018)(970,1135,1300)(973,1137,1303)(974,
     1138,1305)(975,1139,1307)(976,1140,1309)(979,1144,1145)(981,1147,1313)
     (982,1148,1314)(983,1149,1316)(984,1150,1318)(987,1152,1320)(988,1153,
     1322)(989,1154,1324)(990,1155,1326)(992,1157,1329)(994,1159,1332)(996,
     1161,1335)(998,1163,1338)(999,1164,1340)(1001,1166,1343)(1004,1168,1346)
     (1007,1171,1350)(1008,1172,1352)(1009,1173,1354)(1010,1174,1356)(1012,
     1176,1359)(1015,1178,1362)(1016,1179,1364)(1023,1185,1370)(1025,1187,
     1373)(1031,1193,1377)(1038,1201,1386)(1040,1203,1389)(1042,1205,1392)
     (1044,1207,1395)(1056,1217,1404)(1066,1227,1067)(1078,1242,1108)(1079,
     1243,1428)(1084,1251,1252)(1086,1254,1438)(1089,1258,1441)(1091,1261,
     1262)(1093,1197,1381)(1094,1264,1446)(1095,1265,1448)(1096,1266,1191)
     (1099,1268,1451)(1100,1247,1431)(1101,1269,1453)(1102,1270,1455)(1105,
     1274,1275)(1107,1277,1427)(1109,1278,1462)(1112,1280,1465)(1113,1281,
     1467)(1114,1282,1468)(1117,1284,1471)(1120,1287,1474)(1126,1292,1477)
     (1141,1310,1142)(1156,1327,1328)(1158,1330,1512)(1160,1333,1334)(1162,
     1336,1518)(1165,1341,1342)(1167,1344,1345)(1169,1347,1528)(1170,1348,
     1530)(1175,1357,1358)(1177,1360,1542)(1180,1365,1299)(1181,1366,1497)
     (1182,1367,1549)(1186,1371,1372)(1188,1374,1555)(1189,1375,1557)(1190,
     1376,1450)(1194,1378,1561)(1195,1379,1563)(1196,1380,1565)(1199,1383,
     1569)(1202,1387,1388)(1204,1390,1576)(1206,1393,1394)(1208,1396,1582)
     (1209,1397,1584)(1210,1398,1586)(1211,1399,1588)(1212,1400,1590)(1213,
     1401,1592)(1214,1402,1594)(1215,1403,1596)(1218,1405,1599)(1219,1406,
     1601)(1220,1407,1602)(1223,1409,1224)(1226,1411,1606)(1228,1413,1609)
     (1229,1414,1611)(1230,1415,1613)(1231,1416,1615)(1233,1418,1618)(1235,
     1420,1621)(1237,1422,1624)(1239,1424,1627)(1244,1429,1632)(1249,1433,
     1558)(1255,1439,1640)(1259,1442,1641)(1271,1456,1272)(1283,1469,1470)
     (1285,1472,1668)(1286,1473,1440)(1288,1443,1642)(1289,1475,1672)(1290,
     1476,1674)(1293,1478,1677)(1294,1479,1679)(1295,1480,1681)(1296,1481,
     1683)(1297,1482,1685)(1298,1483,1687)(1301,1485,1690)(1302,1486,1692)
     (1304,1488,1695)(1306,1490,1698)(1308,1492,1701)(1311,1495,1705)(1312,
     1496,1548)(1315,1499,1709)(1317,1501,1712)(1319,1502,1713)(1321,1504,
     1716)(1323,1506,1719)(1325,1508,1722)(1331,1513,1726)(1337,1519,1733)
     (1339,1521,1736)(1349,1531,1746)(1351,1533,1749)(1353,1535,1752)(1355,
     1537,1755)(1361,1543,1762)(1363,1545,1765)(1368,1550,1369)(1382,1567,
     1568)(1384,1570,1787)(1385,1571,1788)(1391,1577,1793)(1408,1603,1525)
     (1410,1604,1820)(1412,1607,1824)(1417,1616,1617)(1419,1619,1836)(1421,
     1622,1623)(1423,1625,1626)(1425,1628,1844)(1426,1629,1846)(1430,1633,
     1851)(1432,1635,1636)(1434,1637,1853)(1435,1600,1816)(1436,1638,1855)
     (1437,1639,1857)(1444,1643,1862)(1445,1644,1864)(1447,1646,1867)(1449,
     1648,1870)(1452,1649,1872)(1454,1651,1875)(1457,1654,1878)(1458,1655,
     1880)(1459,1656,1882)(1460,1657,1884)(1461,1658,1885)(1463,1660,1888)
     (1464,1661,1890)(1466,1663,1893)(1484,1688,1916)(1487,1693,1694)(1489,
     1696,1923)(1491,1699,1700)(1493,1702,1929)(1494,1703,1931)(1498,1707,
     1935)(1500,1710,1711)(1503,1714,1715)(1505,1717,1943)(1507,1720,1721)
     (1509,1723,1949)(1510,1724,1951)(1511,1725,1953)(1514,1727,1955)(1515,
     1728,1957)(1516,1729,1959)(1517,1730,1961)(1520,1734,1735)(1522,1737,
     1967)(1523,1738,1969)(1524,1739,1819)(1526,1740,1972)(1527,1741,1974)
     (1529,1743,1977)(1532,1747,1748)(1534,1750,1984)(1536,1753,1754)(1538,
     1756,1989)(1539,1757,1991)(1540,1758,1993)(1541,1759,1995)(1544,1763,
     1764)(1546,1766,2000)(1547,1767,2002)(1551,1770,2005)(1552,1771,2007)
     (1553,1772,2009)(1554,1773,2011)(1556,1775,1860)(1559,1776,2015)(1560,
     1777,2016)(1562,1779,2019)(1564,1781,1964)(1566,1783,1863)(1572,1789,
     2029)(1573,1790,2031)(1574,1791,2033)(1575,1792,2035)(1578,1794,2038)
     (1579,1795,2040)(1580,1796,2042)(1581,1797,2044)(1583,1799,2047)(1585,
     1801,2050)(1587,1803,2053)(1589,1805,2056)(1591,1807,2059)(1593,1809,
     2062)(1595,1811,2065)(1597,1813,2068)(1598,1814,2070)(1605,1821,2075)
     (1608,1825,2078)(1610,1827,2080)(1612,1829,2083)(1614,1831,2086)(1620,
     1837,2089)(1630,1847,2099)(1631,1848,2100)(1634,1852,2102)(1645,1865,
     2111)(1647,1868,1869)(1650,1873,1874)(1652,1876,2119)(1653,1877,2121)
     (1659,1886,2131)(1662,1891,1892)(1664,1894,1934)(1665,1895,2138)(1666,
     1896,2139)(1667,1897,2141)(1669,1818,2074)(1670,1898,2142)(1671,1899,
     2143)(1673,1901,1900)(1675,1903,1832)(1676,1904,2146)(1678,1906,2149)
     (1680,1908,2151)(1682,1910,2154)(1684,1912,2157)(1686,1914,2160)(1689,
     1917,2164)(1691,1919,2167)(1697,1924,2171)(1704,1932,1769)(1706,1849,
     2101)(1708,1936,2180)(1718,1944,2187)(1731,1962,1732)(1742,1975,1976)
     (1744,1978,2217)(1745,1979,2218)(1751,1985,2222)(1760,1996,1761)(1768,
     2003,1823)(1774,2012,2013)(1778,2017,2018)(1780,2020,2248)(1782,2022,
     2023)(1784,2024,2251)(1785,2025,2253)(1786,2026,2254)(1798,2045,2046)
     (1800,2048,2272)(1802,2051,2052)(1804,2054,2278)(1806,2057,2058)(1808,
     2060,2284)(1810,2063,2064)(1812,2066,2290)(1815,2071,2072)(1817,2073,
     1859)(1822,1850,1933)(1826,2037,2079)(1828,2081,2302)(1830,2084,2085)
     (1833,1881,2125)(1834,2087,2306)(1835,2088,2299)(1838,2090,2309)(1839,
     2091,2311)(1840,2092,2312)(1841,2093,2314)(1842,2094,2315)(1843,2095,
     2317)(1845,2097,2318)(1854,2103,2322)(1856,2105,2325)(1858,2107,2328)
     (1861,2108,2329)(1866,2112,2332)(1871,2114,2334)(1879,2123,2343)(1883,
     2127,2347)(1887,2132,2353)(1889,2134,2356)(1902,2144,2364)(1905,2147,
     2148)(1907,2150,2368)(1909,2152,1994)(1911,2155,2156)(1913,2158,2374)
     (1915,2161,2378)(1918,2165,2166)(1920,2168,2384)(1921,2169,2385)(1922,
     2170,2387)(1925,2172,2240)(1926,2173,2391)(1927,2174,2393)(1928,2175,
     2395)(1930,2177,2398)(1937,2181,2402)(1938,2182,2404)(1939,2183,2406)
     (1940,2184,2408)(1941,2185,2409)(1942,2186,2411)(1945,2188,2413)(1946,
     2189,2415)(1947,2190,1948)(1950,2192,2419)(1952,2194,2422)(1954,2196,
     1997)(1956,2198,2203)(1958,2200,2429)(1960,2202,2213)(1963,2205,2250)
     (1965,2206,2435)(1966,2207,2043)(1968,2041,2268)(1970,2209,2439)(1971,
     2210,2440)(1973,2212,2443)(1980,2219,2449)(1981,2030,2258)(1982,2220,
     2096)(1983,2221,2450)(1986,2153,2229)(1987,2223,2453)(1988,2224,2454)
     (1990,2226,2457)(1992,2228,2452)(1998,2232,2463)(1999,2233,2465)(2001,
     2235,2468)(2004,2237,2471)(2006,2239,2390)(2008,2241,2475)(2010,2243,
     2478)(2021,2249,2483)(2027,2255,2488)(2028,2256,2490)(2032,2260,2495)
     (2034,2262,2498)(2036,2264,2501)(2039,2266,2504)(2049,2273,2509)(2055,
     2279,2514)(2061,2285,2519)(2067,2291,2525)(2069,2293,2526)(2076,2297,
     2530)(2077,2298,2531)(2082,2303,2534)(2098,2319,2548)(2104,2323,2324)
     (2106,2326,2554)(2109,2330,2557)(2110,2331,2559)(2113,2333,2561)(2115,
     2335,2564)(2116,2336,2566)(2117,2337,2568)(2118,2338,2570)(2120,2340,
     2573)(2122,2341,2342)(2124,2344,2577)(2126,2145,2346)(2128,2348,2580)
     (2129,2349,2582)(2130,2350,2583)(2133,2354,2355)(2135,2357,2588)(2136,
     2358,2590)(2137,2359,2271)(2140,2361,2594)(2159,2375,2388)(2162,2379,
     2163)(2176,2396,2397)(2178,2304,2535)(2179,2399,2621)(2191,2417,2639)
     (2193,2420,2421)(2195,2423,2645)(2197,2425,2426)(2199,2427,2648)(2201,
     2430,2431)(2204,2432,2652)(2208,2437,2657)(2211,2441,2442)(2214,2444,
     2292)(2215,2445,2663)(2216,2446,2665)(2225,2455,2456)(2227,2458,2674)
     (2230,2460,2676)(2231,2461,2678)(2234,2466,2467)(2236,2469,2686)(2238,
     2472,2473)(2242,2476,2477)(2244,2479,2694)(2245,2480,2696)(2246,2481,
     2484)(2247,2482,2698)(2252,2485,2700)(2257,2491,2492)(2259,2493,2707)
     (2261,2496,2497)(2263,2499,2712)(2265,2502,2503)(2267,2505,2717)(2269,
     2507,2720)(2270,2508,2722)(2274,2510,2725)(2275,2511,2727)(2276,2512,
     2729)(2277,2513,2731)(2280,2515,2734)(2281,2516,2736)(2282,2517,2738)
     (2283,2518,2740)(2286,2520,2743)(2287,2392,2616)(2288,2521,2745)(2289,
     2522,2624)(2294,2527,2749)(2295,2528,2321)(2296,2529,2562)(2300,2532,
     2753)(2301,2533,2755)(2305,2536,2757)(2307,2538,2714)(2308,2539,2761)
     (2310,2541,2764)(2313,2543,2767)(2316,2545,2769)(2320,2549,2772)(2327,
     2555,2434)(2339,2571,2572)(2345,2578,2794)(2351,2584,2352)(2360,2592,
     2593)(2362,2595,2806)(2363,2596,2807)(2365,2597,2809)(2366,2598,2811)
     (2367,2599,2812)(2369,2486,2701)(2370,2600,2814)(2371,2601,2815)(2372,
     2602,2817)(2373,2603,2819)(2376,2386,2613)(2377,2604,2820)(2380,2607,
     2824)(2381,2608,2826)(2382,2609,2828)(2383,2610,2830)(2389,2614,2474)
     (2394,2618,2838)(2400,2622,2841)(2401,2623,2843)(2403,2625,2844)(2405,
     2627,2847)(2407,2629,2850)(2410,2632,2854)(2412,2633,2855)(2414,2635,
     2858)(2416,2637,2861)(2418,2640,2863)(2424,2646,2870)(2428,2649,2872)
     (2433,2653,2876)(2436,2655,2879)(2438,2658,2881)(2447,2666,2888)(2448,
     2667,2890)(2451,2669,2893)(2459,2675,2897)(2462,2679,2902)(2464,2681,
     2905)(2470,2687,2910)(2487,2702,2922)(2489,2704,2925)(2494,2708,2928)
     (2500,2713,2934)(2506,2718,2936)(2523,2746,2524)(2537,2758,2759)(2540,
     2762,2763)(2542,2765,2766)(2544,2768,2976)(2546,2706,2927)(2547,2770,
     2977)(2550,2773,2980)(2551,2774,2981)(2552,2775,2983)(2553,2776,2985)
     (2556,2779,2987)(2558,2781,2988)(2560,2783,2990)(2563,2785,2993)(2565,
     2787,2996)(2567,2788,2997)(2569,2790,3000)(2574,2630,2851)(2575,2792,
     3002)(2576,2793,2715)(2579,2795,3005)(2581,2796,3007)(2585,2798,3009)
     (2586,2799,2989)(2587,2782,2737)(2589,2801,3012)(2591,2803,3014)(2605,
     2821,3026)(2606,2822,3028)(2611,2831,2804)(2612,2832,2833)(2615,2834,
     3037)(2617,2836,2837)(2619,2839,3040)(2620,2840,3042)(2626,2845,3048)
     (2628,2848,2849)(2631,2852,2853)(2634,2856,2857)(2636,2859,3059)(2638,
     2862,3063)(2641,2864,3066)(2642,2865,3068)(2643,2866,3070)(2644,2867,
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