bin1 := (1,2)(3,5)(4,7)(6,10)(8,12)(9,13)(11,16)(14,20)(15,21)(17,24)(18,25)(19,
     27)(22,31)(23,32)(26,36)(28,38)(29,39)(30,41)(33,45)(34,46)(35,48)(37,51)
     (40,55)(42,57)(43,58)(44,60)(47,64)(49,66)(50,67)(52,70)(53,71)(54,73)
     (56,76)(59,80)(61,81)(62,82)(63,84)(65,87)(68,69)(72,94)(74,96)(75,97)
     (77,100)(78,101)(79,103)(83,108)(85,110)(86,111)(88,114)(89,115)(90,117)
     (91,119)(92,120)(93,122)(95,125)(98,99)(102,132)(104,134)(105,135)(106,
     136)(107,138)(109,141)(112,113)(118,149)(121,151)(123,153)(124,154)(126,
     157)(127,158)(128,160)(129,162)(130,163)(131,165)(133,168)(137,173)(139,
     175)(140,176)(142,179)(143,180)(144,182)(145,184)(146,185)(147,187)(148,
     188)(150,191)(152,193)(155,156)(159,200)(161,202)(164,205)(166,207)(167,
     208)(169,211)(170,212)(171,214)(172,216)(174,219)(177,178)(181,226)(183,
     228)(186,231)(189,233)(190,234)(192,237)(194,240)(195,241)(196,243)(197,
     245)(198,246)(199,248)(201,251)(203,254)(204,256)(206,259)(209,210)(213,
     266)(215,268)(217,270)(220,273)(221,274)(222,276)(223,278)(224,279)(225,
     281)(227,284)(229,287)(230,289)(232,292)(235,296)(236,297)(238,239)(242,
     303)(244,305)(247,308)(249,310)(250,311)(252,314)(253,315)(255,318)(257,
     320)(258,321)(260,324)(261,325)(262,327)(263,329)(264,330)(265,332)(267,
     335)(269,338)(271,272)(275,344)(277,346)(280,349)(282,351)(283,352)(285,
     355)(286,356)(288,359)(290,361)(291,362)(293,365)(294,366)(295,368)(298,
     372)(299,373)(300,375)(301,376)(302,378)(304,381)(306,384)(307,386)(309,
     389)(312,313)(316,396)(317,397)(319,400)(322,323)(326,407)(328,409)(331,
     412)(333,414)(334,415)(336,418)(337,419)(339,422)(340,423)(341,425)(342,
     426)(343,428)(345,431)(347,434)(348,436)(350,439)(353,354)(357,446)(358,
     447)(360,450)(363,364)(367,457)(369,459)(370,460)(371,461)(374,465)(377,
     468)(379,470)(380,471)(382,474)(383,475)(385,478)(387,480)(388,481)(390,
     484)(391,485)(392,487)(393,489)(394,490)(395,492)(398,496)(399,497)(401,
     500)(402,501)(403,503)(404,505)(405,506)(406,508)(408,511)(410,514)(411,
     516)(413,519)(416,417)(420,421)(424,529)(427,532)(429,534)(430,535)(432,
     538)(433,539)(435,542)(437,544)(438,545)(440,548)(441,549)(442,551)(443,
     553)(444,554)(445,556)(448,560)(449,561)(451,564)(452,565)(453,567)(454,
     569)(455,570)(456,572)(458,575)(462,579)(463,580)(464,582)(466,585)(467,
     587)(469,590)(472,473)(476,597)(477,598)(479,601)(482,483)(486,608)(491,
     612)(493,614)(494,615)(495,616)(498,499)(502,623)(504,625)(507,628)(509,
     630)(510,631)(512,634)(513,635)(515,638)(517,640)(518,641)(520,644)(521,
     645)(522,647)(523,649)(524,650)(525,652)(526,654)(527,655)(528,657)(530,
     660)(531,662)(533,665)(536,537)(540,672)(541,673)(543,676)(546,547)(550,
     683)(552,685)(555,688)(557,690)(558,691)(559,692)(562,563)(566,699)(568,
     701)(571,704)(573,706)(574,707)(576,710)(577,711)(578,713)(581,717)(583,
     718)(584,719)(586,722)(588,724)(589,725)(591,728)(592,729)(593,731)(594,
     733)(595,734)(596,736)(599,740)(600,741)(602,744)(603,745)(604,747)(605,
     749)(606,750)(607,752)(609,755)(610,757)(611,759)(613,762)(617,766)(618,
     767)(619,769)(620,771)(621,772)(622,774)(624,777)(626,780)(627,782)(629,
     785)(632,633)(636,792)(637,793)(639,796)(642,643)(646,803)(648,805)(651,
     808)(653,810)(656,812)(658,814)(659,815)(661,816)(663,818)(664,819)(666,
     822)(667,823)(668,825)(669,827)(670,828)(671,830)(674,834)(675,835)(677,
     838)(678,839)(679,841)(680,843)(681,844)(682,846)(684,849)(686,852)(687,
     854)(689,857)(693,861)(694,862)(695,864)(696,866)(697,867)(698,869)(700,
     872)(702,875)(703,877)(705,880)(708,709)(712,887)(714,889)(715,890)(716,
     892)(720,897)(721,898)(723,901)(726,727)(730,908)(732,910)(735,913)(737,
     915)(738,916)(739,917)(742,743)(746,924)(748,926)(751,929)(753,931)(754,
     905)(756,934)(758,936)(760,938)(761,939)(763,942)(764,943)(765,945)(768,
     949)(770,951)(773,954)(775,956)(776,957)(778,960)(779,961)(781,964)(783,
     966)(784,967)(786,970)(787,971)(788,973)(789,975)(790,976)(791,978)(794,
     982)(795,983)(797,986)(798,987)(799,989)(800,991)(801,992)(802,994)(804,
     997)(806,1000)(807,1002)(809,1005)(811,1008)(813,1010)(817,1015)(820,821)
     (824,1022)(826,1024)(829,1027)(831,1029)(832,1030)(833,1031)(836,837)
     (840,1038)(842,1040)(845,1043)(847,1045)(848,1046)(850,1049)(851,1050)
     (853,1053)(855,1055)(856,1056)(858,1059)(859,1060)(860,1062)(863,1066)
     (865,1068)(868,1071)(870,1073)(871,1074)(873,1077)(874,1078)(876,1081)
     (878,1083)(879,1084)(881,1085)(882,1086)(883,1088)(884,1090)(885,1091)
     (886,1093)(888,1096)(891,1100)(893,1102)(894,1103)(895,1104)(896,1106)
     (899,1110)(900,1111)(902,1114)(903,1115)(904,1117)(906,1119)(907,1121)
     (909,1124)(911,1127)(912,1129)(914,1132)(918,1136)(919,1137)(920,1139)
     (921,1141)(922,1142)(923,1144)(925,1147)(927,1150)(928,1152)(930,1155)
     (932,933)(935,1160)(937,1163)(940,941)(944,1170)(946,1172)(947,1173)(948,
     1175)(950,1178)(952,1181)(953,1183)(955,1186)(958,959)(962,1193)(963,
     1194)(965,1197)(968,969)(972,1204)(974,1206)(977,1209)(979,1211)(980,
     1212)(981,1213)(984,985)(988,1220)(990,1222)(993,1225)(995,1227)(996,
     1228)(998,1231)(999,1232)(1001,1235)(1003,1237)(1004,1238)(1006,1241)
     (1007,1242)(1009,1245)(1011,1248)(1012,1249)(1013,1251)(1014,1253)(1016,
     1256)(1017,1202)(1018,1258)(1019,1260)(1020,1261)(1021,1263)(1023,1266)
     (1025,1269)(1026,1271)(1028,1274)(1032,1278)(1033,1279)(1034,1281)(1035,
     1283)(1036,1284)(1037,1286)(1039,1289)(1041,1292)(1042,1294)(1044,1297)
     (1047,1048)(1051,1304)(1052,1305)(1054,1308)(1057,1058)(1061,1315)(1063,
     1317)(1065,1319)(1067,1322)(1069,1325)(1070,1327)(1072,1330)(1075,1076)
     (1079,1337)(1080,1338)(1082,1341)(1087,1347)(1089,1349)(1092,1352)(1094,
     1354)(1095,1355)(1097,1358)(1098,1359)(1099,1361)(1101,1364)(1105,1369)
     (1107,1371)(1108,1372)(1109,1373)(1112,1113)(1116,1380)(1118,1382)(1120,
     1384)(1122,1386)(1123,1387)(1125,1390)(1126,1391)(1128,1394)(1130,1396)
     (1131,1397)(1133,1400)(1134,1401)(1135,1403)(1138,1407)(1140,1409)(1143,
     1412)(1145,1414)(1146,1415)(1148,1418)(1149,1419)(1151,1422)(1153,1424)
     (1154,1425)(1156,1428)(1157,1429)(1158,1431)(1159,1432)(1161,1433)(1162,
     1434)(1165,1437)(1166,1439)(1167,1441)(1168,1442)(1169,1444)(1171,1447)
     (1174,1451)(1176,1453)(1177,1454)(1179,1457)(1180,1458)(1182,1461)(1184,
     1463)(1185,1464)(1187,1467)(1188,1468)(1189,1470)(1190,1472)(1191,1473)
     (1192,1475)(1195,1479)(1196,1480)(1198,1483)(1199,1484)(1200,1486)(1201,
     1488)(1203,1490)(1205,1493)(1207,1496)(1208,1498)(1210,1501)(1214,1505)
     (1215,1506)(1216,1508)(1217,1510)(1218,1511)(1219,1513)(1221,1516)(1223,
     1519)(1224,1521)(1226,1524)(1229,1230)(1233,1531)(1234,1532)(1236,1535)
     (1239,1240)(1243,1542)(1244,1543)(1246,1247)(1250,1549)(1252,1551)(1254,
     1255)(1257,1555)(1259,1557)(1262,1560)(1264,1562)(1265,1563)(1267,1566)
     (1268,1567)(1270,1570)(1272,1572)(1273,1573)(1275,1576)(1276,1577)(1277,
     1579)(1280,1583)(1282,1584)(1285,1587)(1287,1589)(1288,1590)(1290,1593)
     (1291,1594)(1293,1597)(1295,1599)(1296,1600)(1298,1603)(1299,1604)(1300,
     1606)(1301,1608)(1302,1609)(1303,1611)(1306,1615)(1307,1616)(1309,1619)
     (1310,1620)(1311,1622)(1312,1624)(1313,1625)(1314,1627)(1316,1630)(1318,
     1633)(1320,1635)(1321,1636)(1323,1639)(1324,1640)(1326,1643)(1328,1645)
     (1329,1646)(1331,1649)(1332,1650)(1333,1652)(1334,1654)(1335,1655)(1336,
     1657)(1339,1661)(1340,1662)(1342,1665)(1343,1666)(1344,1668)(1345,1670)
     (1346,1672)(1348,1675)(1350,1678)(1351,1680)(1353,1683)(1356,1357)(1360,
     1690)(1362,1692)(1363,1693)(1365,1696)(1366,1697)(1367,1699)(1368,1701)
     (1370,1704)(1374,1708)(1375,1709)(1376,1711)(1377,1713)(1378,1714)(1379,
     1716)(1381,1719)(1383,1430)(1385,1724)(1388,1389)(1392,1731)(1393,1732)
     (1395,1734)(1398,1399)(1402,1741)(1404,1743)(1405,1744)(1406,1746)(1408,
     1747)(1410,1750)(1411,1752)(1413,1755)(1416,1417)(1420,1762)(1421,1763)
     (1423,1766)(1426,1427)(1435,1436)(1438,1778)(1440,1780)(1443,1783)(1445,
     1785)(1448,1788)(1449,1789)(1450,1791)(1452,1794)(1455,1456)(1459,1801)
     (1460,1802)(1462,1805)(1465,1466)(1469,1812)(1471,1814)(1474,1817)(1476,
     1819)(1477,1820)(1478,1821)(1481,1482)(1485,1828)(1487,1830)(1489,1832)
     (1491,1834)(1492,1835)(1494,1838)(1495,1839)(1497,1842)(1499,1844)(1500,
     1845)(1502,1848)(1503,1849)(1504,1851)(1507,1855)(1509,1857)(1512,1860)
     (1514,1862)(1515,1863)(1517,1866)(1518,1867)(1520,1870)(1522,1872)(1523,
     1873)(1525,1876)(1526,1877)(1527,1879)(1528,1881)(1529,1882)(1530,1884)
     (1533,1888)(1534,1889)(1536,1892)(1537,1893)(1538,1895)(1539,1897)(1540,
     1898)(1541,1900)(1544,1904)(1545,1905)(1546,1907)(1547,1908)(1548,1910)
     (1550,1913)(1552,1916)(1553,1918)(1554,1919)(1556,1922)(1558,1925)(1559,
     1927)(1561,1930)(1564,1565)(1568,1937)(1569,1938)(1571,1941)(1574,1575)
     (1578,1948)(1580,1950)(1581,1951)(1582,1953)(1585,1957)(1586,1959)(1588,
     1962)(1591,1592)(1595,1969)(1596,1970)(1598,1973)(1601,1602)(1605,1980)
     (1607,1982)(1610,1985)(1612,1987)(1613,1988)(1614,1989)(1617,1618)(1621,
     1996)(1623,1998)(1626,2001)(1628,2003)(1629,2004)(1631,2007)(1632,2008)
     (1634,2011)(1637,1638)(1641,2018)(1642,2019)(1644,2022)(1647,1648)(1651,
     2029)(1653,2031)(1656,2034)(1658,2036)(1659,2037)(1660,2038)(1663,1664)
     (1667,2045)(1669,2047)(1671,2049)(1673,2051)(1674,2052)(1676,2055)(1677,
     2056)(1679,2059)(1681,2061)(1682,2062)(1684,2065)(1685,2066)(1686,2068)
     (1687,2070)(1688,2071)(1689,2073)(1691,2076)(1694,1695)(1698,2083)(1700,
     2085)(1702,2087)(1703,2088)(1705,2091)(1706,2092)(1707,2094)(1710,2098)
     (1712,2100)(1715,2103)(1717,2105)(1720,2108)(1721,2109)(1722,2111)(1723,
     2112)(1725,2115)(1726,2116)(1727,2118)(1728,2120)(1729,2121)(1730,2123)
     (1733,2127)(1735,2129)(1736,2130)(1737,2132)(1738,2134)(1739,2135)(1740,
     2137)(1742,2140)(1745,2144)(1748,2147)(1749,2148)(1751,2151)(1753,2153)
     (1754,2154)(1756,2157)(1757,2158)(1758,2160)(1759,2162)(1760,2163)(1761,
     2165)(1764,2169)(1765,2170)(1767,2173)(1768,2174)(1769,2176)(1770,2178)
     (1771,2179)(1772,2180)(1773,2182)(1774,2184)(1775,2186)(1776,2188)(1777,
     2189)(1779,2192)(1781,2195)(1782,2197)(1784,2200)(1786,1787)(1790,2206)
     (1792,2208)(1793,2209)(1795,2212)(1796,2213)(1797,2215)(1798,2217)(1799,
     2218)(1800,2220)(1803,2224)(1804,2225)(1806,2228)(1807,2229)(1808,2231)
     (1809,2233)(1810,2234)(1811,2236)(1813,2239)(1815,2242)(1816,2244)(1818,
     2247)(1822,2251)(1823,2252)(1824,2254)(1825,2256)(1826,2257)(1827,2259)
     (1829,2262)(1831,2265)(1833,2268)(1836,1837)(1840,2275)(1841,2276)(1843,
     2279)(1846,1847)(1850,2286)(1852,2288)(1853,2289)(1854,2291)(1856,2294)
     (1858,2297)(1859,2299)(1861,2302)(1864,1865)(1868,2309)(1869,2310)(1871,
     2313)(1874,1875)(1878,2320)(1880,2322)(1883,2325)(1885,2327)(1886,2328)
     (1887,2329)(1890,1891)(1894,2336)(1896,2338)(1899,2341)(1901,2343)(1902,
     2344)(1903,2345)(1906,2349)(1909,2352)(1911,2354)(1912,2355)(1914,2358)
     (1915,2359)(1917,2362)(1920,2365)(1921,2366)(1923,2369)(1924,2370)(1926,
     2373)(1928,2375)(1929,2376)(1931,2379)(1932,2380)(1934,2383)(1935,2384)
     (1936,2386)(1939,2390)(1940,2391)(1942,2394)(1943,2395)(1944,2397)(1945,
     2399)(1946,2400)(1947,2402)(1949,2405)(1952,2409)(1954,2411)(1955,2146)
     (1956,2412)(1958,2415)(1960,2417)(1961,2418)(1963,2421)(1964,2422)(1965,
     2424)(1966,2426)(1967,2427)(1968,2429)(1971,2433)(1972,2434)(1974,2437)
     (1975,2438)(1976,2440)(1977,2442)(1978,2443)(1979,2445)(1981,2448)(1983,
     2451)(1984,2453)(1986,2456)(1990,2460)(1991,2461)(1992,2463)(1993,2465)
     (1994,2466)(1995,2468)(1997,2471)(1999,2474)(2000,2476)(2002,2479)(2005,
     2006)(2009,2486)(2010,2487)(2012,2490)(2013,2491)(2014,2493)(2015,2495)
     (2016,2496)(2017,2498)(2020,2502)(2021,2503)(2023,2506)(2024,2507)(2025,
     2509)(2026,2511)(2027,2512)(2028,2514)(2030,2517)(2032,2520)(2033,2522)
     (2035,2525)(2039,2529)(2040,2530)(2041,2532)(2042,2534)(2043,2535)(2044,
     2537)(2046,2540)(2048,2543)(2050,2546)(2053,2054)(2057,2553)(2058,2554)
     (2060,2557)(2063,2064)(2067,2564)(2069,2566)(2072,2569)(2074,2571)(2075,
     2572)(2077,2573)(2078,2574)(2079,2576)(2080,2578)(2081,2579)(2082,2581)
     (2084,2584)(2086,2587)(2089,2090)(2093,2594)(2095,2596)(2096,2597)(2097,
     2599)(2099,2602)(2101,2605)(2102,2607)(2104,2610)(2106,2107)(2110,2616)
     (2113,2114)(2117,2622)(2119,2624)(2122,2627)(2124,2629)(2125,2630)(2126,
     2631)(2131,2636)(2133,2638)(2136,2641)(2138,2643)(2139,2644)(2141,2647)
     (2142,2648)(2143,2650)(2145,2653)(2149,2658)(2150,2659)(2152,2662)(2155,
     2156)(2159,2668)(2161,2670)(2164,2673)(2166,2675)(2168,2676)(2171,2172)
     (2175,2683)(2177,2685)(2181,2688)(2183,2690)(2185,2692)(2187,2694)(2190,
     2697)(2191,2698)(2193,2701)(2194,2702)(2196,2705)(2198,2707)(2199,2708)
     (2201,2711)(2202,2712)(2203,2714)(2204,2715)(2205,2717)(2207,2720)(2210,
     2211)(2214,2727)(2216,2729)(2219,2732)(2221,2734)(2222,2735)(2223,2736)
     (2226,2227)(2230,2743)(2232,2745)(2235,2748)(2237,2750)(2238,2751)(2240,
     2754)(2241,2755)(2243,2758)(2245,2760)(2246,2761)(2248,2764)(2249,2765)
     (2250,2767)(2253,2771)(2255,2773)(2258,2776)(2260,2778)(2261,2779)(2263,
     2782)(2264,2783)(2266,2786)(2267,2787)(2269,2790)(2270,2791)(2271,2793)
     (2272,2795)(2273,2796)(2274,2798)(2277,2802)(2278,2803)(2280,2806)(2281,
     2807)(2282,2809)(2283,2811)(2284,2812)(2285,2814)(2287,2817)(2290,2821)
     (2292,2823)(2293,2824)(2295,2827)(2296,2828)(2298,2831)(2300,2833)(2301,
     2834)(2303,2837)(2304,2838)(2305,2840)(2306,2842)(2307,2843)(2308,2845)
     (2311,2849)(2312,2850)(2314,2853)(2315,2854)(2316,2856)(2317,2858)(2318,
     2859)(2319,2861)(2321,2864)(2323,2867)(2324,2869)(2326,2872)(2330,2876)
     (2331,2877)(2332,2879)(2333,2881)(2334,2882)(2335,2884)(2337,2887)(2339,
     2890)(2340,2892)(2342,2895)(2346,2899)(2347,2900)(2348,2902)(2350,2905)
     (2351,2907)(2353,2910)(2356,2357)(2360,2917)(2361,2918)(2363,2921)(2364,
     2923)(2367,2368)(2371,2930)(2372,2931)(2374,2934)(2377,2378)(2381,2941)
     (2382,2942)(2385,2945)(2387,2947)(2388,2948)(2389,2949)(2392,2393)(2396,
     2956)(2398,2958)(2401,2961)(2403,2963)(2404,2964)(2406,2967)(2407,2968)
     (2408,2970)(2410,2973)(2413,2977)(2414,2978)(2416,2981)(2419,2420)(2423,
     2988)(2425,2990)(2428,2993)(2430,2995)(2431,2996)(2432,2997)(2435,2436)
     (2439,3004)(2441,3006)(2444,3009)(2446,3011)(2447,3012)(2449,3015)(2450,
     3016)(2452,3019)(2454,3021)(2455,3022)(2457,3025)(2458,3026)(2459,3028)
     (2462,3032)(2464,3034)(2467,3037)(2469,3039)(2470,3040)(2472,3043)(2473,
     3044)(2475,3047)(2477,3049)(2478,3050)(2480,3053)(2481,3054)(2482,3056)
     (2483,3058)(2484,3059)(2485,3061)(2488,2489)(2492,3067)(2494,3069)(2497,
     3072)(2499,3074)(2500,3075)(2501,3076)(2504,2505)(2508,3083)(2510,3085)
     (2513,3088)(2515,3090)(2516,3091)(2518,3094)(2519,3095)(2521,3098)(2523,
     3100)(2524,3101)(2526,3104)(2527,3105)(2528,3107)(2531,3111)(2533,3113)
     (2536,3116)(2538,3118)(2539,3119)(2541,3122)(2542,3123)(2544,3126)(2545,
     3127)(2547,3130)(2548,3131)(2549,3133)(2550,3135)(2551,3136)(2552,3138)
     (2555,3142)(2556,3143)(2558,3146)(2559,3147)(2560,3149)(2561,3151)(2562,
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