bin1 := (1,2)(3,5)(4,7)(6,9)(8,11)(10,13)(12,16)(14,19)(15,20)(17,23)(18,24)(21,
     28)(22,29)(25,33)(26,34)(27,36)(30,40)(31,41)(32,43)(35,47)(37,49)(38,50)
     (39,52)(42,56)(44,58)(45,59)(46,61)(48,64)(51,68)(53,70)(54,71)(55,73)
     (57,76)(60,80)(62,82)(63,83)(65,86)(66,87)(67,89)(69,92)(72,96)(74,98)
     (75,99)(77,102)(78,103)(79,105)(81,108)(84,112)(85,113)(88,117)(90,119)
     (91,120)(93,123)(94,124)(95,126)(97,129)(101,133)(104,137)(106,139)(107,
     140)(109,143)(110,144)(111,146)(114,150)(115,151)(116,153)(118,156)(121,
     160)(122,161)(125,165)(127,167)(128,168)(130,171)(131,172)(132,174)(134,
     177)(135,178)(136,180)(138,183)(141,187)(142,188)(145,192)(147,194)(148,
     195)(149,197)(152,201)(154,203)(155,204)(157,207)(158,208)(159,210)(162,
     214)(163,215)(164,217)(166,220)(169,224)(170,225)(173,229)(175,231)(176,
     232)(179,236)(181,238)(182,239)(184,242)(185,243)(186,245)(189,249)(190,
     250)(191,252)(193,255)(196,259)(198,261)(199,262)(200,264)(202,267)(205,
     271)(206,272)(209,276)(211,278)(212,279)(213,281)(216,285)(218,287)(219,
     288)(221,291)(222,292)(223,294)(226,298)(227,299)(228,301)(230,304)(233,
     308)(234,309)(235,311)(237,314)(240,318)(241,319)(244,323)(246,325)(247,
     326)(248,328)(251,332)(253,302)(254,334)(256,337)(257,338)(258,340)(260,
     343)(263,347)(265,349)(266,350)(268,353)(269,354)(270,356)(273,360)(274,
     361)(275,363)(277,366)(280,370)(282,372)(283,373)(284,375)(286,378)(289,
     382)(290,383)(293,387)(295,389)(296,390)(297,392)(300,396)(303,398)(305,
     401)(306,402)(307,404)(310,408)(312,410)(313,411)(315,414)(316,415)(317,
     417)(320,421)(321,422)(322,424)(324,427)(327,431)(329,433)(330,434)(331,
     436)(333,439)(335,442)(336,443)(339,447)(341,449)(342,450)(344,453)(345,
     454)(346,456)(348,459)(351,463)(352,464)(355,468)(357,470)(358,471)(359,
     473)(362,477)(364,479)(365,480)(367,483)(368,484)(369,486)(371,489)(374,
     493)(376,495)(377,496)(379,499)(380,500)(381,502)(384,506)(385,507)(386,
     509)(388,512)(391,516)(393,518)(394,519)(395,521)(397,524)(399,527)(400,
     528)(403,532)(405,534)(406,535)(407,537)(409,540)(412,544)(413,545)(416,
     549)(418,551)(419,552)(420,554)(423,558)(425,560)(426,561)(429,564)(430,
     566)(432,569)(435,573)(437,575)(438,576)(440,579)(441,580)(444,584)(445,
     585)(446,587)(448,590)(451,594)(452,595)(455,599)(457,601)(458,602)(460,
     605)(461,606)(462,608)(465,612)(466,613)(467,615)(469,618)(472,622)(474,
     624)(475,625)(476,627)(478,630)(481,634)(482,635)(485,639)(487,641)(488,
     642)(490,645)(491,646)(492,648)(494,651)(497,655)(498,656)(501,660)(503,
     662)(504,663)(505,665)(508,669)(510,616)(511,671)(513,674)(514,675)(515,
     677)(517,680)(520,684)(522,686)(523,687)(525,690)(526,691)(529,695)(530,
     696)(531,698)(533,701)(536,705)(538,707)(539,708)(541,711)(542,712)(543,
     714)(546,718)(547,719)(548,721)(550,724)(553,728)(555,730)(556,731)(557,
     733)(559,736)(562,740)(563,741)(565,744)(567,746)(568,747)(570,750)(571,
     751)(572,753)(574,756)(577,760)(578,761)(581,765)(582,766)(583,768)(586,
     772)(588,774)(589,775)(591,778)(592,739)(593,780)(596,784)(597,785)(598,
     787)(600,790)(603,794)(604,795)(607,799)(609,801)(610,802)(611,804)(614,
     808)(617,810)(619,813)(620,814)(621,816)(623,819)(626,823)(628,825)(629,
     826)(631,829)(632,738)(633,831)(636,835)(637,836)(638,838)(640,841)(643,
     845)(644,846)(647,850)(649,852)(650,853)(652,856)(653,857)(654,859)(657,
     863)(658,864)(659,866)(661,869)(664,873)(666,875)(667,876)(668,878)(670,
     881)(672,884)(673,885)(676,889)(678,891)(679,892)(681,895)(682,896)(683,
     898)(685,901)(688,905)(689,906)(692,910)(693,911)(694,913)(697,917)(699,
     919)(700,920)(702,923)(703,924)(704,926)(706,929)(709,933)(710,934)(713,
     938)(715,940)(716,941)(717,943)(720,947)(722,949)(723,950)(725,953)(726,
     954)(727,956)(729,959)(732,963)(734,965)(735,966)(737,969)(742,974)(743,
     975)(745,978)(748,982)(749,983)(752,987)(754,989)(755,990)(757,993)(758,
     994)(759,996)(762,1000)(763,1001)(764,1003)(767,1007)(769,1009)(770,1010)
     (771,1012)(773,1015)(776,1019)(777,1020)(779,1023)(781,1025)(782,1026)
     (783,1028)(786,1032)(788,1034)(789,1035)(791,1038)(792,1039)(793,1041)
     (796,1045)(797,1046)(798,1048)(800,1051)(803,1055)(805,1057)(806,1058)
     (807,1060)(809,1063)(812,1066)(815,1070)(817,1072)(818,1073)(820,1076)
     (821,1077)(822,1079)(824,1082)(827,1086)(828,1087)(830,1090)(832,1092)
     (833,1093)(834,1095)(837,1099)(839,1101)(840,1102)(842,1105)(843,1106)
     (844,1108)(847,1112)(848,1113)(849,1115)(851,1118)(854,1122)(855,1123)
     (858,1127)(860,1129)(861,1130)(862,1132)(865,1136)(867,1138)(868,1139)
     (870,1142)(871,1143)(872,1145)(874,1148)(877,1152)(879,1154)(880,1155)
     (882,1158)(883,1159)(886,1163)(887,1164)(888,1166)(890,1169)(893,1173)
     (894,1174)(897,1178)(899,1180)(900,1181)(902,1184)(904,1186)(907,1190)
     (908,1191)(909,1193)(912,1197)(914,1199)(915,1200)(916,1202)(918,1205)
     (921,1209)(922,1210)(925,1214)(927,1216)(928,1217)(930,1220)(931,1221)
     (932,1223)(935,1227)(936,1228)(937,1230)(939,1232)(942,1236)(944,1238)
     (945,1239)(946,1241)(948,1244)(951,1248)(952,1249)(955,1253)(957,1255)
     (958,1256)(960,1259)(961,1260)(962,1262)(964,1265)(967,1269)(968,1270)
     (970,1273)(971,1274)(972,1275)(973,1277)(976,1281)(977,1282)(979,1285)
     (980,1286)(981,1288)(984,1292)(985,1293)(986,1295)(988,1298)(991,1302)
     (992,1303)(995,1307)(997,1309)(998,1310)(999,1312)(1002,1316)(1004,1318)
     (1005,1319)(1006,1321)(1008,1324)(1011,1328)(1013,1330)(1014,1331)(1016,
     1334)(1017,1246)(1018,1336)(1021,1340)(1022,1341)(1024,1344)(1027,1348)
     (1029,1350)(1030,1351)(1031,1353)(1033,1356)(1036,1360)(1037,1361)(1040,
     1365)(1042,1367)(1043,1368)(1044,1370)(1047,1373)(1049,1375)(1050,1376)
     (1052,1379)(1053,1380)(1054,1382)(1056,1385)(1059,1389)(1061,1391)(1062,
     1392)(1064,1395)(1065,1396)(1067,1399)(1068,1400)(1069,1402)(1071,1405)
     (1074,1409)(1075,1410)(1078,1414)(1080,1416)(1081,1417)(1083,1420)(1084,
     1421)(1085,1423)(1088,1427)(1089,1428)(1091,1431)(1094,1435)(1096,1437)
     (1097,1438)(1098,1440)(1100,1443)(1103,1447)(1104,1448)(1107,1452)(1109,
     1454)(1110,1455)(1111,1457)(1114,1461)(1116,1463)(1117,1464)(1119,1467)
     (1120,1468)(1121,1470)(1124,1474)(1125,1475)(1126,1477)(1128,1480)(1131,
     1484)(1133,1486)(1134,1487)(1135,1489)(1137,1492)(1140,1496)(1141,1497)
     (1144,1501)(1146,1503)(1147,1504)(1149,1507)(1150,1508)(1151,1510)(1153,
     1513)(1156,1517)(1157,1518)(1160,1522)(1161,1523)(1162,1525)(1165,1529)
     (1167,1531)(1168,1532)(1170,1535)(1171,1536)(1172,1538)(1175,1542)(1176,
     1543)(1177,1545)(1179,1548)(1182,1552)(1183,1553)(1185,1556)(1187,1558)
     (1188,1559)(1189,1561)(1192,1565)(1194,1567)(1195,1568)(1196,1570)(1198,
     1573)(1201,1577)(1203,1579)(1204,1580)(1206,1583)(1207,1494)(1208,1585)
     (1211,1589)(1212,1590)(1213,1592)(1215,1595)(1218,1599)(1219,1600)(1222,
     1604)(1224,1606)(1225,1607)(1226,1609)(1229,1613)(1231,1615)(1233,1617)
     (1234,1618)(1235,1620)(1237,1623)(1240,1627)(1242,1629)(1243,1630)(1245,
     1633)(1247,1635)(1250,1638)(1251,1639)(1252,1640)(1254,1643)(1258,1647)
     (1261,1651)(1263,1653)(1264,1654)(1267,1657)(1268,1659)(1271,1663)(1272,
     1664)(1276,1669)(1278,1671)(1279,1672)(1280,1674)(1283,1678)(1284,1679)
     (1287,1683)(1289,1685)(1290,1686)(1291,1688)(1294,1692)(1296,1694)(1297,
     1695)(1299,1698)(1300,1699)(1301,1701)(1304,1705)(1305,1706)(1306,1708)
     (1308,1710)(1311,1714)(1313,1716)(1314,1717)(1315,1719)(1317,1722)(1320,
     1726)(1322,1728)(1323,1729)(1325,1732)(1326,1733)(1327,1735)(1329,1738)
     (1332,1742)(1333,1743)(1335,1746)(1337,1748)(1338,1749)(1339,1751)(1342,
     1755)(1343,1756)(1345,1759)(1346,1760)(1347,1762)(1349,1765)(1352,1769)
     (1354,1771)(1355,1772)(1357,1775)(1358,1776)(1359,1777)(1362,1781)(1363,
     1782)(1364,1784)(1366,1787)(1369,1791)(1371,1793)(1372,1794)(1374,1797)
     (1377,1801)(1378,1802)(1381,1806)(1383,1808)(1384,1809)(1386,1812)(1387,
     1813)(1388,1815)(1390,1818)(1393,1822)(1394,1823)(1397,1827)(1398,1828)
     (1401,1832)(1403,1834)(1404,1835)(1406,1838)(1407,1839)(1408,1841)(1411,
     1845)(1412,1846)(1413,1848)(1415,1850)(1418,1854)(1419,1855)(1422,1858)
     (1424,1860)(1425,1861)(1426,1863)(1429,1867)(1430,1868)(1432,1871)(1433,
     1872)(1434,1874)(1436,1877)(1439,1881)(1441,1883)(1442,1511)(1444,1886)
     (1445,1799)(1446,1888)(1449,1892)(1450,1893)(1451,1895)(1453,1898)(1456,
     1902)(1458,1904)(1459,1905)(1460,1907)(1462,1910)(1465,1914)(1466,1915)
     (1469,1919)(1471,1921)(1472,1922)(1473,1924)(1476,1927)(1478,1929)(1479,
     1930)(1481,1933)(1482,1934)(1483,1936)(1485,1939)(1488,1943)(1490,1945)
     (1491,1946)(1493,1949)(1495,1951)(1498,1955)(1499,1956)(1500,1958)(1502,
     1961)(1505,1965)(1506,1966)(1509,1970)(1512,1972)(1514,1975)(1515,1976)
     (1516,1978)(1519,1982)(1520,1983)(1521,1985)(1524,1989)(1526,1991)(1527,
     1992)(1528,1994)(1530,1997)(1533,2001)(1534,2002)(1537,2006)(1539,2008)
     (1540,2009)(1541,2011)(1544,2015)(1546,2017)(1547,2018)(1549,2021)(1550,
     2022)(1551,2024)(1554,2028)(1555,2029)(1557,2032)(1560,2036)(1563,2038)
     (1564,2040)(1566,2043)(1569,2047)(1571,2049)(1572,2050)(1574,2053)(1575,
     2054)(1576,2056)(1578,2059)(1581,2063)(1582,2064)(1584,2067)(1586,2069)
     (1587,2070)(1588,2072)(1591,2075)(1593,2077)(1594,2078)(1596,2081)(1597,
     2082)(1598,2084)(1601,2088)(1602,2089)(1603,2091)(1605,2094)(1608,2098)
     (1610,2099)(1611,2100)(1612,2102)(1614,2105)(1616,2108)(1619,2112)(1621,
     1649)(1622,2114)(1624,2117)(1625,2118)(1626,2120)(1628,2123)(1631,2127)
     (1632,2128)(1634,2131)(1636,2133)(1637,2135)(1641,2140)(1642,2141)(1644,
     2144)(1645,2145)(1646,2147)(1648,2150)(1650,2152)(1652,2155)(1655,2159)
     (1656,2160)(1658,2163)(1660,2165)(1661,2166)(1662,2168)(1665,2172)(1666,
     2173)(1667,2175)(1668,2177)(1670,2179)(1673,2183)(1675,2185)(1676,2107)
     (1677,2187)(1680,2190)(1681,2191)(1682,2193)(1684,2196)(1687,2200)(1689,
     2202)(1690,2203)(1691,2205)(1693,2208)(1696,2212)(1697,2213)(1700,2217)
     (1702,2219)(1703,2220)(1704,2222)(1707,2226)(1709,2228)(1711,2231)(1712,
     2232)(1713,2234)(1715,2237)(1718,2240)(1720,2242)(1721,2243)(1723,2246)
     (1724,2247)(1725,2249)(1727,2252)(1730,2256)(1731,2257)(1734,2261)(1736,
     2263)(1737,2264)(1739,2267)(1740,2268)(1741,2270)(1744,2274)(1745,2275)
     (1747,2278)(1750,2282)(1752,2284)(1753,2285)(1754,2287)(1757,2291)(1758,
     2292)(1761,2296)(1763,2298)(1764,2299)(1766,2302)(1767,2303)(1768,2305)
     (1770,2308)(1773,2312)(1774,2313)(1778,2318)(1779,2319)(1780,2321)(1783,
     2325)(1785,2327)(1786,2328)(1788,2331)(1789,2332)(1790,2334)(1792,2337)
     (1795,2341)(1796,2342)(1798,2345)(1800,2347)(1803,2351)(1804,2352)(1805,
     2354)(1807,2357)(1810,2361)(1811,2362)(1814,2366)(1816,2368)(1817,2369)
     (1819,2372)(1820,2373)(1821,2375)(1824,2379)(1825,2380)(1826,2382)(1829,
     2386)(1830,2387)(1831,2389)(1833,2392)(1836,2396)(1837,2397)(1840,2401)
     (1842,2403)(1843,2404)(1844,2406)(1847,2410)(1849,2412)(1851,2414)(1852,
     2415)(1853,2417)(1856,2421)(1857,2422)(1859,2425)(1862,2429)(1864,2431)
     (1865,2432)(1866,2434)(1869,2438)(1870,2439)(1873,2443)(1875,2445)(1876,
     2446)(1878,2449)(1879,2450)(1880,2452)(1882,2455)(1884,2458)(1885,2459)
     (1887,2462)(1889,2464)(1890,2465)(1891,2350)(1894,2470)(1896,2472)(1897,
     2473)(1899,2476)(1900,2477)(1901,2479)(1903,2482)(1906,2486)(1908,2488)
     (1909,2489)(1911,2492)(1912,2493)(1913,2495)(1916,2499)(1917,2500)(1918,
     2502)(1920,2505)(1923,2509)(1925,2511)(1926,2512)(1928,2515)(1931,2519)
     (1932,2520)(1935,2524)(1937,2526)(1938,2527)(1940,2530)(1941,2531)(1942,
     2533)(1944,2536)(1947,2540)(1948,2541)(1950,2544)(1952,2546)(1953,2547)
     (1954,2549)(1957,2553)(1959,2555)(1960,2556)(1962,2559)(1963,2560)(1964,
     2562)(1967,2566)(1968,2567)(1969,2569)(1971,2572)(1973,2575)(1974,2576)
     (1977,2580)(1979,2582)(1980,2583)(1981,2585)(1984,2589)(1986,2591)(1987,
     2592)(1988,2594)(1990,2597)(1993,2601)(1995,2603)(1996,2604)(1998,2607)
     (1999,2517)(2000,2609)(2003,2613)(2004,2614)(2005,2616)(2007,2619)(2010,
     2623)(2012,2625)(2013,2626)(2014,2628)(2016,2631)(2019,2635)(2020,2636)
     (2023,2640)(2025,2642)(2026,2643)(2027,2645)(2030,2649)(2031,2650)(2033,
     2653)(2034,2654)(2035,2656)(2037,2659)(2039,2662)(2041,2664)(2042,2665)
     (2044,2668)(2045,2669)(2046,2671)(2048,2674)(2051,2678)(2052,2679)(2055,
     2683)(2057,2685)(2058,2686)(2060,2689)(2061,2690)(2062,2692)(2065,2696)
     (2066,2697)(2068,2700)(2071,2704)(2073,2705)(2074,2706)(2076,2709)(2079,
     2713)(2080,2714)(2083,2718)(2085,2720)(2086,2721)(2087,2723)(2090,2727)
     (2092,2729)(2093,2730)(2095,2733)(2096,2734)(2097,2736)(2101,2741)(2103,
     2743)(2104,2744)(2106,2746)(2109,2749)(2110,2750)(2111,2752)(2113,2755)
     (2115,2758)(2116,2759)(2119,2763)(2121,2348)(2122,2765)(2124,2768)(2125,
     2769)(2126,2771)(2129,2775)(2130,2776)(2132,2778)(2134,2781)(2136,2783)
     (2137,2784)(2138,2785)(2139,2787)(2142,2791)(2143,2792)(2146,2796)(2148,
     2798)(2149,2799)(2151,2802)(2153,2804)(2154,2805)(2156,2808)(2157,2809)
     (2158,2811)(2161,2815)(2162,2816)(2164,2819)(2167,2823)(2169,2825)(2170,
     2826)(2171,2828)(2174,2832)(2176,2834)(2178,2836)(2180,2838)(2181,2839)
     (2182,2841)(2184,2844)(2186,2847)(2188,2849)(2189,2850)(2192,2854)(2194,
     2856)(2195,2857)(2197,2860)(2199,2862)(2201,2865)(2204,2869)(2206,2871)
     (2207,2872)(2209,2875)(2210,2876)(2211,2878)(2214,2882)(2215,2883)(2216,
     2885)(2218,2888)(2221,2892)(2223,2894)(2224,2895)(2225,2897)(2227,2900)
     (2229,2903)(2230,2904)(2233,2908)(2235,2910)(2236,2911)(2238,2914)(2239,
     2915)(2241,2918)(2244,2922)(2245,2923)(2248,2927)(2250,2929)(2251,2930)
     (2253,2933)(2254,2934)(2255,2936)(2258,2940)(2259,2941)(2260,2943)(2262,
     2946)(2265,2950)(2266,2951)(2269,2955)(2271,2957)(2272,2958)(2273,2960)
     (2276,2964)(2277,2965)(2279,2968)(2280,2969)(2281,2971)(2283,2974)(2286,
     2978)(2288,2980)(2289,2981)(2290,2983)(2293,2987)(2294,2988)(2295,2990)
     (2297,2993)(2300,2997)(2301,2998)(2304,3002)(2306,3004)(2307,3005)(2309,
     3008)(2310,3009)(2311,3011)(2314,3015)(2315,3016)(2316,3018)(2317,3020)
     (2320,3024)(2322,3026)(2323,3027)(2324,3029)(2326,3032)(2329,2646)(2330,
     3036)(2333,3040)(2335,3042)(2336,3043)(2338,3046)(2339,3047)(2340,3049)
     (2343,3053)(2344,3054)(2346,3057)(2349,3059)(2353,3064)(2355,3066)(2356,
     3067)(2358,3070)(2359,3071)(2360,3073)(2363,3077)(2364,3078)(2365,3080)
     (2367,3083)(2371,3087)(2374,3091)(2376,3093)(2377,3094)(2378,3096)(2381,
     3100)(2383,3102)(2384,3103)(2385,3105)(2388,3109)(2390,2673)(2391,3111)
     (2393,3114)(2394,3034)(2395,3116)(2398,3120)(2399,3121)(2400,3123)(2402,
     3126)(2405,3130)(2407,3132)(2408,3133)(2409,3135)(2411,3138)(2413,3141)
     (2416,3145)(2418,3147)(2419,3148)(2420,3150)(2423,3154)(2424,3155)(2426,
     3157)(2427,2846)(2428,3159)(2430,3162)(2433,3166)(2435,3168)(2436,3169)
     (2437,3171)(2440,3175)(2441,3176)(2442,3178)(2444,3181)(2447,3185)(2448,
     3186)(2451,3190)(2453,3192)(2454,3193)(2456,3195)(2457,3196)(2460,3200)
     (2461,3201)(2463,3204)(2466,3208)(2467,3209)(2468,3210)(2469,3212)(2471,
     3215)(2474,3218)(2475,3219)(2478,3223)(2480,3225)(2481,3226)(2483,3227)
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