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)(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)(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)(371,449)(373,553)(375,556)(377,558)
     (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)(492,610)(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)(581,701)(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)(611,875)(615,881)(616,883)(618,885)(619,886)
     (620,887)(621,889)(623,893)(625,894)(627,897)(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)(787,876)(788,1112)(791,1115)(792,938)(794,1118)
     (795,1119)(796,1120)(798,1122)(801,1124)(802,945)(803,1125)(804,1126)
     (805,947)(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)(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)(874,1213)(877,1216)(878,1217)(879,1191)(880,1218)
     (884,1221)(888,1227)(890,1230)(891,1231)(892,1233)(895,1236)(896,1238)
     (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)(1200,1642)(1205,1651)(1206,1653)(1207,1655)(1211,1661)
     (1212,1663)(1214,1666)(1215,1667)(1220,1361)(1222,1676)(1223,1678)(1224,
     1680)(1225,1681)(1226,1682)(1228,1684)(1229,1686)(1232,1690)(1234,1693)
     (1235,1694)(1237,1697)(1239,1700)(1240,1701)(1241,1702)(1242,1703)(1243,
     1704)(1244,1705)(1246,1707)(1247,1709)(1248,1711)(1251,1715)(1252,1717)
     (1256,1723)(1259,1725)(1261,1728)(1262,1729)(1263,1730)(1264,1731)(1265,
     1733)(1266,1734)(1268,1737)(1269,1738)(1270,1739)(1272,1742)(1273,1743)
     (1274,1744)(1276,1747)(1278,1749)(1279,1750)(1281,1753)(1283,1754)(1284,
     1755)(1285,1756)(1286,1758)(1288,1469)(1290,1762)(1291,1763)(1293,1764)
     (1296,1769)(1297,1771)(1299,1775)(1303,1781)(1305,1784)(1306,1664)(1307,
     1785)(1309,1788)(1310,1789)(1311,1560)(1312,1790)(1313,1791)(1317,1796)
     (1321,1800)(1323,1801)(1324,1803)(1325,1805)(1328,1810)(1329,1812)(1330,
     1814)(1334,1819)(1336,1822)(1337,1824)(1341,1786)(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)(1432,1719)(1434,1952)(1435,1954)(1437,1958)(1439,
     1962)(1440,1964)(1444,1972)(1446,1975)(1450,1982)(1452,1539)(1453,1984)
     (1454,1735)(1455,1986)(1460,1994)(1461,1996)(1466,2003)(1467,2005)(1470,
     1748)(1474,2016)(1475,2017)(1480,1757)(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)(1521,1765)(1522,
     2073)(1523,2074)(1526,2077)(1528,1772)(1529,2080)(1531,2081)(1536,1776)
     (1537,1777)(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)(1564,2116)(1565,2118)(1570,2122)(1575,
     2130)(1577,2133)(1580,2137)(1581,2139)(1582,2141)(1586,2148)(1587,2149)
     (1589,2151)(1590,1799)(1594,2160)(1596,2162)(1597,2163)(1599,2166)(1600,
     2167)(1603,2172)(1605,2175)(1608,2179)(1610,2180)(1611,2182)(1612,2184)
     (1613,1809)(1615,2187)(1617,2189)(1619,2192)(1622,2195)(1623,1816)(1624,
     2196)(1625,2197)(1627,2200)(1628,2201)(1629,2202)(1630,2203)(1632,2205)
     (1634,2208)(1635,2209)(1636,2210)(1637,2211)(1638,2212)(1639,2213)(1640,
     2214)(1641,1830)(1643,2217)(1644,2218)(1645,2219)(1646,2220)(1648,2221)
     (1649,2222)(1650,2223)(1652,2226)(1654,2229)(1656,2232)(1657,2143)(1658,
     2233)(1659,2234)(1660,2235)(1662,2238)(1665,2240)(1668,2245)(1669,2246)
     (1670,2247)(1671,2248)(1672,2249)(1673,1855)(1674,2250)(1675,2251)(1677,
     2254)(1679,2257)(1683,2262)(1685,2264)(1687,2267)(1688,2268)(1689,2269)
     (1691,2273)(1692,2275)(1695,2258)(1696,2281)(1698,2284)(1699,2286)(1706,
     2293)(1708,2295)(1710,2297)(1713,2300)(1714,2301)(1716,2304)(1718,2307)
     (1721,2310)(1722,2312)(1724,2315)(1726,2318)(1727,2320)(1732,2330)(1736,
     2335)(1740,2339)(1741,2340)(1745,2343)(1746,2345)(1751,2351)(1752,2352)
     (1759,2361)(1760,2362)(1761,2363)(1766,2368)(1767,2071)(1770,1883)(1773,
     2373)(1779,2375)(1780,2376)(1782,2377)(1783,2379)(1787,2383)(1793,2069)
     (1794,2391)(1795,2393)(1797,2395)(1798,2396)(1802,2402)(1804,2405)(1806,
     2152)(1808,2408)(1811,2411)(1813,2413)(1815,2416)(1817,2417)(1818,2418)
     (1820,2421)(1821,2114)(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)(1843,2142)(1844,2394)(1845,2224)(1846,2445)(1847,
     2446)(1849,2449)(1853,2124)(1854,2455)(1856,2456)(1857,1912)(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,
     2319)(1897,1925)(1898,2510)(1899,2511)(1902,2515)(1903,1963)(1904,1983)
     (1905,2518)(1907,2520)(1908,2521)(1910,2524)(1913,2527)(1915,2529)(1917,
     2291)(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)(1945,2303)(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)
     (1974,2601)(1976,2602)(1977,2603)(1978,2332)(1979,2605)(1980,2607)(1981,
     2609)(1985,2612)(1987,2336)(1988,2615)(1989,2616)(1991,2617)(1992,2618)
     (1997,2623)(1998,2624)(2000,2625)(2001,2626)(2002,2627)(2004,2630)(2006,
     2633)(2007,2634)(2008,2635)(2009,2636)(2010,2637)(2011,2638)(2012,2639)
     (2013,2640)(2015,2641)(2018,2646)(2019,2647)(2020,2354)(2021,2648)(2022,
     2649)(2023,2357)(2024,2358)(2025,2653)(2026,2655)(2029,2659)(2032,2662)
     (2033,2664)(2035,2668)(2036,2299)(2039,2675)(2041,2678)(2042,2680)(2043,
     2682)(2044,2684)(2048,2689)(2049,2691)(2051,2695)(2052,2697)(2054,2062)
     (2055,2700)(2056,2702)(2057,2169)(2059,2707)(2063,2709)(2065,2713)(2066,
     2714)(2072,2367)(2075,2726)(2078,2729)(2079,2731)(2082,2737)(2083,2738)
     (2084,2086)(2085,2739)(2090,2744)(2091,2745)(2094,2749)(2095,2751)(2096,
     2753)(2098,2756)(2105,2767)(2106,2769)(2108,2771)(2109,2773)(2115,2781)
     (2117,2783)(2119,2786)(2120,2787)(2123,2790)(2125,2791)(2126,2386)(2127,
     2792)(2128,2793)(2129,2795)(2131,2799)(2132,2801)(2134,2803)(2135,2804)
     (2136,2805)(2138,2807)(2140,2810)(2144,2164)(2145,2813)(2146,2814)(2147,
     2815)(2150,2818)(2153,2820)(2154,2287)(2155,2497)(2157,2822)(2158,2823)
     (2159,2399)(2161,2827)(2165,2831)(2168,2834)(2170,2837)(2171,2839)(2173,
     2842)(2174,2404)(2176,2845)(2177,2846)(2178,2848)(2183,2854)(2185,2857)
     (2186,2858)(2188,2861)(2190,2863)(2191,2864)(2193,2867)(2194,2869)(2198,
     2875)(2199,2876)(2204,2422)(2206,2886)(2207,2888)(2215,2901)(2216,2903)
     (2225,2915)(2227,2919)(2228,2921)(2231,2812)(2236,2931)(2237,2933)(2241,
     2937)(2242,2939)(2243,2941)(2244,2943)(2252,2949)(2253,2951)(2255,2954)
     (2259,2957)(2260,2958)(2261,2959)(2263,2961)(2265,2780)(2266,2963)(2270,
     2970)(2271,2971)(2272,2972)(2274,2974)(2276,2977)(2277,2978)(2278,2979)
     (2279,2980)(2280,2981)(2282,2983)(2283,2984)(2285,2987)(2288,2990)(2289,
     2991)(2290,2992)(2292,2993)(2294,2996)(2296,2999)(2298,3002)(2302,3007)
     (2305,3009)(2306,3011)(2308,3014)(2309,3015)(2311,3017)(2314,3020)(2316,
     3023)(2317,3024)(2321,3029)(2322,3030)(2324,3031)(2325,3033)(2326,3035)
     (2327,3037)(2328,3038)(2329,2576)(2331,3039)(2333,3041)(2334,3043)(2337,
     3046)(2338,3047)(2341,3052)(2342,3053)(2344,3056)(2346,3059)(2347,3060)
     (2348,3061)(2349,3062)(2353,3067)(2355,3068)(2356,3069)(2359,3073)(2360,
     3075)(2364,3078)(2365,3079)(2369,3083)(2371,3086)(2372,3088)(2374,3091)
     (2378,3096)(2380,3099)(2381,3100)(2384,3103)(2385,3104)(2387,3105)(2388,
     3106)(2389,3107)(2390,3108)(2392,3111)(2397,3116)(2398,3117)(2400,3120)
     (2401,3122)(2403,3125)(2406,3128)(2407,3130)(2409,3134)(2410,3135)(2412,
     3138)(2414,2565)(2415,2558)(2419,3145)(2420,3146)(2424,3148)(2425,3150)
     (2431,3160)(2432,3162)(2438,3169)(2440,3173)(2441,3175)(2444,3113)(2447,
     3183)(2448,3185)(2451,3188)(2452,3190)(2453,3192)(2454,3193)(2457,3184)
     (2461,3198)(2463,2736)(2464,3200)(2465,3201)(2467,2865)(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)(2512,2600)(2513,
     3025)(2516,3268)(2517,3269)(2519,3271)(2522,3275)(2523,3276)(2525,3279)
     (2526,3281)(2528,3285)(2530,3287)(2531,3288)(2533,3291)(2534,3292)(2537,
     2734)(2539,3297)(2540,3298)(2545,3304)(2546,3305)(2548,3308)(2549,2997)
     (2550,3309)(2555,3313)(2556,3314)(2557,3315)(2561,3318)(2563,3321)(2566,
     3324)(2567,3325)(2569,3327)(2571,3329)(2572,3330)(2575,3335)(2579,3340)
     (2581,3344)(2582,3022)(2585,2945)(2586,3026)(2587,3353)(2588,3355)(2592,
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