bin1 := (2,6)(4,12)(7,18)(8,15)(9,17)(11,23)(13,26)(14,27)(16,33)(19,36)(20,38) (21,31)(22,40)(24,43)(25,46)(28,52)(29,49)(30,51)(32,57)(34,60)(35,61) (37,67)(39,65)(41,71)(42,73)(44,77)(45,76)(47,81)(48,82)(50,88)(53,91) (54,93)(55,86)(56,95)(58,98)(59,101)(62,107)(63,104)(64,106)(66,112)(68, 115)(69,116)(70,118)(72,121)(74,124)(75,127)(78,131)(79,132)(80,135)(83, 141)(84,138)(85,140)(87,146)(89,149)(90,150)(92,156)(94,154)(96,160)(97, 162)(99,166)(100,165)(102,170)(103,171)(105,177)(108,179)(109,180)(110, 175)(111,182)(113,185)(114,188)(117,192)(119,195)(120,197)(122,200)(123, 202)(125,206)(126,205)(128,210)(129,211)(130,214)(133,219)(134,218)(136, 223)(137,224)(139,230)(142,233)(143,235)(144,228)(145,237)(147,240)(148, 243)(151,212)(152,246)(153,248)(155,253)(157,256)(158,257)(159,259)(161, 262)(163,265)(164,268)(167,272)(168,273)(169,276)(172,282)(173,279)(174, 281)(176,287)(178,290)(181,291)(183,294)(184,296)(186,300)(187,299)(189, 304)(190,305)(191,307)(193,310)(194,312)(196,315)(198,318)(199,320)(201, 323)(203,326)(204,328)(207,332)(208,333)(209,336)(213,340)(215,344)(216, 345)(217,348)(220,352)(221,271)(222,355)(225,361)(226,358)(227,360)(229, 366)(231,369)(232,370)(234,376)(236,374)(238,380)(239,382)(241,386)(242, 385)(244,390)(247,396)(249,319)(250,341)(251,394)(252,399)(254,402)(255, 405)(258,409)(260,412)(261,414)(263,417)(264,419)(266,423)(267,422)(269, 427)(270,428)(274,433)(275,432)(277,437)(278,438)(280,444)(283,447)(284, 449)(285,442)(286,451)(288,454)(289,457)(292,459)(293,461)(295,464)(297, 467)(298,470)(301,474)(302,475)(303,478)(306,482)(308,485)(309,487)(311, 490)(313,493)(314,494)(316,497)(317,499)(321,504)(322,506)(324,416)(325, 510)(327,513)(329,516)(330,517)(331,520)(334,525)(335,524)(337,529)(338, 530)(339,533)(342,535)(343,538)(346,543)(347,542)(349,547)(350,548)(351, 551)(353,553)(354,431)(356,557)(357,558)(359,564)(362,567)(363,569)(364, 562)(365,571)(367,574)(368,577)(371,429)(372,580)(373,582)(375,587)(377, 590)(378,591)(379,593)(381,596)(383,598)(384,601)(387,605)(388,606)(389, 445)(391,610)(395,615)(397,618)(398,486)(400,621)(401,623)(403,625)(404, 435)(406,629)(407,630)(408,632)(410,635)(411,637)(413,640)(415,643)(418, 645)(421,649)(424,653)(425,654)(426,657)(430,661)(434,665)(436,667)(439, 670)(440,647)(441,669)(443,675)(446,512)(448,682)(450,680)(452,686)(453, 688)(455,692)(456,691)(458,696)(460,699)(462,702)(463,704)(465,707)(466, 709)(468,713)(469,712)(471,717)(472,718)(473,721)(476,726)(477,725)(479, 730)(480,731)(481,732)(483,735)(484,737)(488,742)(489,744)(491,634)(492, 748)(495,753)(496,755)(498,624)(500,760)(501,762)(502,763)(503,765)(505, 768)(507,771)(508,773)(509,774)(511,777)(514,781)(515,784)(518,549)(519, 787)(521,791)(522,792)(523,795)(526,797)(528,800)(531,805)(532,804)(534, 809)(536,813)(537,812)(539,815)(540,816)(541,817)(544,820)(545,821)(546, 824)(550,827)(552,831)(554,834)(555,835)(556,838)(559,843)(560,840)(561, 842)(563,848)(565,851)(566,852)(568,858)(570,856)(572,862)(573,864)(575, 868)(576,867)(578,872)(581,878)(583,644)(584,662)(585,876)(586,881)(588, 884)(589,887)(592,891)(594,893)(595,895)(597,898)(599,902)(600,901)(602, 906)(603,907)(604,910)(607,914)(608,913)(609,674)(611,794)(612,756)(614, 917)(616,920)(617,923)(619,666)(620,926)(622,928)(626,933)(627,934)(628, 937)(631,941)(633,942)(636,944)(639,947)(641,950)(642,658)(646,955)(650, 958)(651,959)(652,962)(655,892)(656,966)(659,967)(660,970)(664,974)(668, 978)(671,980)(672,982)(673,946)(676,985)(677,719)(678,750)(679,780)(681, 990)(683,993)(684,994)(685,996)(687,999)(689,948)(690,1003)(693,1007) (694,1008)(695,1011)(697,964)(698,1014)(700,1017)(701,1019)(703,1021) (705,1024)(706,1026)(708,1029)(710,1032)(711,912)(714,1037)(715,1038) (716,1039)(720,1042)(722,1046)(723,1047)(724,1050)(727,1054)(728,1055) (729,1058)(733,1064)(734,1066)(736,927)(738,1070)(739,1072)(740,1005) (741,1074)(743,1075)(745,1078)(746,1080)(747,1081)(749,1084)(751,1086) (752,1088)(754,772)(757,1093)(759,1095)(761,1098)(764,1102)(766,1103) (767,1104)(769,1107)(770,1109)(775,1115)(776,1117)(778,1121)(779,1120) (782,1126)(783,1125)(785,1129)(786,1130)(788,828)(789,1132)(790,1135) (793,1137)(796,1141)(798,1142)(801,1146)(802,1147)(803,1150)(806,1154) (807,1155)(808,1158)(810,1160)(811,995)(814,1165)(818,1170)(819,1173) (822,1178)(823,1177)(825,1182)(826,1183)(829,1185)(830,1188)(832,1190) (833,1193)(836,1198)(837,1197)(839,1201)(841,1204)(844,1207)(845,1209) (846,1202)(847,1211)(849,1214)(850,1217)(853,908)(854,1220)(855,1222) (857,1227)(859,1230)(860,1231)(861,1233)(863,1235)(865,1097)(866,971) (869,1242)(870,1243)(871,1244)(873,1245)(877,1250)(879,1253)(880,943) (882,1256)(883,1258)(885,1262)(886,1261)(888,1266)(889,1267)(890,1269) (894,1274)(896,1277)(897,1279)(899,1280)(900,1283)(903,1286)(904,1287) (905,1289)(909,1293)(911,1297)(915,1300)(916,1301)(918,1304)(919,1306) (921,1310)(922,1309)(924,1313)(925,1314)(929,1319)(930,1321)(931,1322) (932,1139)(935,1329)(936,1328)(938,1333)(940,1334)(945,1341)(949,1345) (951,1347)(952,1349)(954,1351)(956,1353)(957,1356)(960,972)(961,1359) (963,1299)(965,1033)(968,1367)(969,1366)(975,1373)(976,1374)(977,1355) (979,1378)(981,1384)(983,1382)(984,1386)(986,1025)(987,1043)(988,1061) (989,1389)(991,1392)(992,1395)(997,1335)(998,1401)(1000,1403)(1001,1405) (1002,1406)(1004,1409)(1009,1415)(1010,1414)(1012,1419)(1013,1420)(1015, 1421)(1016,1423)(1018,1426)(1020,1429)(1022,1432)(1023,1433)(1027,1437) (1028,1292)(1030,1441)(1031,1443)(1034,1446)(1035,1447)(1036,1450)(1040, 1456)(1041,1284)(1044,1460)(1045,1463)(1048,1467)(1049,1466)(1051,1470) (1052,1471)(1053,1474)(1056,1479)(1057,1478)(1059,1483)(1060,1484)(1062, 1486)(1063,1128)(1065,1079)(1067,1323)(1069,1492)(1071,1495)(1073,1498) (1076,1501)(1077,1502)(1082,1507)(1083,1509)(1085,1512)(1087,1515)(1089, 1516)(1090,1517)(1091,1519)(1092,1520)(1094,1521)(1096,1524)(1099,1528) (1100,1530)(1101,1531)(1105,1538)(1106,1540)(1108,1179)(1110,1545)(1111, 1546)(1112,1189)(1113,1548)(1114,1550)(1116,1553)(1118,1482)(1119,1557) (1122,1561)(1123,1562)(1124,1565)(1127,1569)(1131,1572)(1133,1574)(1134, 1568)(1136,1578)(1138,1581)(1140,1582)(1143,1585)(1144,1586)(1145,1589) (1148,1594)(1149,1593)(1151,1597)(1152,1598)(1153,1601)(1156,1606)(1157, 1605)(1159,1610)(1162,1613)(1163,1614)(1164,1617)(1166,1619)(1167,1169) (1168,1621)(1171,1191)(1172,1625)(1174,1629)(1176,1632)(1180,1634)(1181, 1637)(1184,1641)(1186,1645)(1187,1644)(1192,1649)(1194,1653)(1195,1654) (1196,1655)(1199,1658)(1200,1659)(1203,1205)(1206,1662)(1208,1668)(1210, 1666)(1212,1672)(1213,1674)(1215,1678)(1216,1677)(1218,1680)(1219,1681) (1221,1687)(1223,1278)(1224,1294)(1225,1685)(1226,1690)(1228,1693)(1229, 1696)(1232,1698)(1234,1494)(1236,1701)(1237,1702)(1238,1703)(1239,1338) (1240,1704)(1241,1707)(1246,1714)(1247,1716)(1249,1718)(1251,1721)(1252, 1724)(1254,1726)(1255,1728)(1257,1731)(1259,1734)(1260,1737)(1263,1741) (1264,1742)(1265,1745)(1268,1749)(1270,1751)(1271,1753)(1272,1754)(1273, 1756)(1275,1758)(1276,1290)(1281,1766)(1282,1765)(1285,1769)(1288,1773) (1295,1777)(1296,1364)(1298,1781)(1302,1787)(1303,1789)(1305,1792)(1307, 1794)(1308,1797)(1311,1800)(1312,1782)(1315,1802)(1316,1804)(1317,1620) (1318,1325)(1320,1807)(1324,1622)(1326,1810)(1327,1813)(1330,1817)(1331, 1818)(1332,1380)(1336,1784)(1337,1824)(1340,1623)(1342,1828)(1343,1830) (1344,1350)(1346,1363)(1348,1834)(1352,1836)(1354,1838)(1357,1842)(1358, 1843)(1360,1370)(1361,1793)(1362,1845)(1365,1848)(1368,1850)(1369,1596) (1371,1851)(1372,1499)(1375,1857)(1376,1856)(1377,1821)(1379,1410)(1381, 1860)(1383,1579)(1385,1785)(1387,1863)(1388,1422)(1390,1866)(1391,1868) (1393,1872)(1394,1871)(1396,1876)(1397,1608)(1398,1877)(1399,1879)(1400, 1880)(1404,1884)(1407,1889)(1408,1497)(1412,1711)(1413,1894)(1416,1898) (1417,1899)(1418,1444)(1424,1907)(1425,1760)(1427,1911)(1428,1913)(1430, 1916)(1431,1918)(1434,1923)(1435,1723)(1436,1925)(1438,1927)(1439,1928) (1440,1930)(1442,1933)(1445,1936)(1448,1472)(1449,1939)(1451,1942)(1452, 1943)(1453,1945)(1454,1946)(1455,1772)(1457,1951)(1458,1950)(1459,1748) (1461,1954)(1462,1719)(1464,1958)(1465,1959)(1468,1963)(1469,1964)(1473, 1968)(1475,1972)(1476,1973)(1477,1976)(1480,1980)(1481,1981)(1485,1987) (1487,1989)(1488,1990)(1489,1991)(1490,1993)(1491,1994)(1493,1997)(1496, 2001)(1500,2006)(1503,2011)(1504,2012)(1505,2013)(1506,2015)(1508,2016) (1510,1935)(1511,2018)(1513,1646)(1514,2022)(1518,2026)(1522,2032)(1523, 2034)(1525,2037)(1526,2038)(1527,2040)(1529,2043)(1532,2045)(1533,2047) (1534,2048)(1535,1537)(1536,2049)(1539,1549)(1542,2054)(1543,2055)(1544, 2057)(1547,1564)(1551,2066)(1552,2067)(1554,2070)(1555,2071)(1556,1984) (1558,2075)(1559,2076)(1560,2079)(1566,2082)(1567,2083)(1570,2086)(1571, 1901)(1573,2089)(1575,2092)(1576,2093)(1577,2096)(1580,2099)(1583,2101) (1584,1783)(1587,2108)(1588,2107)(1590,2112)(1591,2113)(1592,2116)(1595, 2120)(1599,1615)(1600,2123)(1602,2127)(1603,2128)(1604,2131)(1607,1962) (1609,2031)(1611,2029)(1612,1809)(1616,2137)(1618,2140)(1624,2145)(1626, 1650)(1627,2147)(1628,2150)(1630,2152)(1633,2156)(1635,1897)(1636,2159) (1638,1888)(1639,2162)(1640,2165)(1642,2167)(1643,2170)(1647,2173)(1648, 2176)(1651,2178)(1652,2181)(1656,2187)(1657,2189)(1660,2193)(1661,2194) (1663,1705)(1664,2196)(1665,2198)(1667,2203)(1669,2206)(1670,2207)(1671, 1774)(1673,2211)(1675,2212)(1676,2214)(1679,2218)(1682,2223)(1683,2220) (1684,2222)(1686,1710)(1688,1712)(1689,1752)(1691,2231)(1692,2233)(1694, 2237)(1695,2236)(1697,2241)(1699,2157)(1700,2245)(1706,2250)(1708,2254) (1709,2255)(1713,2258)(1715,2264)(1717,2262)(1720,2268)(1722,2270)(1725, 2274)(1727,2277)(1729,2280)(1730,2282)(1732,2285)(1733,2287)(1735,2291) (1736,2290)(1738,2295)(1739,2296)(1740,2299)(1743,2304)(1744,2303)(1746, 2308)(1747,2309)(1750,2312)(1755,2318)(1757,2320)(1761,2323)(1762,1832) (1763,2325)(1764,2328)(1767,2330)(1768,2331)(1770,2334)(1771,2335)(1775, 2149)(1778,2342)(1779,2341)(1780,1847)(1786,2347)(1788,2350)(1790,2352) (1791,2354)(1795,2359)(1796,2358)(1798,2362)(1799,2363)(1801,2345)(1803, 2367)(1805,2369)(1806,2371)(1808,2374)(1811,2379)(1812,2378)(1814,2383) (1815,2384)(1816,2387)(1819,2392)(1820,2391)(1822,2394)(1823,1826)(1825, 2397)(1827,2398)(1829,2400)(1831,2351)(1833,2404)(1835,2405)(1837,2385) (1839,2409)(1840,2410)(1841,2413)(1844,2417)(1846,2418)(1849,2422)(1852, 2426)(1853,2425)(1854,2427)(1855,2430)(1858,2432)(1859,2433)(1861,2435) (1862,2104)(1864,2437)(1865,2439)(1867,2442)(1869,2445)(1870,2448)(1873, 2452)(1874,2453)(1875,2456)(1878,2459)(1881,2462)(1882,2248)(1883,2464) (1885,2467)(1886,1914)(1887,2469)(1890,2103)(1891,2473)(1892,2474)(1893, 2246)(1895,2478)(1896,2479)(1900,2483)(1902,1915)(1903,2485)(1904,2487) (1905,2488)(1906,2489)(1908,2490)(1909,2491)(1910,2252)(1912,2495)(1917, 1929)(1919,2125)(1920,2338)(1921,2502)(1922,2322)(1924,2506)(1926,2412) (1931,2513)(1932,2515)(1934,2518)(1937,2521)(1938,2524)(1940,1969)(1941, 2526)(1944,2528)(1947,2531)(1948,2532)(1949,2535)(1952,2539)(1953,2540) (1955,2543)(1956,2544)(1957,2547)(1960,2401)(1961,2550)(1965,2051)(1966, 2555)(1967,2558)(1970,2560)(1971,2243)(1974,2565)(1975,2564)(1977,2340) (1978,2568)(1979,2571)(1982,2576)(1983,2575)(1985,2497)(1986,2579)(1988, 2582)(1992,2585)(1995,2589)(1996,2591)(1998,2594)(1999,2595)(2000,2597) (2002,2553)(2003,2600)(2004,2142)(2005,2014)(2008,2472)(2009,2604)(2010, 2416)(2017,2616)(2019,2619)(2020,2620)(2023,2621)(2024,2087)(2025,2622) (2027,2625)(2028,2627)(2030,2629)(2033,2631)(2035,2634)(2036,2636)(2039, 2046)(2041,2642)(2042,2644)(2044,2588)(2050,2651)(2052,2653)(2053,2654) (2056,2466)(2058,2659)(2059,2661)(2060,2158)(2061,2663)(2062,2664)(2063, 2666)(2064,2667)(2065,2669)(2068,2674)(2069,2675)(2072,2678)(2073,2679) (2074,2682)(2077,2084)(2078,2686)(2080,2690)(2085,2693)(2088,2460)(2090, 2694)(2091,2697)(2094,2702)(2095,2701)(2097,2706)(2098,2102)(2100,2477) (2105,2484)(2106,2293)(2109,2712)(2110,2713)(2111,2716)(2114,2720)(2115, 2719)(2117,2724)(2118,2725)(2119,2728)(2121,2730)(2122,2733)(2124,2138) (2126,2735)(2129,2739)(2130,2738)(2132,2743)(2133,2744)(2134,2154)(2135, 2745)(2136,2748)(2139,2750)(2141,2752)(2143,2754)(2144,2755)(2146,2757) (2148,2758)(2151,2762)(2153,2765)(2155,2767)(2160,2482)(2161,2770)(2163, 2774)(2164,2773)(2166,2778)(2168,2780)(2169,2779)(2171,2784)(2174,2788) (2175,2787)(2177,2792)(2179,2796)(2180,2795)(2182,2800)(2183,2801)(2184, 2803)(2185,2804)(2186,2806)(2188,2809)(2190,2812)(2191,2813)(2192,2816) (2195,2820)(2197,2826)(2199,2244)(2200,2251)(2201,2824)(2202,2829)(2204, 2832)(2205,2835)(2208,2839)(2209,2840)(2210,2841)(2213,2846)(2215,2849) (2216,2850)(2217,2853)(2219,2855)(2221,2861)(2224,2864)(2225,2866)(2226, 2859)(2227,2247)(2228,2868)(2229,2869)(2230,2871)(2232,2874)(2234,2877) (2238,2883)(2239,2884)(2240,2887)(2242,2656)(2249,2892)(2253,2895)(2256, 2898)(2257,2899)(2259,2297)(2260,2865)(2261,2901)(2263,2906)(2265,2909) (2266,2910)(2267,2911)(2269,2914)(2271,2915)(2272,2916)(2273,2326)(2275, 2920)(2276,2921)(2278,2741)(2279,2924)(2281,2329)(2283,2928)(2284,2572) (2286,2931)(2288,2934)(2289,2443)(2292,2317)(2294,2475)(2298,2943)(2300, 2517)(2301,2946)(2302,2599)(2305,2951)(2306,2952)(2307,2955)(2310,2958) (2311,2959)(2314,2961)(2315,2395)(2316,2963)(2319,2965)(2321,2968)(2324, 2971)(2327,2974)(2332,2978)(2333,2981)(2336,2986)(2337,2985)(2339,2988) 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3173)(2516,3175)(2519,3178)(2520,2709)(2523,3181)(2525,3185)(2527,3188) (2529,3191)(2533,2918)(2534,3196)(2536,3199)(2537,3025)(2538,3201)(2541, 2573)(2542,3205)(2545,3210)(2546,3209)(2548,3066)(2549,3213)(2551,2569) (2552,3214)(2554,3216)(2556,3220)(2557,3219)(2559,3224)(2561,3228)(2562, 3227)(2563,3229)(2566,3233)(2567,3234)(2570,3177)(2574,3155)(2577,3241) (2578,3242)(2580,3244)(2581,3245)(2583,3246)(2584,2687)(2586,3249)(2587, 3251)(2590,3253)(2592,3256)(2593,3257)(2596,2601)(2598,3262)(2602,3266) (2603,3267)(2605,3126)(2606,3268)(2607,3270)(2608,2657)(2609,3272)(2610, 3273)(2611,3275)(2612,3276)(2613,3278)(2614,3279)(2615,3040)(2617,3014) (2623,3287)(2624,3289)(2626,3292)(2630,2927)(2632,3297)(2633,3299)(2637, 3303)(2638,3305)(2639,3306)(2640,3308)(2641,3309)(2643,3312)(2645,2945) (2646,3238)(2647,2680)(2648,3207)(2649,3315)(2650,3316)(2652,3318)(2655, 3323)(2658,3325)(2660,2695)(2662,3329)(2665,3184)(2668,3338)(2670,2776) 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