bin1 := (1,2)(3,7)(4,9)(5,11)(6,13)(8,17)(10,20)(12,23)(14,26)(15,27)(16,29)(19,
     34)(21,38)(22,40)(25,45)(28,51)(30,54)(31,55)(32,57)(33,59)(35,62)(36,63)
     (37,65)(39,69)(41,72)(42,73)(43,75)(44,77)(46,80)(47,81)(48,83)(49,85)
     (50,87)(52,91)(53,93)(56,99)(60,104)(61,106)(66,114)(67,115)(68,117)(70,
     121)(71,123)(74,128)(78,132)(79,134)(84,142)(86,144)(88,147)(89,148)(90,
     120)(92,152)(94,155)(95,156)(96,157)(97,126)(98,159)(100,162)(101,164)
     (102,166)(103,167)(105,133)(107,171)(108,172)(109,173)(110,174)(111,176)
     (112,178)(113,180)(116,183)(118,186)(119,187)(122,191)(124,194)(125,195)
     (127,197)(129,200)(130,202)(131,204)(135,208)(136,209)(137,210)(138,211)
     (139,213)(140,215)(141,217)(145,222)(146,224)(149,230)(150,231)(153,236)
     (154,238)(160,248)(161,199)(163,251)(165,254)(168,258)(169,260)(170,262)
     (175,272)(177,275)(179,278)(181,218)(184,283)(185,285)(188,290)(189,291)
     (192,295)(193,297)(198,304)(201,307)(203,310)(205,312)(206,314)(207,316)
     (212,324)(214,327)(216,330)(219,333)(220,334)(221,335)(223,338)(225,341)
     (226,342)(227,343)(228,344)(229,345)(232,350)(233,351)(234,352)(235,353)
     (237,356)(239,359)(240,360)(242,362)(243,364)(244,366)(245,367)(246,368)
     (247,370)(249,374)(250,376)(252,379)(255,383)(256,384)(257,386)(259,390)
     (261,393)(263,396)(264,397)(265,398)(266,318)(267,400)(268,402)(269,404)
     (270,405)(271,407)(273,391)(274,410)(276,414)(277,416)(279,331)(280,420)
     (281,422)(282,423)(284,425)(286,428)(287,429)(288,430)(289,431)(292,435)
     (293,436)(294,437)(296,440)(298,443)(299,444)(301,445)(302,446)(303,448)
     (305,452)(306,337)(308,456)(311,459)(313,462)(315,465)(317,468)(319,470)
     (320,472)(321,473)(322,474)(323,476)(325,463)(326,479)(328,483)(329,485)
     (332,489)(336,497)(339,500)(340,502)(347,514)(348,515)(349,517)(354,526)
     (355,528)(357,532)(358,534)(361,539)(363,542)(365,545)(369,447)(371,449)
     (373,553)(375,556)(377,558)(378,455)(380,561)(381,562)(382,563)(385,568)
     (387,571)(388,572)(389,574)(392,579)(394,582)(395,583)(399,469)(401,591)
     (403,594)(406,599)(408,602)(409,603)(411,606)(412,607)(413,608)(417,612)
     (418,613)(419,614)(421,617)(424,622)(426,624)(427,626)(433,635)(434,637)
     (438,643)(439,645)(441,648)(442,650)(451,659)(453,662)(454,663)(457,666)
     (458,667)(460,669)(461,671)(464,675)(466,677)(467,678)(471,683)(475,690)
     (477,693)(478,694)(480,697)(481,698)(482,699)(486,703)(487,704)(488,705)
     (490,708)(491,709)(492,701)(493,710)(494,711)(495,713)(496,715)(498,719)
     (499,720)(501,722)(503,725)(504,726)(505,727)(506,728)(507,730)(508,732)
     (509,733)(510,734)(511,736)(512,738)(513,740)(516,744)(518,638)(519,747)
     (520,748)(522,749)(523,642)(524,750)(525,752)(527,756)(529,759)(530,760)
     (533,763)(535,765)(536,766)(537,767)(538,769)(540,772)(541,567)(543,775)
     (544,777)(546,780)(547,781)(548,782)(549,784)(550,786)(552,789)(554,793)
     (555,661)(557,797)(559,800)(564,808)(565,809)(566,810)(569,757)(570,815)
     (573,820)(575,823)(576,824)(577,825)(578,826)(580,829)(581,610)(584,833)
     (585,834)(586,836)(587,838)(588,839)(589,840)(590,842)(592,846)(593,847)
     (595,850)(597,853)(598,855)(601,860)(604,866)(605,868)(609,873)(611,876)
     (615,881)(616,883)(618,885)(619,886)(620,887)(621,889)(623,893)(625,895)
     (627,874)(628,898)(629,899)(630,900)(631,901)(632,903)(633,905)(634,907)
     (636,910)(639,913)(640,914)(641,915)(644,918)(646,920)(647,921)(649,924)
     (651,926)(652,927)(653,928)(654,930)(655,932)(656,933)(658,935)(660,939)
     (664,943)(668,948)(670,951)(672,954)(673,955)(674,956)(676,959)(679,962)
     (680,963)(681,831)(682,965)(684,968)(685,969)(686,970)(688,973)(689,975)
     (692,979)(695,983)(696,985)(700,990)(702,992)(706,995)(707,997)(712,1005)
     (714,1007)(716,1010)(717,1011)(718,1013)(721,1019)(723,1022)(724,1024)
     (729,1032)(731,1033)(735,902)(737,1041)(739,1043)(741,771)(742,1046)(743,
     1048)(745,1052)(746,1054)(751,1063)(753,1064)(754,1065)(755,917)(758,
     1070)(761,1076)(762,1078)(764,1082)(768,1089)(770,931)(773,1094)(774,
     1095)(776,1097)(778,1100)(779,1101)(783,1107)(785,1109)(787,877)(788,
     1112)(790,936)(791,1115)(792,938)(794,1118)(795,1119)(796,1120)(798,1122)
     (801,1124)(802,945)(803,1125)(804,1126)(805,947)(806,849)(807,1127)(811,
     1132)(812,1133)(813,1134)(814,1135)(816,1138)(817,1139)(818,1140)(819,
     1142)(821,952)(822,1146)(827,1156)(828,1158)(830,1162)(832,1164)(835,
     1170)(837,1172)(841,964)(844,1180)(845,1181)(848,1185)(851,1188)(852,
     1189)(854,1192)(856,1195)(857,1196)(858,1197)(859,1198)(861,1201)(862,
     1148)(863,1202)(864,1203)(865,1155)(867,1157)(869,1208)(870,1209)(872,
     1210)(875,1213)(878,1216)(879,1191)(880,1217)(884,1220)(888,1226)(890,
     1229)(891,1230)(892,1232)(894,1234)(896,1236)(897,1238)(904,1249)(906,
     1250)(908,1253)(909,1255)(911,1258)(912,1260)(916,1267)(919,1271)(922,
     1275)(923,1277)(925,1280)(929,1287)(934,1292)(937,1295)(940,1298)(941,
     1014)(944,1300)(946,1301)(949,1302)(950,1304)(953,1308)(957,1314)(958,
     1316)(960,1318)(961,1319)(967,1327)(971,1332)(972,1333)(974,1335)(976,
     1338)(977,1339)(978,1340)(980,1343)(981,1344)(982,1345)(984,1315)(986,
     1350)(987,1351)(989,1352)(991,1355)(993,1358)(994,1359)(998,1362)(999,
     1363)(1000,1364)(1001,1365)(1002,1367)(1003,1369)(1004,1371)(1006,1374)
     (1008,1377)(1009,1379)(1012,1384)(1015,1387)(1016,1388)(1017,1389)(1018,
     1390)(1020,1393)(1021,1394)(1023,1397)(1025,1400)(1026,1401)(1027,1403)
     (1028,1405)(1029,1407)(1030,1408)(1031,1410)(1034,1413)(1035,1414)(1036,
     1415)(1038,1417)(1039,1419)(1040,1421)(1042,1425)(1044,1428)(1045,1430)
     (1047,1254)(1049,1436)(1051,1074)(1053,1438)(1055,1441)(1056,1442)(1057,
     1443)(1058,1445)(1059,1447)(1060,1448)(1061,1449)(1062,1451)(1066,1456)
     (1067,1457)(1068,1458)(1069,1459)(1071,1462)(1072,1463)(1073,1464)(1075,
     1465)(1077,1468)(1079,1471)(1080,1472)(1081,1473)(1083,1476)(1084,1282)
     (1085,1477)(1086,1478)(1087,1479)(1088,1481)(1090,1484)(1092,1487)(1093,
     1489)(1096,1494)(1098,1497)(1099,1499)(1102,1504)(1103,1506)(1104,1508)
     (1105,1509)(1106,1511)(1108,1514)(1110,1516)(1111,1518)(1113,1520)(1114,
     1294)(1116,1525)(1117,1527)(1121,1533)(1123,1535)(1128,1542)(1129,1544)
     (1130,1546)(1131,1548)(1136,1555)(1137,1557)(1141,1563)(1143,1566)(1144,
     1567)(1145,1568)(1147,1571)(1149,1572)(1150,1503)(1151,1573)(1152,1574)
     (1153,1576)(1154,1578)(1159,1583)(1160,1584)(1161,1585)(1163,1588)(1166,
     1591)(1167,1592)(1168,1593)(1169,1595)(1171,1598)(1173,1601)(1175,1602)
     (1176,1604)(1177,1606)(1178,1607)(1179,1326)(1182,1614)(1183,1616)(1184,
     1618)(1186,1621)(1187,1331)(1190,1626)(1193,1631)(1194,1633)(1199,1569)
     (1200,1641)(1204,1346)(1205,1650)(1206,1652)(1207,1654)(1211,1660)(1212,
     1662)(1214,1664)(1215,1665)(1219,1361)(1221,1674)(1222,1676)(1223,1678)
     (1224,1679)(1225,1680)(1227,1682)(1228,1684)(1231,1688)(1233,1691)(1235,
     1693)(1237,1696)(1239,1699)(1240,1700)(1241,1701)(1242,1702)(1243,1703)
     (1244,1704)(1246,1706)(1247,1708)(1248,1710)(1251,1714)(1252,1716)(1256,
     1722)(1259,1724)(1261,1727)(1262,1728)(1263,1729)(1264,1730)(1265,1732)
     (1266,1733)(1268,1736)(1269,1737)(1270,1738)(1272,1741)(1273,1742)(1274,
     1743)(1276,1746)(1278,1748)(1279,1749)(1281,1752)(1283,1753)(1284,1754)
     (1285,1755)(1286,1757)(1288,1469)(1290,1761)(1291,1762)(1293,1763)(1296,
     1768)(1297,1770)(1299,1774)(1303,1779)(1305,1782)(1306,1783)(1307,1784)
     (1309,1787)(1310,1788)(1311,1560)(1312,1789)(1313,1790)(1317,1795)(1321,
     1800)(1323,1801)(1324,1803)(1325,1805)(1328,1810)(1329,1812)(1330,1814)
     (1334,1819)(1336,1822)(1337,1824)(1341,1785)(1342,1831)(1347,1838)(1348,
     1840)(1349,1842)(1353,1848)(1354,1850)(1356,1851)(1357,1852)(1366,1863)
     (1368,1866)(1370,1868)(1372,1870)(1373,1871)(1375,1874)(1376,1875)(1378,
     1877)(1380,1880)(1381,1881)(1382,1882)(1383,1884)(1385,1888)(1386,1890)
     (1391,1900)(1392,1901)(1395,1867)(1396,1906)(1398,1909)(1399,1911)(1402,
     1916)(1404,1919)(1406,1921)(1409,1924)(1411,1534)(1412,1926)(1416,1932)
     (1418,1934)(1420,1936)(1423,1939)(1424,1940)(1426,1943)(1427,1914)(1429,
     1946)(1431,1949)(1432,1718)(1434,1952)(1435,1954)(1437,1958)(1439,1962)
     (1440,1964)(1444,1972)(1446,1975)(1450,1982)(1452,1539)(1453,1984)(1454,
     1734)(1455,1986)(1460,1994)(1461,1996)(1466,2003)(1467,2005)(1470,1747)
     (1474,2016)(1475,2017)(1480,1756)(1482,2027)(1483,2028)(1485,2030)(1486,
     2031)(1488,2034)(1491,2037)(1492,1496)(1493,2038)(1495,2040)(1498,1995)
     (1500,2045)(1501,2046)(1502,2047)(1505,2050)(1507,2053)(1510,2058)(1512,
     2060)(1513,2061)(1515,2064)(1517,2067)(1519,2070)(1521,1764)(1522,2073)
     (1523,2074)(1526,2077)(1528,1771)(1529,2080)(1531,2081)(1536,1671)(1537,
     1775)(1540,2087)(1541,2089)(1543,2092)(1545,1999)(1547,2097)(1550,2100)
     (1551,2101)(1552,2102)(1553,2103)(1554,2104)(1556,2107)(1558,2110)(1559,
     2111)(1561,2112)(1562,2113)(1564,2117)(1565,2119)(1570,2124)(1575,2132)
     (1577,2135)(1579,1791)(1580,2069)(1581,2140)(1582,2142)(1586,2149)(1587,
     2150)(1589,2152)(1590,1799)(1594,2161)(1596,2163)(1597,2164)(1599,2167)
     (1600,2168)(1603,2173)(1605,2176)(1608,2180)(1609,1807)(1610,2181)(1611,
     2183)(1612,2185)(1613,1809)(1615,2188)(1617,2191)(1619,2194)(1622,2197)
     (1623,1816)(1624,2198)(1625,2199)(1627,2202)(1628,2203)(1629,2204)(1630,
     2205)(1632,2207)(1634,2210)(1635,2211)(1636,2212)(1637,2213)(1638,2214)
     (1639,2215)(1640,1830)(1642,2218)(1643,2219)(1644,2220)(1645,2221)(1647,
     2222)(1648,2223)(1649,2224)(1651,2227)(1653,2230)(1655,2233)(1656,2144)
     (1657,2234)(1658,2235)(1659,2236)(1661,2239)(1663,2241)(1666,2246)(1667,
     2247)(1668,2248)(1669,1855)(1670,2250)(1672,2251)(1673,2252)(1675,2255)
     (1677,2121)(1681,2261)(1683,2263)(1685,2266)(1686,2267)(1687,2268)(1689,
     2272)(1690,2274)(1692,2278)(1694,2258)(1695,2281)(1697,2283)(1698,2285)
     (1705,2292)(1707,2294)(1709,2296)(1712,2299)(1713,2300)(1715,2303)(1717,
     2306)(1720,2309)(1721,2311)(1723,2314)(1725,2317)(1726,2319)(1731,2329)
     (1735,2334)(1739,2338)(1740,2339)(1744,2342)(1745,2344)(1750,2350)(1751,
     2351)(1758,2360)(1759,2361)(1760,2362)(1765,2368)(1766,2071)(1769,1883)
     (1772,2373)(1777,2375)(1778,2376)(1780,2377)(1781,2379)(1786,2383)(1792,
     2366)(1793,2391)(1794,2393)(1796,2395)(1797,2396)(1798,2397)(1802,2403)
     (1804,2406)(1806,2153)(1808,2409)(1811,2411)(1813,2413)(1815,2416)(1817,
     2417)(1818,2418)(1820,2421)(1821,2115)(1823,2423)(1825,2426)(1826,2427)
     (1827,2428)(1828,2429)(1829,2430)(1832,2433)(1833,2434)(1834,2435)(1836,
     2436)(1837,2437)(1839,2439)(1841,2442)(1843,2143)(1844,2394)(1845,2225)
     (1846,2445)(1847,2446)(1849,2449)(1853,2126)(1854,2455)(1856,2456)(1857,
     2286)(1858,2458)(1860,2459)(1861,2460)(1862,2462)(1864,2466)(1869,2469)
     (1872,2474)(1873,2476)(1876,2479)(1878,2482)(1879,2484)(1885,2493)(1886,
     2494)(1887,2495)(1889,2498)(1891,2501)(1892,2502)(1893,2503)(1894,2505)
     (1895,2507)(1896,2318)(1897,1925)(1898,2510)(1899,2511)(1902,2515)(1903,
     1963)(1904,1983)(1905,2518)(1907,2520)(1908,2521)(1910,2524)(1912,2155)
     (1913,2527)(1915,2529)(1917,2290)(1918,2532)(1920,2535)(1922,2536)(1923,
     2538)(1927,2541)(1928,2093)(1929,2542)(1930,2543)(1931,2544)(1933,2547)
     (1935,2551)(1937,2554)(1938,2099)(1941,2560)(1942,2562)(1944,2564)(1945,
     2302)(1947,2568)(1948,2570)(1950,2573)(1951,2574)(1953,2577)(1957,2580)
     (1959,2583)(1960,2584)(1965,2589)(1966,2590)(1968,2591)(1969,2593)(1970,
     2595)(1971,2597)(1973,2599)(1974,2600)(1976,2601)(1977,2602)(1978,2331)
     (1979,2604)(1980,2606)(1981,2608)(1985,2611)(1987,2335)(1988,2614)(1989,
     2615)(1991,2616)(1992,2617)(1997,2622)(1998,2623)(2000,2624)(2001,2625)
     (2002,2626)(2004,2629)(2006,2632)(2007,2633)(2008,2634)(2009,2635)(2010,
     2636)(2011,2637)(2012,2638)(2013,2639)(2015,2640)(2018,2645)(2019,2646)
     (2020,2353)(2021,2647)(2022,2648)(2023,2356)(2024,2357)(2025,2652)(2026,
     2654)(2029,2658)(2032,2661)(2033,2663)(2035,2667)(2036,2298)(2039,2674)
     (2041,2677)(2042,2679)(2043,2681)(2044,2683)(2048,2688)(2049,2690)(2051,
     2694)(2052,2696)(2054,2062)(2055,2699)(2056,2701)(2057,2170)(2059,2706)
     (2063,2708)(2065,2712)(2066,2713)(2068,2365)(2072,2367)(2075,2725)(2078,
     2728)(2079,2730)(2082,2736)(2083,2737)(2084,2086)(2085,2738)(2088,2182)
     (2090,2743)(2091,2744)(2094,2748)(2095,2750)(2096,2752)(2098,2755)(2105,
     2766)(2106,2768)(2108,2770)(2109,2772)(2114,2779)(2116,2780)(2118,2782)
     (2120,2785)(2122,2786)(2125,2789)(2127,2790)(2128,2386)(2129,2791)(2130,
     2792)(2131,2794)(2133,2798)(2134,2800)(2136,2802)(2137,2803)(2138,2804)
     (2139,2805)(2141,2808)(2145,2165)(2146,2811)(2147,2812)(2148,2813)(2151,
     2816)(2154,2818)(2156,2497)(2158,2820)(2159,2821)(2160,2400)(2162,2825)
     (2166,2829)(2169,2832)(2171,2835)(2172,2837)(2174,2840)(2175,2405)(2177,
     2843)(2178,2844)(2179,2846)(2184,2852)(2186,2855)(2187,2856)(2189,2859)
     (2190,2860)(2192,2862)(2193,2863)(2195,2866)(2196,2868)(2200,2874)(2201,
     2876)(2206,2422)(2208,2886)(2209,2888)(2216,2900)(2217,2902)(2226,2914)
     (2228,2918)(2229,2920)(2232,2810)(2237,2929)(2238,2931)(2242,2935)(2243,
     2937)(2244,2939)(2245,2941)(2249,2943)(2253,2949)(2254,2951)(2256,2954)
     (2259,2957)(2260,2958)(2262,2960)(2264,2961)(2265,2963)(2269,2970)(2270,
     2971)(2271,2972)(2273,2974)(2275,2977)(2276,2978)(2277,2979)(2279,2981)
     (2280,2982)(2282,2984)(2284,2987)(2287,2990)(2288,2991)(2289,2992)(2291,
     2993)(2293,2996)(2295,2999)(2297,3002)(2301,3007)(2304,3009)(2305,3011)
     (2307,3014)(2308,3015)(2310,3017)(2313,3020)(2315,3023)(2316,3024)(2320,
     3029)(2321,3030)(2323,3031)(2324,3033)(2325,3035)(2326,3037)(2327,3038)
     (2328,2576)(2330,3039)(2332,3041)(2333,3043)(2336,3046)(2337,3047)(2340,
     3052)(2341,3053)(2343,3056)(2345,3059)(2346,3060)(2347,3061)(2348,3062)
     (2352,3067)(2354,3068)(2355,3069)(2358,3073)(2359,3075)(2363,3078)(2364,
     3079)(2369,3084)(2371,3087)(2372,3089)(2374,3093)(2378,3098)(2380,3101)
     (2381,3102)(2384,3105)(2385,3106)(2387,3107)(2388,3108)(2389,3109)(2390,
     3110)(2392,3113)(2398,3118)(2399,3119)(2401,3122)(2402,3124)(2404,3127)
     (2407,3130)(2408,3132)(2410,3136)(2412,3139)(2414,2565)(2415,2558)(2419,
     2948)(2420,3146)(2424,3148)(2425,3150)(2431,3160)(2432,3162)(2438,3169)
     (2440,3173)(2441,3175)(2444,3115)(2447,3183)(2448,3185)(2451,3188)(2452,
     3190)(2453,3192)(2454,3193)(2457,2930)(2461,3198)(2463,2735)(2464,3200)
     (2465,3201)(2467,2864)(2468,3203)(2470,3206)(2471,3208)(2472,3210)(2473,
     3211)(2475,3214)(2477,3217)(2478,3218)(2480,3221)(2481,3222)(2483,3223)
     (2485,3226)(2486,3224)(2487,3227)(2488,3228)(2489,3229)(2490,3231)(2491,
     3233)(2492,3235)(2496,3243)(2499,2975)(2500,3247)(2504,3057)(2506,3256)
     (2508,3258)(2509,3259)(2512,2980)(2513,3025)(2516,3268)(2517,3269)(2519,
     3271)(2522,3275)(2523,3277)(2525,3280)(2526,3282)(2528,3286)(2530,3288)
     (2531,3289)(2533,3292)(2534,3293)(2537,2733)(2539,3298)(2540,3299)(2545,
     3305)(2546,3306)(2548,3309)(2549,2997)(2550,3310)(2555,3314)(2556,3315)
     (2557,3316)(2561,3319)(2563,3322)(2566,3325)(2567,3326)(2569,3328)(2571,
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