bin1 := (1,2)(3,5)(4,7)(6,10)(8,13)(9,15)(11,18)(12,20)(14,23)(16,26)(17,28)(19,
     31)(21,34)(22,36)(24,39)(25,41)(27,44)(29,47)(30,49)(32,52)(33,54)(35,57)
     (37,60)(38,62)(40,65)(42,68)(43,70)(45,73)(46,75)(48,78)(50,81)(51,83)
     (53,86)(55,89)(56,91)(58,94)(59,96)(61,99)(63,102)(64,104)(66,107)(67,
     109)(69,112)(71,115)(72,117)(74,120)(76,123)(77,125)(79,128)(80,130)(82,
     133)(84,136)(85,138)(87,141)(88,143)(90,146)(92,149)(93,151)(95,154)(97,
     157)(98,159)(100,162)(101,164)(103,167)(105,170)(106,172)(108,175)(110,
     178)(111,180)(113,183)(114,185)(116,188)(118,191)(119,193)(121,196)(122,
     198)(124,200)(126,203)(127,205)(129,208)(131,211)(132,213)(134,216)(135,
     218)(137,221)(139,224)(140,226)(142,229)(144,232)(145,234)(147,237)(148,
     239)(150,242)(152,245)(153,247)(155,250)(156,252)(158,255)(160,258)(161,
     260)(163,263)(165,266)(166,267)(168,270)(169,272)(171,275)(173,278)(174,
     280)(176,283)(177,285)(179,288)(181,291)(182,293)(184,296)(186,299)(187,
     301)(189,304)(192,308)(195,312)(197,315)(199,318)(201,321)(202,323)(204,
     326)(206,329)(207,331)(209,334)(210,336)(212,339)(214,342)(215,344)(217,
     347)(219,350)(220,352)(222,355)(223,357)(225,360)(227,363)(228,365)(230,
     368)(231,370)(233,373)(235,376)(236,378)(238,381)(240,383)(241,385)(243,
     388)(244,390)(246,393)(248,395)(249,397)(251,400)(253,403)(254,405)(256,
     408)(257,410)(259,413)(261,415)(262,417)(264,420)(265,422)(268,425)(269,
     427)(271,430)(273,433)(274,435)(276,436)(277,432)(279,440)(281,443)(282,
     445)(284,448)(286,451)(287,453)(289,455)(290,457)(292,460)(294,463)(295,
     464)(297,467)(300,471)(302,474)(303,476)(305,478)(306,480)(307,482)(309,
     485)(310,487)(311,489)(313,492)(314,494)(316,497)(317,499)(319,502)(320,
     504)(322,507)(325,510)(327,513)(328,515)(330,518)(332,520)(333,522)(335,
     525)(337,528)(338,530)(340,533)(341,535)(343,538)(345,541)(346,543)(348,
     546)(349,548)(351,551)(353,554)(354,556)(356,486)(358,561)(359,563)(361,
     566)(362,568)(364,571)(366,574)(367,575)(369,578)(371,580)(372,582)(374,
     585)(375,587)(377,590)(379,593)(380,595)(382,598)(384,601)(386,604)(387,
     606)(389,608)(391,611)(392,613)(394,616)(396,619)(398,622)(399,624)(401,
     627)(402,629)(404,632)(406,635)(407,637)(409,640)(411,642)(412,644)(414,
     646)(416,649)(418,652)(419,654)(421,657)(423,660)(424,662)(426,665)(428,
     668)(429,670)(431,673)(434,677)(437,680)(438,682)(439,684)(441,687)(442,
     689)(444,692)(446,695)(447,697)(449,700)(450,702)(452,705)(454,708)(456,
     711)(458,714)(459,716)(461,719)(462,721)(465,725)(466,727)(468,729)(469,
     731)(470,733)(472,736)(473,738)(475,740)(477,742)(479,745)(481,748)(483,
     589)(484,599)(488,756)(490,758)(491,760)(493,762)(495,765)(496,767)(498,
     770)(500,773)(501,775)(503,778)(505,781)(506,783)(508,786)(509,788)(511,
     791)(512,793)(514,796)(516,799)(517,800)(519,803)(521,806)(523,809)(524,
     811)(526,813)(527,815)(529,583)(531,819)(532,821)(534,824)(536,827)(537,
     829)(539,830)(540,832)(542,835)(544,838)(545,840)(547,842)(549,845)(550,
     847)(552,664)(553,851)(555,853)(557,855)(558,857)(559,859)(560,861)(562,
     864)(564,867)(565,869)(567,872)(569,875)(570,877)(572,681)(573,880)(576,
     884)(577,886)(579,889)(584,895)(586,898)(588,901)(591,656)(592,906)(594,
     909)(596,912)(597,914)(600,918)(602,920)(603,922)(605,925)(607,928)(609,
     930)(610,932)(612,935)(614,938)(615,940)(617,943)(618,945)(620,948)(621,
     950)(623,953)(625,956)(626,958)(628,960)(630,962)(631,964)(633,967)(634,
     969)(636,972)(638,975)(639,976)(641,979)(643,981)(645,984)(647,987)(648,
     989)(650,992)(651,994)(653,997)(655,1000)(658,1004)(659,1006)(661,1009)
     (663,1011)(666,1015)(667,1017)(669,1020)(671,1023)(672,1025)(674,1028)
     (675,1030)(676,1032)(678,1035)(679,1037)(683,1042)(685,1045)(686,1047)
     (688,1050)(690,1053)(691,1055)(693,1058)(694,1060)(696,1063)(698,1065)
     (699,1067)(701,1070)(703,1071)(704,1073)(706,1074)(707,900)(709,1078)
     (710,1080)(712,1083)(713,1085)(715,1087)(717,1090)(718,1092)(720,1095)
     (722,1098)(723,1100)(724,1102)(726,1105)(728,1108)(730,1111)(732,1114)
     (734,1117)(735,1119)(737,1122)(739,1124)(741,1127)(743,1130)(744,1132)
     (746,1135)(747,1137)(749,1140)(750,1142)(751,1144)(752,1146)(753,1148)
     (754,1150)(755,1152)(757,1154)(759,1157)(761,1160)(763,1163)(764,1165)
     (766,1168)(768,1171)(769,1173)(771,882)(772,1177)(774,1180)(776,1183)
     (777,1185)(779,1188)(780,1190)(782,951)(784,1010)(785,1196)(787,1199)
     (789,1202)(790,1204)(792,1206)(794,1209)(795,1211)(797,1214)(798,1216)
     (801,1220)(802,1221)(804,1224)(807,1227)(808,1229)(812,1234)(814,1237)
     (816,1240)(817,1242)(818,1244)(820,1247)(822,1250)(823,1252)(825,1255)
     (826,1257)(828,1260)(831,1263)(833,1266)(834,1268)(836,1271)(837,1273)
     (841,1277)(843,1280)(844,1282)(846,1283)(848,1286)(849,1288)(850,1290)
     (852,1293)(854,1014)(856,1298)(858,1301)(860,1304)(862,970)(863,1307)
     (865,1310)(866,1312)(868,1315)(870,1318)(871,1320)(873,1323)(874,1325)
     (876,1328)(878,1331)(879,1333)(881,1336)(883,1338)(885,1341)(887,1344)
     (888,1346)(890,1349)(891,1278)(892,1352)(893,1354)(894,1356)(896,1359)
     (897,1361)(899,1364)(902,1368)(903,1370)(904,1372)(905,1374)(907,1376)
     (908,1378)(910,1381)(911,1103)(913,1384)(915,1387)(916,1212)(917,1390)
     (919,1393)(921,1396)(923,1399)(924,1401)(926,1403)(927,1405)(929,1408)
     (931,1411)(933,1414)(934,1416)(936,1419)(937,1421)(939,1158)(941,1425)
     (942,1427)(944,1430)(946,1432)(947,1434)(949,1437)(952,1441)(954,1444)
     (955,1446)(957,1449)(959,1451)(961,1454)(963,1101)(965,1457)(966,1459)
     (968,1462)(971,1466)(973,1468)(974,1470)(977,1473)(978,1475)(980,1478)
     (982,1480)(983,1482)(985,1485)(986,1487)(988,1489)(990,1492)(991,1493)
     (993,1496)(995,1498)(996,1500)(998,1306)(999,1504)(1001,1506)(1002,1507)
     (1003,1509)(1005,1512)(1007,1514)(1008,1516)(1012,1521)(1013,1523)(1016,
     1526)(1018,1528)(1019,1530)(1021,1269)(1022,1533)(1024,1536)(1026,1537)
     (1027,1539)(1029,1162)(1031,1544)(1033,1113)(1034,1302)(1036,1549)(1038,
     1551)(1039,1553)(1040,1555)(1041,1557)(1044,1561)(1046,1564)(1048,1194)
     (1049,1567)(1051,1570)(1052,1572)(1054,1575)(1056,1578)(1057,1580)(1059,
     1583)(1061,1586)(1064,1589)(1066,1321)(1068,1594)(1069,1596)(1072,1599)
     (1075,1603)(1076,1576)(1077,1606)(1079,1609)(1081,1612)(1082,1614)(1084,
     1617)(1086,1620)(1088,1623)(1089,1625)(1091,1628)(1093,1631)(1094,1633)
     (1096,1636)(1097,1638)(1099,1641)(1104,1647)(1106,1649)(1107,1651)(1109,
     1654)(1110,1656)(1112,1621)(1115,1662)(1116,1213)(1118,1279)(1120,1668)
     (1121,1670)(1123,1672)(1125,1675)(1126,1543)(1128,1679)(1129,1681)(1131,
     1683)(1133,1294)(1134,1687)(1136,1690)(1138,1693)(1139,1695)(1141,1697)
     (1143,1700)(1145,1702)(1147,1704)(1149,1706)(1151,1707)(1153,1710)(1155,
     1542)(1156,1714)(1159,1718)(1164,1545)(1167,1727)(1169,1730)(1170,1433)
     (1172,1733)(1174,1241)(1175,1503)(1176,1738)(1178,1740)(1179,1742)(1181,
     1745)(1182,1747)(1184,1749)(1186,1752)(1187,1592)(1189,1755)(1191,1758)
     (1192,1760)(1193,1761)(1195,1763)(1197,1766)(1198,1569)(1200,1770)(1201,
     1771)(1203,1774)(1205,1777)(1207,1780)(1208,1782)(1210,1785)(1215,1791)
     (1217,1793)(1218,1795)(1219,1797)(1222,1801)(1223,1802)(1225,1805)(1226,
     1807)(1228,1810)(1230,1813)(1231,1815)(1232,1817)(1233,1629)(1235,1821)
     (1236,1823)(1238,1826)(1239,1828)(1245,1835)(1246,1836)(1248,1558)(1249,
     1840)(1251,1842)(1253,1844)(1254,1587)(1256,1848)(1258,1850)(1259,1852)
     (1261,1854)(1262,1856)(1264,1754)(1265,1860)(1267,1863)(1270,1867)(1272,
     1870)(1274,1873)(1275,1875)(1276,1877)(1281,1882)(1284,1886)(1285,1604)
     (1287,1889)(1289,1892)(1291,1895)(1292,1897)(1295,1900)(1296,1902)(1297,
     1904)(1299,1907)(1300,1909)(1303,1912)(1305,1915)(1308,1511)(1309,1919)
     (1311,1921)(1313,1505)(1314,1924)(1316,1855)(1317,1928)(1319,1931)(1322,
     1935)(1324,1938)(1326,1941)(1327,1360)(1329,1945)(1330,1947)(1332,1949)
     (1334,1822)(1335,1953)(1337,1954)(1339,1957)(1340,1959)(1342,1962)(1343,
     1963)(1345,1966)(1347,1969)(1348,1971)(1350,1519)(1351,1974)(1353,1976)
     (1355,1977)(1357,1980)(1358,1982)(1362,1987)(1363,1989)(1365,1992)(1366,
     1994)(1367,1996)(1369,1999)(1371,2002)(1373,2005)(1375,1950)(1377,2010)
     (1379,2013)(1380,2015)(1382,1524)(1383,2018)(1385,1984)(1386,2021)(1388,
     2023)(1389,2025)(1391,2028)(1392,2030)(1394,2033)(1395,1934)(1397,2037)
     (1398,2039)(1400,2042)(1402,2044)(1404,2047)(1406,2050)(1407,2052)(1409,
     2054)(1410,2056)(1413,2059)(1415,2061)(1417,2064)(1418,2066)(1420,2069)
     (1422,2071)(1423,2072)(1424,1878)(1426,2076)(1428,2078)(1429,2080)(1431,
     2024)(1435,2086)(1436,2088)(1438,1993)(1439,2092)(1440,2093)(1442,2096)
     (1443,1932)(1445,2100)(1447,2103)(1448,2105)(1450,2108)(1452,2111)(1453,
     2113)(1455,1837)(1456,2115)(1458,2117)(1460,2118)(1461,2120)(1463,1725)
     (1464,2121)(1465,2123)(1467,2126)(1469,2128)(1471,2130)(1472,2131)(1474,
     2133)(1476,2135)(1477,2136)(1479,2138)(1481,2141)(1483,2144)(1484,2146)
     (1486,2148)(1488,2151)(1490,2154)(1491,1983)(1494,2159)(1495,2160)(1497,
     2098)(1499,2163)(1501,2166)(1502,2168)(1508,2175)(1510,2177)(1513,2180)
     (1515,2183)(1517,2006)(1518,2187)(1520,2190)(1522,2193)(1525,2196)(1527,
     2198)(1529,2201)(1531,2204)(1532,2206)(1534,2208)(1535,2209)(1538,2212)
     (1540,2214)(1541,2216)(1546,2222)(1547,2224)(1548,2226)(1550,2229)(1552,
     2232)(1554,1839)(1556,2236)(1559,2240)(1560,2242)(1562,2245)(1563,2247)
     (1565,2249)(1566,2250)(1568,1891)(1571,2254)(1573,2257)(1574,2259)(1577,
     2263)(1579,2027)(1581,2268)(1582,2270)(1584,2273)(1585,2275)(1588,1634)
     (1590,2280)(1591,2282)(1593,2284)(1595,2287)(1597,2290)(1598,2292)(1600,
     2293)(1601,2295)(1602,2297)(1605,2301)(1607,2304)(1608,2306)(1610,2308)
     (1611,2310)(1613,2313)(1615,2314)(1616,2089)(1618,2318)(1619,2320)(1622,
     2324)(1624,2326)(1626,2328)(1627,2330)(1630,2334)(1632,2337)(1635,2341)
     (1637,2344)(1639,2347)(1640,1724)(1642,2349)(1644,2351)(1645,2353)(1646,
     2355)(1648,2358)(1650,2361)(1652,2364)(1653,2366)(1655,2368)(1657,2370)
     (1658,2372)(1659,2106)(1661,2055)(1663,2376)(1664,2377)(1665,2378)(1666,
     2379)(1667,2381)(1669,2384)(1671,2387)(1673,2390)(1674,2392)(1676,2394)
     (1677,2045)(1678,2397)(1680,2399)(1682,2402)(1684,2404)(1685,2405)(1686,
     2406)(1688,2408)(1689,2410)(1691,2412)(1692,2413)(1694,2415)(1696,2034)
     (1698,2418)(1699,2420)(1701,2423)(1703,2424)(1705,2427)(1708,2430)(1709,
     2432)(1711,2434)(1712,2436)(1713,2438)(1715,2020)(1716,2439)(1717,1922)
     (1719,2442)(1720,2444)(1721,2446)(1722,2448)(1723,2450)(1726,2454)(1728,
     2456)(1729,2457)(1732,1901)(1734,2461)(1735,2463)(1736,2070)(1737,2466)
     (1739,2469)(1741,2471)(1743,2473)(1744,2474)(1746,2476)(1750,2480)(1751,
     2482)(1753,2484)(1756,2487)(1757,2489)(1759,1764)(1762,2494)(1765,2496)
     (1767,2497)(1768,2499)(1769,2500)(1772,2504)(1773,2506)(1775,2509)(1776,
     2511)(1778,2513)(1779,2300)(1781,2516)(1783,2157)(1784,2520)(1786,2523)
     (1787,2518)(1788,2525)(1789,2527)(1790,2262)(1792,2531)(1794,2534)(1796,
     2176)(1798,2536)(1799,2538)(1800,2540)(1803,2543)(1804,2544)(1806,2546)
     (1808,2549)(1809,2550)(1811,2551)(1812,2528)(1814,2554)(1816,2556)(1818,
     1871)(1819,2559)(1820,2561)(1824,2563)(1825,2565)(1827,2568)(1829,2571)
     (1830,2573)(1831,2574)(1832,2576)(1833,2578)(1834,2580)(1838,2583)(1841,
     2585)(1843,2588)(1846,2591)(1847,2593)(1849,2595)(1851,2597)(1853,2017)
     (1857,2601)(1858,2603)(1859,2605)(1861,2608)(1862,2609)(1864,2231)(1865,
     2613)(1866,2615)(1868,2618)(1869,2620)(1872,2624)(1874,2627)(1876,2630)
     (1879,2633)(1880,2635)(1881,2637)(1883,2639)(1884,2640)(1885,2642)(1887,
     2645)(1888,2647)(1890,2650)(1893,2653)(1894,2202)(1896,2657)(1898,2659)
     (1899,2661)(1903,2666)(1905,2227)(1906,2669)(1908,2671)(1910,2674)(1911,
     2143)(1913,2677)(1914,2678)(1916,2681)(1917,2682)(1918,2684)(1920,2685)
     (1923,2689)(1925,2692)(1926,2693)(1929,2697)(1930,2699)(1933,2701)(1936,
     2705)(1937,2707)(1939,2709)(1940,2711)(1942,2714)(1943,2716)(1944,2717)
     (1946,2464)(1948,2722)(1951,2724)(1952,2357)(1955,2729)(1956,2194)(1958,
     2732)(1960,2734)(1961,2736)(1964,2739)(1965,2741)(1967,2743)(1968,2745)
     (1970,2003)(1972,2749)(1973,2706)(1975,2750)(1978,2753)(1979,2754)(1981,
     2757)(1985,2762)(1986,2764)(1988,2702)(1990,2768)(1991,2770)(1995,2773)
     (1997,2775)(1998,2776)(2000,2778)(2001,2780)(2004,2784)(2007,2723)(2008,
     2789)(2009,2790)(2011,2793)(2012,2795)(2014,2668)(2016,2798)(2019,2801)
     (2022,2805)(2026,2178)(2029,2812)(2031,2813)(2032,2814)(2035,2817)(2036,
     2818)(2038,2821)(2040,2727)(2041,2825)(2043,2090)(2046,2830)(2048,2833)
     (2049,2835)(2051,2837)(2053,2840)(2057,2844)(2058,2846)(2060,2848)(2062,
     2311)(2063,2852)(2065,2855)(2067,2629)(2068,2859)(2073,2863)(2074,2865)
     (2075,2867)(2077,2869)(2079,2870)(2081,2558)(2082,2873)(2083,2875)(2084,
     2876)(2085,2878)(2087,2881)(2091,2883)(2094,2886)(2095,2888)(2097,2890)
     (2099,2893)(2101,2895)(2102,2897)(2104,2899)(2107,2903)(2109,2905)(2110,
     2425)(2112,2908)(2114,2911)(2116,2359)(2119,2914)(2122,2882)(2124,2294)
     (2125,2383)(2127,2921)(2129,2923)(2132,2927)(2134,2429)(2137,2909)(2139,
     2907)(2140,2934)(2142,2935)(2145,2939)(2147,2656)(2149,2944)(2150,2945)
     (2152,2947)(2153,2949)(2155,2952)(2156,2953)(2161,2958)(2162,2960)(2164,
     2962)(2165,2964)(2167,2797)(2169,2967)(2170,2968)(2171,2970)(2172,2972)
     (2173,2973)(2174,2974)(2179,2978)(2181,2309)(2182,2951)(2184,2983)(2185,
     2985)(2186,2987)(2188,2990)(2189,2991)(2191,2994)(2192,2478)(2195,2998)
     (2197,2965)(2199,2611)(2200,3004)(2203,3008)(2205,3011)(2207,3013)(2210,
     3016)(2211,3018)(2213,2380)(2215,3020)(2217,3022)(2218,3024)(2219,3026)
     (2220,2303)(2221,3029)(2223,3031)(2225,3033)(2228,2759)(2230,2362)(2233,
     3038)(2234,2492)(2235,3040)(2237,3041)(2238,3042)(2239,3044)(2241,3046)
     (2243,3049)(2244,3051)(2246,3054)(2248,3056)(2251,2779)(2252,3060)(2253,
     2614)(2255,3063)(2256,3064)(2258,3067)(2260,2443)(2261,3069)(2264,3072)
     (2265,3073)(2266,3074)(2267,3075)(2269,2488)(2271,3078)(2272,2315)(2274,
     3082)(2276,2956)(2277,3085)(2278,2490)(2279,3088)(2281,2360)(2283,3092)
     (2285,3094)(2286,3096)(2288,3099)(2289,3100)(2291,3102)(2296,3107)(2298,
     3109)(2299,2719)(2302,3113)(2305,2333)(2307,3117)(2312,3050)(2316,3125)
     (2317,3127)(2319,3128)(2321,3131)(2322,2831)(2323,2572)(2325,3134)(2327,
     3137)(2329,3139)(2331,3142)(2332,3144)(2335,3146)(2336,3148)(2338,3150)
     (2340,2367)(2342,2374)(2343,3154)(2345,3157)(2348,2787)(2350,3161)(2352,
     3164)(2354,3167)(2356,3169)(2363,3173)(2365,3175)(2369,3179)(2371,3182)
     (2373,3185)(2375,3187)(2382,3194)(2385,3197)(2386,3199)(2388,3202)(2389,
     2767)(2391,2802)(2393,3207)(2395,3210)(2396,2673)(2398,3212)(2400,3214)
     (2401,3215)(2403,3218)(2407,3221)(2409,3223)(2411,3226)(2414,2877)(2416,
     3231)(2417,3232)(2419,3235)(2421,3236)(2422,3237)(2426,3242)(2431,2533)
     (2433,2584)(2435,3249)(2437,3251)(2440,2785)(2441,3253)(2445,3256)(2447,
     3259)(2449,3261)(2451,3263)(2452,3264)(2453,3124)(2455,3266)(2458,3268)
     (2459,3270)(2460,3272)(2462,3274)(2465,3277)(2467,3280)(2468,3282)(2470,
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