bin1 := (1,2)(3,6)(4,7)(5,9)(8,14)(10,17)(11,19)(12,20)(13,22)(15,25)(16,27)(18,
     30)(21,35)(23,38)(24,40)(26,43)(28,46)(29,48)(31,51)(32,53)(33,54)(34,56)
     (36,59)(37,61)(39,63)(41,66)(42,68)(44,71)(45,73)(47,76)(49,79)(50,81)
     (52,84)(55,89)(57,91)(58,93)(60,96)(62,99)(64,102)(65,104)(67,107)(69,
     109)(70,110)(72,113)(74,116)(75,118)(77,121)(78,123)(80,126)(82,128)(83,
     130)(85,133)(86,135)(87,136)(88,138)(90,141)(92,124)(94,146)(95,148)(97,
     151)(98,153)(100,156)(101,157)(103,158)(105,159)(106,161)(108,164)(111,
     169)(112,171)(114,174)(115,176)(117,179)(119,181)(120,183)(122,185)(125,
     182)(127,189)(129,192)(131,195)(132,196)(134,198)(137,203)(139,206)(140,
     208)(142,211)(143,213)(144,214)(145,216)(147,219)(149,222)(150,224)(152,
     227)(154,230)(155,232)(160,241)(162,244)(163,246)(165,249)(166,251)(167,
     252)(168,254)(170,256)(172,259)(173,261)(175,264)(177,267)(178,269)(180,
     272)(184,277)(186,280)(187,282)(188,283)(190,286)(191,288)(193,291)(194,
     293)(197,298)(199,301)(200,303)(201,304)(202,306)(204,309)(205,311)(207,
     314)(209,284)(210,318)(212,321)(215,326)(217,329)(218,331)(220,334)(221,
     336)(223,339)(225,342)(226,344)(228,347)(229,349)(231,352)(233,354)(234,
     356)(235,357)(236,359)(237,360)(238,361)(239,362)(240,364)(242,367)(245,
     370)(247,373)(248,375)(250,378)(253,383)(255,386)(257,389)(258,391)(260,
     394)(262,395)(263,397)(265,400)(266,402)(268,405)(270,408)(271,410)(273,
     413)(274,415)(275,416)(276,377)(278,327)(279,421)(281,422)(285,426)(287,
     429)(289,432)(290,434)(292,437)(294,371)(295,441)(296,442)(297,444)(299,
     446)(300,448)(302,451)(305,456)(307,459)(308,461)(310,463)(312,466)(313,
     468)(315,471)(316,473)(317,474)(319,477)(320,479)(322,482)(323,484)(324,
     485)(325,487)(328,491)(330,494)(332,497)(333,499)(335,502)(337,353)(338,
     505)(340,508)(341,509)(343,512)(345,515)(346,517)(348,520)(350,523)(351,
     524)(363,537)(365,540)(366,541)(368,543)(369,545)(372,549)(374,552)(376,
     555)(379,559)(380,561)(381,562)(382,564)(384,567)(385,569)(387,572)(388,
     574)(390,577)(392,580)(393,460)(396,586)(398,589)(399,591)(401,594)(403,
     596)(404,598)(406,601)(407,603)(409,605)(411,607)(412,609)(414,611)(417,
     616)(418,617)(419,618)(420,619)(423,624)(424,626)(425,627)(427,630)(428,
     632)(430,635)(431,637)(433,638)(435,529)(436,641)(438,644)(439,646)(440,
     647)(443,652)(445,655)(447,658)(449,661)(450,663)(452,666)(453,454)(455,
     668)(457,669)(458,671)(462,675)(464,678)(465,581)(467,682)(469,685)(470,
     686)(472,689)(475,692)(476,694)(478,697)(480,700)(481,702)(483,705)(486,
     709)(488,712)(489,714)(490,715)(492,718)(495,721)(496,723)(498,725)(500,
     728)(501,730)(503,733)(504,734)(506,735)(507,736)(510,739)(511,649)(513,
     742)(514,744)(516,747)(518,750)(519,752)(521,755)(522,757)(525,760)(526,
     762)(527,763)(528,764)(530,766)(531,768)(532,769)(533,771)(534,772)(535,
     761)(536,774)(538,775)(539,777)(542,782)(544,785)(546,713)(547,788)(548,
     789)(550,792)(551,794)(553,796)(554,798)(556,801)(557,802)(558,803)(560,
     804)(563,809)(565,811)(566,812)(568,815)(570,817)(571,819)(573,822)(575,
     825)(576,827)(578,830)(579,832)(582,833)(583,701)(584,834)(585,612)(587,
     838)(588,840)(590,843)(592,846)(593,848)(595,851)(597,853)(599,856)(600,
     858)(602,861)(604,863)(606,864)(608,867)(610,870)(613,874)(614,875)(615,
     877)(620,884)(621,886)(622,887)(623,889)(625,892)(628,708)(629,895)(631,
     898)(633,901)(634,903)(636,906)(639,888)(640,908)(642,911)(643,913)(645,
     916)(648,921)(650,923)(651,925)(653,928)(654,930)(656,933)(657,935)(659,
     936)(660,938)(662,940)(664,942)(665,943)(667,946)(670,951)(672,954)(673,
     955)(674,957)(676,960)(677,962)(679,963)(680,964)(681,966)(683,968)(684,
     970)(687,971)(688,973)(690,976)(691,978)(693,776)(695,983)(696,985)(698,
     988)(699,990)(703,995)(704,997)(706,1000)(707,1002)(710,1005)(711,1007)
     (716,1013)(717,1015)(719,1018)(720,1020)(722,1023)(724,1024)(726,1027)
     (727,1029)(729,1032)(731,1035)(732,1037)(737,1041)(738,1043)(740,1046)
     (741,1048)(743,1051)(745,1054)(746,1056)(748,1059)(749,1061)(751,1064)
     (753,1066)(754,1068)(756,1071)(758,1073)(759,1075)(765,1084)(767,1087)
     (770,1092)(773,1095)(779,1101)(780,914)(781,1103)(783,1106)(784,1108)
     (786,1110)(787,1112)(790,1115)(791,1117)(793,1120)(795,939)(797,1124)
     (799,1127)(800,1129)(805,1137)(806,1139)(807,1140)(808,1142)(810,1145)
     (813,1150)(814,1152)(816,1155)(818,1158)(820,1160)(821,1162)(823,1165)
     (824,1167)(826,1170)(828,1173)(829,1175)(831,1178)(835,1021)(836,1183)
     (837,1185)(839,1188)(841,1191)(842,1193)(844,1006)(845,1197)(847,1200)
     (849,1203)(850,1205)(852,1208)(854,1211)(855,1169)(857,1215)(859,1218)
     (860,1220)(862,1177)(865,1225)(866,1182)(868,1229)(869,1199)(871,1233)
     (872,1234)(873,1235)(876,1240)(878,1241)(879,1242)(880,1243)(881,1245)
     (882,1246)(883,1248)(885,1251)(890,1256)(891,1258)(893,1259)(894,1004)
     (896,1262)(897,1264)(899,1267)(900,1268)(902,1271)(904,1274)(905,1276)
     (907,1279)(909,1282)(910,1284)(912,1287)(915,1290)(918,1293)(919,1294)
     (920,1295)(922,1077)(924,1300)(926,1303)(927,1304)(929,1307)(931,1310)
     (932,1312)(934,1315)(937,1319)(941,1324)(944,1328)(945,1330)(947,1333)
     (948,1335)(949,1336)(950,1338)(952,1317)(953,1342)(956,1100)(958,1349)
     (959,1351)(961,1042)(965,1034)(967,1003)(969,1364)(972,1366)(974,1369)
     (975,1371)(977,1374)(979,1376)(980,1378)(981,1379)(982,1381)(984,1384)
     (986,1386)(987,1388)(989,1391)(991,1363)(992,1395)(993,1396)(994,1398)
     (996,1360)(998,1403)(999,1405)(1001,1408)(1008,1414)(1009,1404)(1010,
     1416)(1011,1417)(1012,1419)(1014,1194)(1016,1424)(1017,1426)(1019,1429)
     (1022,1433)(1025,1370)(1026,1436)(1028,1437)(1030,1440)(1031,1442)(1033,
     1420)(1036,1447)(1038,1450)(1039,1452)(1040,1453)(1044,1458)(1045,1460)
     (1047,1463)(1049,1465)(1050,1467)(1052,1469)(1053,1471)(1055,1474)(1057,
     1477)(1058,1099)(1060,1480)(1062,1483)(1063,1485)(1065,1487)(1067,1490)
     (1069,1493)(1070,1495)(1072,1498)(1074,1500)(1076,1502)(1078,1504)(1079,
     1506)(1080,1507)(1081,1509)(1082,1510)(1083,1512)(1085,1515)(1086,1517)
     (1088,1520)(1089,1522)(1090,1523)(1091,1525)(1093,1528)(1094,1530)(1096,
     1531)(1097,1533)(1098,1195)(1102,1288)(1104,1537)(1105,1539)(1107,1541)
     (1109,1505)(1111,1546)(1113,1549)(1114,1551)(1116,1554)(1118,1557)(1119,
     1144)(1121,1559)(1122,1560)(1123,1562)(1125,1565)(1126,1567)(1128,1569)
     (1130,1385)(1131,1573)(1132,1574)(1133,1576)(1134,1577)(1135,1159)(1136,
     1343)(1138,1581)(1141,1585)(1143,1588)(1146,1590)(1147,1591)(1148,1283)
     (1149,1593)(1151,1596)(1153,1598)(1154,1600)(1156,1603)(1157,1604)(1161,
     1606)(1163,1550)(1164,1608)(1166,1286)(1168,1587)(1171,1616)(1172,1618)
     (1176,1611)(1180,1626)(1181,1595)(1184,1629)(1186,1632)(1187,1634)(1189,
     1637)(1190,1639)(1192,1468)(1196,1644)(1198,1647)(1201,1651)(1202,1653)
     (1204,1439)(1206,1658)(1207,1660)(1209,1663)(1210,1665)(1212,1535)(1213,
     1668)(1214,1670)(1216,1671)(1217,1673)(1219,1676)(1221,1677)(1222,1679)
     (1223,1680)(1224,1682)(1226,1685)(1227,1686)(1228,1688)(1230,1691)(1231,
     1692)(1232,1694)(1236,1700)(1237,1702)(1238,1703)(1239,1705)(1244,1712)
     (1247,1716)(1249,1719)(1250,1721)(1252,1723)(1253,1724)(1254,1650)(1257,
     1311)(1260,1728)(1261,1730)(1263,1732)(1265,1735)(1266,1737)(1269,1741)
     (1270,1743)(1272,1744)(1273,1746)(1275,1749)(1277,1752)(1278,1754)(1280,
     1757)(1281,1759)(1285,1764)(1289,1766)(1291,1768)(1292,1770)(1296,1776)
     (1297,1777)(1298,1778)(1299,1780)(1301,1783)(1302,1785)(1305,1790)(1306,
     1792)(1308,1570)(1309,1633)(1313,1800)(1314,1802)(1316,1805)(1318,1807)
     (1320,1809)(1321,1811)(1322,1812)(1323,1814)(1325,1817)(1326,1819)(1327,
     1820)(1329,1822)(1331,1825)(1332,1827)(1334,1829)(1337,1834)(1339,1837)
     (1340,1839)(1341,1840)(1345,1579)(1346,1845)(1347,1361)(1348,1846)(1350,
     1849)(1352,1852)(1353,1853)(1354,1826)(1355,1855)(1356,1856)(1357,1857)
     (1358,1714)(1359,1859)(1362,1524)(1365,1864)(1367,1867)(1368,1869)(1372,
     1874)(1373,1875)(1375,1589)(1377,1466)(1380,1884)(1382,1886)(1383,1887)
     (1387,1773)(1389,1893)(1390,1895)(1392,1898)(1393,1900)(1394,1901)(1397,
     1527)(1399,1908)(1400,1866)(1401,1910)(1402,1912)(1406,1916)(1407,1918)
     (1409,1921)(1410,1923)(1411,1924)(1412,1925)(1413,1926)(1415,1928)(1418,
     1931)(1421,1935)(1422,1936)(1423,1938)(1425,1940)(1427,1943)(1428,1945)
     (1430,1948)(1431,1950)(1432,1892)(1434,1953)(1435,1955)(1438,1678)(1441,
     1961)(1443,1964)(1444,1965)(1445,1966)(1446,1911)(1448,1970)(1449,1972)
     (1451,1973)(1454,1975)(1455,1976)(1456,1977)(1457,1978)(1459,1981)(1461,
     1984)(1462,1986)(1464,1989)(1470,1992)(1472,1995)(1473,1997)(1475,2000)
     (1476,2002)(1478,2003)(1479,2005)(1481,2008)(1482,2010)(1484,2013)(1486,
     2016)(1488,2018)(1489,2020)(1491,2023)(1492,2024)(1494,2027)(1496,2030)
     (1497,2032)(1499,2033)(1501,2035)(1503,1808)(1508,2042)(1511,1960)(1513,
     2047)(1514,2049)(1516,2052)(1518,2055)(1519,2037)(1521,2058)(1526,2065)
     (1529,2069)(1534,2074)(1536,2076)(1538,2077)(1540,2079)(1542,2082)(1543,
     2084)(1544,2085)(1545,2087)(1547,2090)(1548,2092)(1552,2095)(1553,2097)
     (1555,2099)(1556,2101)(1558,2103)(1561,2107)(1563,2110)(1564,2111)(1566,
     2114)(1568,1793)(1571,2118)(1572,2119)(1575,2120)(1578,1974)(1580,2124)
     (1582,2127)(1583,2071)(1584,2129)(1586,2131)(1592,2138)(1594,2141)(1597,
     2144)(1599,1709)(1601,2146)(1602,2135)(1605,2150)(1607,2153)(1609,2154)
     (1610,1697)(1612,2133)(1613,2156)(1614,2157)(1615,2159)(1617,2162)(1619,
     1729)(1620,2165)(1621,2167)(1622,2168)(1623,2169)(1624,2171)(1625,2172)
     (1627,2148)(1628,2175)(1630,2177)(1631,2179)(1635,2184)(1636,1718)(1638,
     2188)(1640,2190)(1641,2192)(1642,2193)(1643,2195)(1645,2197)(1646,2198)
     (1648,2201)(1649,2202)(1652,2206)(1654,2209)(1655,2211)(1656,2212)(1657,
     2214)(1659,2217)(1661,2220)(1662,2222)(1664,2223)(1666,2226)(1667,2228)
     (1669,2166)(1672,2034)(1674,1919)(1675,2235)(1681,1813)(1683,2242)(1689,
     2246)(1690,2248)(1693,2252)(1695,1959)(1696,1996)(1698,1717)(1699,2130)
     (1701,2134)(1704,1954)(1706,2261)(1707,2262)(1708,2254)(1710,2264)(1711,
     2266)(1713,2267)(1715,2104)(1720,2272)(1722,2275)(1725,1818)(1726,2278)
     (1727,2279)(1731,2282)(1733,2285)(1734,2287)(1736,2290)(1738,2293)(1739,
     2294)(1740,2296)(1742,2299)(1745,2304)(1747,2305)(1748,2078)(1750,2306)
     (1751,2308)(1753,2311)(1755,2314)(1756,2316)(1758,2319)(1760,1810)(1761,
     2094)(1762,1944)(1763,2139)(1765,2324)(1767,1904)(1769,2326)(1771,2327)
     (1772,2329)(1774,2331)(1775,2310)(1779,2189)(1781,2338)(1782,2339)(1784,
     2342)(1786,2213)(1787,1951)(1788,2345)(1789,2347)(1791,2350)(1794,1844)
     (1795,2353)(1796,2181)(1797,2354)(1798,2355)(1799,2357)(1801,2358)(1803,
     2359)(1804,1937)(1806,2362)(1815,2365)(1816,2367)(1821,2369)(1823,2372)
     (1824,2374)(1828,2378)(1830,2380)(1831,2382)(1832,2383)(1833,2385)(1835,
     2388)(1836,2389)(1838,2364)(1841,2396)(1842,2089)(1843,2022)(1848,2401)
     (1850,2404)(1851,2406)(1854,2411)(1858,2416)(1860,2163)(1861,2419)(1862,
     2420)(1863,2422)(1865,2425)(1868,2031)(1870,2429)(1871,2430)(1872,2431)
     (1873,2433)(1876,2435)(1877,2436)(1878,2437)(1879,2439)(1880,2440)(1881,
     2442)(1882,2443)(1883,2445)(1885,2446)(1888,2450)(1889,2028)(1890,2260)
     (1891,2044)(1894,2454)(1896,2457)(1897,2459)(1899,2461)(1902,2465)(1903,
     2466)(1905,2185)(1906,2468)(1907,2469)(1909,2471)(1913,2476)(1914,2477)
     (1915,2479)(1917,2482)(1920,2485)(1922,2488)(1927,2491)(1929,2494)(1930,
     2496)(1932,2497)(1933,2498)(1934,2402)(1939,2504)(1941,2187)(1942,2508)
     (1946,2511)(1947,2512)(1949,2514)(1952,2518)(1956,2075)(1957,2524)(1958,
     2525)(1962,2529)(1963,2530)(1967,2333)(1968,2536)(1969,2537)(1971,2123)
     (1979,2547)(1980,2549)(1982,2298)(1983,2551)(1985,2553)(1987,2523)(1988,
     2556)(1990,2558)(1991,2538)(1993,2559)(1994,2561)(1998,2565)(1999,2566)
     (2001,2568)(2004,2572)(2006,2575)(2007,2155)(2009,2577)(2011,2580)(2012,
     2582)(2014,2229)(2015,2100)(2017,2232)(2019,2332)(2021,2589)(2025,2593)
     (2026,2595)(2029,2599)(2036,2567)(2038,2519)(2039,2343)(2040,2608)(2041,
     2610)(2043,2344)(2045,2611)(2046,2452)(2048,2613)(2050,2257)(2051,2615)
     (2053,2616)(2056,2542)(2057,2618)(2059,2620)(2060,2622)(2061,2623)(2062,
     2428)(2063,2313)(2064,2626)(2066,2627)(2068,2083)(2070,2200)(2072,2632)
     (2073,2633)(2080,2642)(2081,2644)(2086,2650)(2088,2631)(2091,2160)(2093,
     2421)(2096,2196)(2098,2661)(2102,2517)(2105,2668)(2106,2669)(2108,2672)
     (2109,2674)(2112,2676)(2113,2678)(2115,2681)(2116,2683)(2117,2684)(2121,
     2663)(2122,2690)(2125,2692)(2126,2693)(2128,2696)(2132,2701)(2136,2702)
     (2137,2204)(2140,2705)(2142,2708)(2143,2236)(2145,2710)(2147,2545)(2149,
     2712)(2151,2715)(2152,2478)(2158,2718)(2161,2722)(2164,2726)(2170,2730)
     (2173,2734)(2174,2667)(2176,2738)(2178,2741)(2180,2744)(2182,2746)(2183,
     2748)(2186,2412)(2191,2752)(2194,2756)(2199,2759)(2203,2762)(2205,2764)
     (2207,2230)(2208,2768)(2210,2771)(2215,2775)(2216,2777)(2218,2780)(2219,
     2781)(2221,2784)(2224,2704)(2225,2460)(2227,2789)(2231,2791)(2233,2597)
     (2234,2793)(2237,2796)(2238,2798)(2239,2799)(2240,2800)(2241,2699)(2243,
     2802)(2244,2803)(2245,2805)(2247,2808)(2249,2811)(2250,2813)(2251,2814)
     (2253,2815)(2255,2543)(2256,2816)(2258,2818)(2259,2520)(2263,2822)(2265,
     2825)(2268,2828)(2269,2829)(2270,2830)(2271,2774)(2273,2834)(2274,2836)
     (2276,2837)(2277,2502)(2280,2840)(2281,2841)(2283,2842)(2284,2844)(2286,
     2751)(2288,2848)(2289,2849)(2291,2850)(2292,2851)(2295,2853)(2297,2855)
     (2300,2858)(2301,2860)(2302,2861)(2303,2863)(2307,2356)(2309,2868)(2312,
     2870)(2315,2727)(2317,2874)(2318,2876)(2320,2877)(2321,2878)(2322,2879)
     (2323,2880)(2325,2881)(2328,2884)(2330,2886)(2334,2887)(2335,2889)(2336,
     2890)(2337,2892)(2340,2894)(2341,2895)(2346,2897)(2348,2898)(2349,2770)
     (2351,2418)(2352,2903)(2360,2914)(2361,2916)(2363,2456)(2366,2919)(2370,
     2924)(2371,2925)(2373,2928)(2375,2930)(2376,2932)(2377,2933)(2379,2935)
     (2381,2938)(2384,2629)(2386,2941)(2387,2942)(2390,2946)(2391,2948)(2392,
     2949)(2393,2951)(2394,2952)(2395,2953)(2397,2955)(2398,2956)(2399,2957)
     (2400,2885)(2403,2432)(2405,2962)(2407,2481)(2408,2965)(2409,2510)(2410,
     2967)(2413,2795)(2414,2969)(2415,2971)(2417,2846)(2423,2980)(2424,2509)
     (2426,2981)(2427,2982)(2434,2807)(2438,2989)(2441,2991)(2444,2996)(2447,
     2999)(2448,3000)(2449,3002)(2451,3005)(2453,2872)(2455,3009)(2458,3011)
     (2462,3016)(2463,3017)(2464,3018)(2467,3019)(2470,3022)(2472,3025)(2473,
     2963)(2474,2917)(2475,3028)(2480,3032)(2483,3036)(2484,2685)(2486,3038)
     (2487,2507)(2489,3042)(2490,3044)(2492,3046)(2493,3047)(2495,2852)(2499,
     3053)(2500,3054)(2501,3055)(2503,3013)(2505,3056)(2506,3058)(2513,3060)
     (2515,3062)(2516,3064)(2521,3067)(2522,3024)(2526,3069)(2527,3070)(2528,
     3072)(2531,3073)(2532,3063)(2534,2901)(2535,3076)(2539,3077)(2540,3078)
     (2541,3080)(2544,3081)(2548,3082)(2550,2943)(2552,3086)(2554,3087)(2555,
     3089)(2557,3090)(2560,2638)(2562,3097)(2563,2651)(2564,3099)(2569,3101)
     (2570,3102)(2571,3104)(2573,3021)(2574,3107)(2576,3108)(2578,3110)(2579,
     2598)(2581,3113)(2584,3114)(2585,3115)(2586,3116)(2587,3117)(2588,3119)
     (2590,2788)(2591,2694)(2592,3020)(2594,3123)(2596,3124)(2600,3126)(2601,
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