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)(33,53)(35,56)(37,59)
     (38,61)(40,64)(42,67)(43,69)(45,72)(46,74)(48,77)(50,80)(51,82)(52,84)
     (54,87)(55,89)(57,92)(58,94)(60,97)(62,100)(63,102)(65,105)(66,107)(68,
     110)(70,113)(71,115)(73,118)(75,121)(76,123)(78,126)(79,128)(81,131)(83,
     134)(85,137)(86,139)(88,142)(90,145)(91,147)(93,150)(95,153)(96,155)(98,
     158)(99,160)(101,163)(103,166)(104,168)(106,171)(108,174)(109,176)(111,
     179)(112,181)(114,184)(116,187)(117,189)(119,192)(120,194)(122,197)(124,
     200)(125,202)(127,205)(129,208)(130,210)(132,213)(133,215)(135,218)(136,
     220)(138,223)(140,226)(141,228)(143,231)(144,233)(146,236)(148,239)(149,
     241)(151,244)(152,246)(154,249)(156,252)(157,254)(161,259)(162,261)(164,
     264)(165,266)(167,269)(169,272)(170,274)(172,277)(173,279)(175,282)(177,
     285)(178,287)(180,290)(182,293)(183,295)(185,298)(186,300)(188,303)(190,
     306)(191,308)(193,311)(195,314)(196,316)(198,319)(199,321)(201,324)(203,
     327)(204,329)(206,332)(207,334)(209,337)(211,340)(212,342)(214,345)(216,
     348)(217,350)(219,353)(221,356)(224,360)(225,362)(227,365)(229,368)(230,
     370)(232,373)(234,375)(235,377)(237,380)(238,382)(240,385)(242,388)(243,
     390)(247,395)(248,397)(250,400)(251,402)(253,405)(255,408)(256,410)(257,
     412)(258,414)(260,417)(262,420)(263,422)(265,425)(267,428)(268,430)(270,
     433)(271,435)(273,438)(275,441)(276,443)(278,446)(280,449)(281,451)(283,
     454)(284,456)(286,459)(288,462)(289,464)(291,467)(292,469)(294,472)(296,
     475)(297,477)(299,480)(301,483)(302,485)(304,488)(305,490)(307,493)(309,
     496)(310,498)(312,501)(313,503)(315,506)(317,509)(318,511)(320,514)(322,
     517)(323,519)(325,522)(326,524)(328,527)(330,530)(331,532)(333,535)(335,
     538)(336,540)(338,543)(339,545)(341,548)(343,551)(344,553)(346,556)(347,
     558)(349,561)(351,564)(352,566)(354,569)(355,571)(357,574)(358,576)(359,
     578)(361,581)(363,584)(364,586)(366,589)(367,591)(369,594)(371,597)(372,
     580)(374,600)(376,603)(378,606)(379,608)(381,611)(383,614)(384,616)(386,
     619)(387,621)(389,624)(391,627)(392,629)(393,631)(394,633)(396,636)(398,
     639)(399,641)(401,644)(403,647)(404,649)(406,652)(407,654)(409,657)(411,
     660)(413,663)(415,666)(416,668)(418,671)(419,605)(421,675)(423,678)(424,
     680)(426,683)(427,685)(429,688)(431,691)(432,693)(434,696)(436,699)(437,
     701)(439,704)(440,706)(442,709)(444,712)(445,714)(447,717)(448,719)(450,
     722)(452,725)(453,727)(455,730)(457,732)(458,734)(460,737)(461,739)(465,
     744)(466,746)(468,749)(470,752)(471,754)(473,757)(474,759)(476,762)(478,
     765)(479,767)(481,770)(482,772)(484,775)(486,778)(487,780)(489,783)(491,
     786)(492,788)(494,791)(495,793)(497,796)(499,799)(500,801)(502,804)(504,
     807)(505,809)(507,812)(508,814)(510,817)(512,820)(513,822)(515,825)(516,
     827)(518,830)(520,833)(521,835)(523,838)(525,841)(526,843)(528,846)(529,
     848)(531,851)(533,854)(534,856)(536,859)(537,861)(539,864)(541,867)(542,
     869)(544,871)(546,874)(547,876)(549,879)(550,881)(552,884)(554,887)(555,
     889)(557,892)(559,895)(560,897)(562,900)(563,902)(565,905)(567,908)(568,
     910)(570,913)(572,916)(573,918)(575,921)(577,924)(579,927)(582,931)(583,
     932)(585,935)(587,938)(588,940)(590,943)(592,946)(593,923)(595,950)(596,
     952)(598,955)(599,957)(601,960)(602,962)(604,965)(607,969)(609,972)(610,
     974)(612,977)(613,979)(615,982)(617,985)(618,987)(620,990)(622,993)(623,
     995)(625,998)(626,1000)(628,1003)(630,1006)(632,1009)(634,1012)(635,1014)
     (637,1017)(640,1021)(642,1024)(643,1026)(645,1029)(646,1031)(648,1034)
     (650,1037)(651,1039)(653,1042)(655,1045)(656,1047)(658,1050)(659,1052)
     (661,1055)(662,1057)(664,1060)(665,959)(667,1064)(669,1067)(670,1069)
     (672,1072)(673,1074)(674,1076)(676,1079)(677,1081)(679,1084)(681,1087)
     (682,1089)(684,1092)(686,1095)(687,1097)(689,1100)(690,1102)(692,1105)
     (694,1108)(695,1110)(697,1113)(698,1115)(700,1118)(702,1121)(703,1123)
     (705,1126)(707,1129)(708,1131)(710,1134)(711,1136)(713,1139)(715,1142)
     (716,1144)(718,1147)(720,1149)(721,1151)(723,1154)(724,1156)(726,1159)
     (728,1162)(729,1164)(731,1166)(733,1169)(735,1172)(736,1174)(738,1177)
     (740,1180)(741,1182)(742,1184)(743,1186)(745,1189)(747,1192)(748,1194)
     (750,1197)(751,1199)(753,1202)(755,1205)(756,1207)(758,1210)(760,1213)
     (761,1215)(763,776)(764,1219)(766,1222)(768,1225)(769,1227)(771,1230)
     (773,1233)(774,1235)(777,1239)(779,1242)(781,1245)(782,1247)(784,1250)
     (785,1252)(787,1255)(789,1258)(790,1260)(792,1262)(794,1265)(795,1267)
     (797,1270)(798,1272)(800,1275)(802,1278)(803,1280)(805,1283)(806,1285)
     (808,1288)(810,1291)(811,1293)(813,1296)(815,1299)(816,1301)(818,1304)
     (819,1306)(821,1309)(823,1312)(824,1314)(826,1317)(828,1320)(829,1322)
     (831,1325)(832,1327)(834,1330)(836,1333)(837,1335)(839,1338)(840,1340)
     (842,1343)(844,1346)(845,1348)(847,1351)(849,1354)(850,1356)(852,1359)
     (853,1361)(855,1364)(857,1367)(858,1369)(860,1372)(862,1375)(863,1377)
     (865,1380)(866,1382)(868,1385)(870,1388)(872,1391)(873,1393)(875,1396)
     (877,1399)(878,1401)(880,1404)(882,1407)(883,1409)(885,1412)(886,1414)
     (888,1417)(890,1420)(891,1422)(893,1425)(894,1427)(896,1430)(898,1433)
     (899,1435)(901,1438)(903,1441)(904,1443)(906,1446)(907,1448)(909,1451)
     (911,1454)(912,1456)(914,1458)(915,1460)(917,1463)(919,1466)(920,1468)
     (922,1471)(925,1474)(926,1476)(928,1479)(929,1481)(930,1483)(933,1487)
     (934,1489)(936,1492)(939,1496)(941,1499)(942,1501)(945,1505)(947,1508)
     (948,1510)(949,1512)(951,1515)(953,1518)(954,1520)(958,1525)(961,1529)
     (963,1532)(964,1534)(966,1537)(967,1539)(968,1541)(970,1544)(971,1546)
     (973,1549)(975,1552)(976,1554)(978,1557)(980,1560)(981,1562)(983,1565)
     (984,1567)(986,1570)(988,1573)(989,1575)(991,1578)(992,1580)(994,1583)
     (996,1586)(997,1588)(999,1591)(1001,1594)(1002,1596)(1004,1599)(1005,
     1601)(1007,1604)(1008,1606)(1010,1609)(1013,1613)(1015,1616)(1016,1618)
     (1018,1621)(1019,1623)(1020,1625)(1022,1628)(1023,1630)(1025,1633)(1027,
     1636)(1028,1638)(1030,1641)(1032,1644)(1033,1646)(1035,1649)(1036,1651)
     (1038,1654)(1040,1657)(1041,1659)(1043,1662)(1044,1664)(1046,1667)(1048,
     1670)(1049,1672)(1051,1675)(1053,1678)(1054,1680)(1056,1683)(1058,1686)
     (1059,1688)(1061,1691)(1062,1693)(1063,1695)(1065,1698)(1066,1700)(1068,
     1703)(1070,1706)(1071,1708)(1073,1711)(1075,1714)(1077,1717)(1078,1719)
     (1082,1724)(1083,1726)(1085,1729)(1086,1731)(1088,1734)(1090,1732)(1091,
     1738)(1093,1741)(1094,1743)(1096,1746)(1098,1749)(1099,1751)(1101,1754)
     (1103,1757)(1104,1759)(1106,1762)(1107,1764)(1109,1767)(1111,1770)(1112,
     1772)(1114,1775)(1116,1778)(1117,1780)(1119,1783)(1120,1785)(1122,1788)
     (1124,1791)(1125,1793)(1127,1796)(1128,1798)(1130,1801)(1132,1804)(1133,
     1806)(1135,1809)(1137,1811)(1138,1813)(1140,1816)(1141,1818)(1143,1821)
     (1145,1824)(1148,1828)(1150,1831)(1152,1834)(1153,1836)(1155,1839)(1157,
     1842)(1158,1844)(1160,1847)(1161,1848)(1163,1851)(1165,1854)(1167,1857)
     (1168,1859)(1170,1862)(1171,1864)(1173,1867)(1175,1870)(1176,1872)(1178,
     1875)(1179,1877)(1181,1880)(1183,1883)(1185,1349)(1187,1888)(1188,1890)
     (1190,1893)(1191,1895)(1193,1898)(1195,1901)(1196,1903)(1198,1906)(1200,
     1909)(1201,1911)(1203,1914)(1204,1916)(1206,1919)(1208,1922)(1209,1924)
     (1211,1927)(1212,1929)(1214,1932)(1216,1935)(1217,1937)(1218,1939)(1220,
     1942)(1221,1944)(1223,1947)(1224,1949)(1226,1952)(1228,1955)(1231,1959)
     (1232,1961)(1234,1964)(1236,1967)(1237,1969)(1238,1971)(1240,1974)(1241,
     1976)(1243,1979)(1244,1981)(1246,1984)(1248,1987)(1249,1989)(1251,1992)
     (1253,1995)(1254,1997)(1256,2000)(1257,2002)(1259,2004)(1261,2007)(1263,
     2010)(1264,2012)(1266,2015)(1268,2018)(1269,2020)(1271,2023)(1273,2026)
     (1274,2028)(1276,2031)(1277,2033)(1279,2036)(1281,2039)(1282,2041)(1284,
     2044)(1286,2046)(1287,2048)(1289,2051)(1290,2053)(1292,2056)(1294,2059)
     (1295,2061)(1297,2064)(1298,2066)(1300,2069)(1302,2072)(1303,2074)(1305,
     2077)(1307,2080)(1308,2082)(1310,2085)(1311,2087)(1313,2090)(1315,2093)
     (1316,2095)(1318,2097)(1319,2099)(1321,2102)(1323,2105)(1324,2107)(1326,
     2110)(1328,2113)(1329,2115)(1331,2118)(1332,2120)(1334,2123)(1336,2126)
     (1337,2128)(1339,2131)(1341,2133)(1342,2135)(1344,2138)(1345,2140)(1347,
     2143)(1350,2147)(1352,2150)(1353,2152)(1355,2155)(1357,2158)(1358,2160)
     (1360,2163)(1362,2166)(1363,2168)(1365,2171)(1366,2173)(1368,2176)(1370,
     2179)(1371,2181)(1373,2184)(1374,2186)(1376,2189)(1378,2192)(1379,2194)
     (1381,2197)(1383,2200)(1384,2202)(1386,2205)(1387,2207)(1389,2210)(1390,
     2212)(1392,2215)(1394,2218)(1395,2220)(1397,2223)(1398,2225)(1400,2228)
     (1402,2231)(1403,2233)(1405,2236)(1406,2238)(1408,2241)(1410,2244)(1411,
     2246)(1413,2248)(1415,2251)(1416,2253)(1418,2256)(1419,2258)(1421,2261)
     (1423,2264)(1424,2266)(1426,2269)(1428,2272)(1429,2274)(1431,2277)(1432,
     2279)(1434,2282)(1436,2285)(1437,2287)(1439,2290)(1440,2292)(1442,2295)
     (1444,2298)(1445,2300)(1447,2303)(1449,2306)(1450,2308)(1452,2311)(1453,
     2313)(1455,2316)(1457,2319)(1459,2322)(1461,2325)(1462,2327)(1464,2330)
     (1465,2332)(1467,2335)(1469,2338)(1470,2340)(1472,2343)(1473,2344)(1475,
     2347)(1477,2349)(1478,2351)(1480,2354)(1482,2357)(1484,2360)(1485,2362)
     (1488,2366)(1490,2369)(1491,2371)(1493,2374)(1494,2376)(1495,2378)(1497,
     2381)(1498,2383)(1500,2386)(1502,2389)(1503,2391)(1504,2393)(1506,2396)
     (1507,2398)(1509,2401)(1511,2404)(1513,1865)(1514,2408)(1517,2412)(1519,
     2415)(1521,2418)(1522,2420)(1523,2422)(1524,2424)(1526,2427)(1527,2429)
     (1528,2431)(1530,2434)(1531,2436)(1533,2439)(1535,2442)(1536,2444)(1538,
     2447)(1540,2450)(1542,2317)(1543,2454)(1545,2457)(1547,2460)(1548,2462)
     (1550,2465)(1551,2467)(1553,2470)(1555,2468)(1556,2474)(1558,2477)(1559,
     2479)(1561,2482)(1563,2485)(1564,2487)(1566,2490)(1568,2493)(1569,2495)
     (1571,2498)(1572,2500)(1574,2503)(1576,2506)(1577,2508)(1579,2511)(1581,
     2514)(1582,2516)(1584,2519)(1585,2521)(1587,2524)(1589,2527)(1590,2529)
     (1592,2532)(1593,2534)(1595,2537)(1597,2540)(1598,2542)(1600,2545)(1602,
     2548)(1603,2550)(1605,2553)(1607,2556)(1608,2558)(1610,2561)(1611,2562)
     (1612,2564)(1614,2567)(1615,2569)(1617,2572)(1619,2575)(1620,2577)(1622,
     2580)(1624,2583)(1626,2586)(1627,2588)(1629,2591)(1631,2594)(1632,2596)
     (1634,2599)(1635,2601)(1637,2604)(1639,2602)(1640,2607)(1642,2610)(1643,
     2612)(1645,2614)(1647,2617)(1648,2101)(1650,2621)(1652,2624)(1653,2626)
     (1655,2629)(1656,2631)(1658,2634)(1660,2637)(1661,2639)(1663,2642)(1665,
     2645)(1666,2647)(1668,2650)(1669,2652)(1671,2655)(1673,2658)(1674,2660)
     (1676,2663)(1677,2665)(1679,2668)(1681,2671)(1682,2673)(1684,2676)(1685,
     2678)(1687,2681)(1689,2684)(1690,2686)(1692,2689)(1694,2691)(1696,2694)
     (1697,2696)(1699,2699)(1701,2702)(1702,2704)(1704,2707)(1705,2709)(1707,
     2712)(1709,2710)(1710,2716)(1712,2719)(1713,2721)(1715,2724)(1716,2726)
     (1718,2729)(1720,2732)(1721,2734)(1722,2736)(1723,2738)(1725,2741)(1727,
     2744)(1728,2740)(1730,2748)(1733,2752)(1735,2755)(1736,2757)(1737,2759)
     (1739,2762)(1740,2764)(1742,2767)(1744,2770)(1745,2772)(1747,2775)(1748,
     2777)(1750,2780)(1752,2782)(1753,2784)(1755,2787)(1756,2789)(1758,2792)
     (1760,2795)(1761,2797)(1763,2800)(1765,2803)(1766,2805)(1768,2808)(1769,
     2810)(1771,2813)(1773,2816)(1774,2818)(1776,2821)(1777,2823)(1779,2826)
     (1781,2829)(1782,2831)(1784,2834)(1786,2837)(1787,2839)(1789,2842)(1790,
     2844)(1792,2847)(1794,2850)(1795,2852)(1797,2855)(1799,2858)(1800,2860)
     (1802,2863)(1803,2865)(1805,2868)(1807,2871)(1808,2873)(1810,2876)(1812,
     2879)(1814,2877)(1815,2883)(1817,2886)(1819,2888)(1822,2892)(1823,2887)
     (1825,2896)(1826,2898)(1827,2900)(1829,2903)(1830,2905)(1832,2908)(1833,
     2910)(1835,2913)(1837,2916)(1838,2918)(1840,2921)(1841,2923)(1843,2926)
     (1845,2929)(1846,2931)(1849,2935)(1850,2937)(1852,2940)(1853,2942)(1855,
     2945)(1856,2947)(1858,2950)(1860,2953)(1861,2955)(1863,2958)(1866,2962)
     (1868,2965)(1869,2967)(1871,2970)(1873,2973)(1874,2975)(1876,2978)(1878,
     2981)(1879,2417)(1881,2985)(1882,2987)(1884,2990)(1885,2648)(1886,2993)
     (1887,2995)(1889,2998)(1891,3001)(1892,3003)(1894,3006)(1896,3009)(1897,
     3011)(1899,3014)(1900,3016)(1902,3019)(1904,3022)(1905,3024)(1907,3027)
     (1908,3029)(1912,3034)(1913,3036)(1915,3039)(1917,3042)(1918,3044)(1920,
     3047)(1921,3049)(1923,3052)(1925,3055)(1926,3057)(1928,3060)(1930,3063)
     (1931,3065)(1933,3068)(1934,3070)(1936,3073)(1938,3076)(1940,3079)(1941,
     3081)(1943,3084)(1945,3087)(1946,3089)(1948,3092)(1950,3095)(1953,3099)
     (1954,3101)(1956,3104)(1957,3106)(1958,3108)(1960,3111)(1962,3114)(1963,
     3116)(1965,3119)(1966,3121)(1968,3124)(1970,3127)(1972,3130)(1973,3132)
     (1975,3135)(1977,3138)(1978,3140)(1980,3143)(1982,3146)(1983,3148)(1985,
     3151)(1986,3153)(1988,3156)(1990,3159)(1991,3161)(1993,3164)(1994,3166)
     (1996,3169)(1998,3172)(1999,3174)(2001,3177)(2003,3180)(2005,3183)(2006,
     3185)(2008,3188)(2009,3190)(2011,3193)(2013,3196)(2014,3198)(2016,3201)
     (2017,3203)(2019,3206)(2021,3209)(2022,3211)(2024,3214)(2025,3216)(2027,
     3219)(2029,3222)(2030,3224)(2032,3227)(2034,3229)(2035,3231)(2037,3234)
     (2038,3236)(2040,3239)(2042,3242)(2043,3244)(2045,3247)(2047,3250)(2049,
     3253)(2050,3255)(2052,3258)(2054,3261)(2055,3263)(2057,3266)(2058,3268)
     (2060,3271)(2062,3274)(2063,3276)(2065,3279)(2067,3282)(2068,3284)(2070,
     3287)(2071,3289)(2073,3292)(2075,3295)(2076,3297)(2078,3300)(2079,3302)
     (2081,3305)(2083,3308)(2084,3310)(2086,3313)(2088,3316)(2089,3318)(2091,
     3321)(2092,3323)(2094,3326)(2096,3329)(2098,3332)(2100,3335)(2103,3339)
     (2104,3341)(2106,3344)(2108,2956)(2109,3348)(2111,3351)(2112,3353)(2114,
     3356)(2116,3359)(2117,3361)(2119,3364)(2121,3367)(2122,3369)(2124,3372)
     (2125,3374)(2127,3377)(2129,3380)(2130,3382)(2132,3385)(2134,3388)(2136,
     3391)(2137,3393)(2139,3396)(2141,2988)(2142,3400)(2144,3402)(2145,3404)
     (2146,3406)(2148,3409)(2149,3411)(2151,3414)(2153,3417)(2154,3419)(2156,
     3422)(2157,3424)(2159,3427)(2161,3430)(2162,3432)(2164,3435)(2165,3437)
     (2167,3440)(2169,3443)(2170,3445)(2172,3448)(2174,3451)(2175,3453)(2177,
     3456)(2178,3458)(2180,3461)(2182,3464)(2183,3466)(2185,3469)(2187,3471)
     (2188,3473)(2190,3476)(2191,3478)(2193,3481)(2195,3484)(2196,3486)(2198,
     3489)(2199,3491)(2201,3494)(2203,3497)(2204,3499)(2206,3502)(2208,3505)
     (2209,3507)(2211,3510)(2213,3513)(2214,3515)(2216,3518)(2217,3520)(2219,
     3523)(2221,3525)(2222,3527)(2224,3530)(2226,3533)(2227,3535)(2229,3538)
     (2230,3540)(2232,3543)(2234,3546)(2235,3548)(2237,3551)(2239,3554)(2240,
     3556)(2242,3559)(2243,3561)(2245,3564)(2247,3567)(2249,3570)(2250,3572)
     (2252,3575)(2254,3578)(2255,3580)(2257,3583)(2259,3586)(2260,3588)(2262,
     3591)(2263,3593)(2265,3596)(2267,3599)(2268,3601)(2270,3604)(2271,3606)
     (2273,3609)(2275,3612)(2276,3614)(2278,3617)(2280,3620)(2281,3622)(2283,
     2307)(2284,3626)(2286,3629)(2288,3632)(2289,3634)(2291,3637)(2293,3640)
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