bin1 := (1,2)(3,5)(4,7)(6,10)(8,12)(9,13)(11,16)(14,20)(15,21)(17,24)(18,25)(19,
     27)(22,31)(23,32)(26,36)(28,38)(29,39)(30,41)(33,45)(34,46)(35,48)(37,51)
     (40,55)(42,57)(43,58)(44,59)(47,63)(50,65)(52,66)(53,67)(54,69)(56,72)
     (60,76)(61,77)(62,79)(64,82)(68,87)(70,89)(71,90)(73,91)(74,92)(75,94)
     (78,98)(80,100)(81,101)(83,102)(84,103)(85,105)(86,107)(88,110)(93,116)
     (95,118)(96,119)(97,121)(99,124)(104,129)(106,131)(108,133)(109,134)(111,
     135)(112,136)(113,138)(114,140)(115,142)(117,145)(120,149)(122,151)(123,
     152)(125,153)(126,154)(127,156)(128,158)(130,160)(132,163)(137,169)(139,
     171)(141,173)(143,175)(144,176)(146,177)(147,178)(148,180)(150,183)(155,
     189)(157,191)(159,193)(161,196)(162,197)(164,198)(165,199)(166,201)(167,
     203)(168,205)(170,208)(172,211)(174,214)(179,220)(181,221)(182,222)(184,
     223)(185,224)(186,226)(187,228)(188,230)(190,233)(192,236)(194,195)(200,
     244)(202,246)(204,248)(206,250)(207,251)(209,252)(210,253)(213,256)(215,
     257)(216,258)(217,260)(218,262)(219,264)(225,271)(227,273)(229,275)(231,
     277)(232,278)(234,279)(235,280)(237,283)(238,284)(239,286)(240,287)(241,
     289)(242,291)(243,293)(245,296)(247,299)(249,302)(254,255)(259,312)(261,
     314)(263,316)(265,318)(266,319)(267,320)(268,322)(269,324)(270,326)(272,
     329)(274,332)(276,335)(281,282)(285,344)(288,347)(292,350)(294,352)(295,
     353)(297,354)(298,355)(300,358)(301,359)(303,360)(304,361)(305,363)(306,
     365)(307,367)(308,369)(309,370)(310,372)(311,374)(313,377)(315,380)(317,
     383)(321,388)(323,390)(325,392)(327,394)(328,395)(330,396)(331,397)(333,
     400)(334,401)(336,402)(337,403)(338,405)(339,407)(340,409)(341,411)(342,
     412)(343,413)(345,416)(346,418)(348,420)(349,421)(351,424)(356,357)(362,
     435)(364,437)(366,439)(368,441)(371,443)(373,445)(375,447)(376,448)(378,
     449)(379,450)(381,453)(382,454)(384,455)(385,456)(386,458)(387,460)(389,
     463)(391,466)(393,468)(398,399)(404,478)(406,480)(408,482)(410,484)(414,
     487)(415,488)(417,491)(419,493)(422,494)(423,495)(425,496)(426,497)(427,
     499)(428,501)(429,503)(430,505)(431,506)(432,508)(433,510)(434,512)(436,
     515)(438,518)(440,521)(442,524)(444,526)(446,529)(451,452)(457,539)(459,
     541)(461,543)(462,544)(464,545)(465,546)(467,536)(469,549)(470,550)(471,
     552)(472,554)(473,555)(474,556)(475,558)(476,560)(477,562)(479,565)(481,
     568)(483,571)(485,574)(486,576)(489,580)(490,581)(492,584)(498,590)(500,
     592)(502,594)(504,596)(507,599)(509,601)(511,603)(513,605)(514,606)(516,
     607)(517,608)(519,611)(520,612)(522,613)(523,614)(525,617)(527,620)(528,
     621)(530,622)(531,623)(532,625)(533,627)(534,629)(535,631)(537,633)(538,
     635)(540,638)(542,641)(547,548)(551,650)(553,652)(557,656)(559,658)(561,
     660)(563,662)(564,663)(566,664)(567,665)(569,668)(570,669)(572,670)(575,
     673)(577,675)(578,676)(579,678)(582,681)(583,682)(585,683)(586,684)(587,
     653)(588,687)(589,689)(591,692)(593,695)(595,698)(597,701)(598,703)(600,
     706)(602,709)(604,712)(609,610)(615,723)(616,724)(618,619)(624,732)(626,
     734)(628,736)(630,738)(632,740)(634,742)(636,744)(637,745)(639,746)(640,
     747)(642,748)(643,749)(644,751)(645,753)(646,755)(647,757)(648,758)(649,
     760)(651,763)(654,685)(655,768)(657,771)(659,774)(661,777)(666,667)(671,
     787)(672,788)(674,791)(677,679)(680,795)(686,800)(688,802)(690,804)(691,
     805)(693,806)(694,807)(696,810)(697,811)(699,812)(700,813)(702,816)(704,
     818)(705,819)(707,820)(708,821)(710,824)(711,825)(713,826)(714,827)(715,
     829)(716,831)(717,833)(718,835)(719,836)(720,838)(721,840)(722,842)(725,
     845)(726,846)(727,848)(728,849)(729,851)(730,853)(731,855)(733,858)(735,
     861)(737,864)(739,867)(741,870)(743,873)(750,881)(752,883)(754,885)(756,
     887)(759,890)(761,892)(762,893)(764,894)(765,895)(767,896)(769,898)(770,
     899)(772,900)(773,901)(775,904)(776,905)(778,906)(779,907)(780,909)(781,
     911)(782,913)(783,915)(784,916)(785,918)(786,920)(789,923)(790,924)(792,
     925)(793,926)(794,928)(796,931)(797,933)(798,935)(799,937)(801,939)(803,
     942)(808,809)(814,953)(815,954)(817,957)(822,823)(828,968)(830,970)(832,
     972)(834,974)(837,977)(839,979)(841,981)(843,983)(844,984)(847,987)(850,
     990)(852,992)(854,994)(856,996)(857,997)(859,998)(860,999)(862,1002)(863,
     1003)(865,1004)(866,1005)(868,889)(869,1008)(871,1011)(872,1012)(874,
     1013)(875,1014)(876,1016)(877,1018)(878,1020)(879,1022)(880,1024)(882,
     1027)(884,1030)(886,1033)(888,1036)(891,1040)(897,1047)(902,903)(908,
     1058)(910,1060)(912,1062)(914,1064)(917,1067)(919,1069)(921,1071)(922,
     1072)(927,1077)(929,1078)(930,1079)(932,1082)(934,1084)(936,1086)(938,
     1088)(940,1089)(941,1090)(943,1091)(944,1092)(945,1094)(946,1096)(947,
     1098)(948,1100)(949,1101)(950,1103)(951,1105)(952,1107)(955,1110)(956,
     1111)(958,1112)(959,1113)(960,1115)(961,1117)(962,1119)(963,1121)(964,
     1122)(965,1124)(966,1126)(967,1128)(969,1131)(971,1134)(973,1137)(975,
     1140)(976,1142)(978,1145)(980,1148)(982,1151)(985,1155)(986,1156)(988,
     1159)(989,1161)(991,1164)(993,1167)(995,1170)(1000,1001)(1006,1180)(1007,
     1181)(1009,1010)(1015,1189)(1017,1191)(1019,1193)(1021,1195)(1023,1197)
     (1026,1199)(1028,1200)(1029,1201)(1031,1204)(1032,1205)(1034,1206)(1035,
     1207)(1037,1210)(1038,1211)(1039,1212)(1041,1213)(1042,1214)(1043,1216)
     (1044,1218)(1045,1220)(1046,1221)(1048,1222)(1049,1223)(1050,1225)(1051,
     1227)(1052,1229)(1053,1231)(1054,1232)(1055,1234)(1056,1236)(1057,1238)
     (1059,1241)(1061,1244)(1063,1247)(1065,1250)(1066,1252)(1068,1255)(1070,
     1258)(1073,1260)(1074,1262)(1075,1264)(1076,1266)(1080,1270)(1081,1271)
     (1083,1274)(1085,1277)(1087,1280)(1093,1287)(1095,1289)(1097,1291)(1099,
     1293)(1102,1296)(1104,1298)(1106,1300)(1108,1302)(1109,1179)(1114,1306)
     (1116,1308)(1118,1310)(1120,1312)(1123,1315)(1125,1317)(1127,1319)(1129,
     1321)(1130,1322)(1132,1323)(1133,1324)(1135,1327)(1136,1328)(1138,1329)
     (1139,1330)(1141,1333)(1143,1335)(1144,1336)(1146,1337)(1147,1338)(1149,
     1341)(1150,1342)(1152,1343)(1153,1344)(1154,1346)(1157,1349)(1158,1350)
     (1160,1353)(1162,1355)(1163,1356)(1165,1357)(1166,1358)(1168,1361)(1169,
     1362)(1171,1363)(1172,1364)(1173,1366)(1174,1368)(1175,1370)(1176,1371)
     (1177,1373)(1178,1375)(1182,1378)(1183,1379)(1184,1381)(1185,1382)(1186,
     1384)(1187,1386)(1188,1388)(1190,1391)(1192,1394)(1194,1397)(1196,1400)
     (1198,1403)(1202,1203)(1208,1412)(1209,1413)(1215,1420)(1217,1422)(1219,
     1424)(1224,1429)(1226,1431)(1228,1433)(1230,1435)(1233,1438)(1235,1440)
     (1237,1442)(1239,1444)(1240,1445)(1242,1446)(1243,1447)(1245,1450)(1246,
     1451)(1248,1452)(1249,1453)(1251,1456)(1253,1458)(1254,1459)(1256,1460)
     (1257,1461)(1259,1409)(1261,1465)(1263,1467)(1265,1469)(1267,1471)(1268,
     1472)(1269,1473)(1272,1476)(1273,1477)(1275,1478)(1276,1479)(1278,1482)
     (1279,1483)(1281,1484)(1282,1485)(1283,1487)(1284,1489)(1285,1491)(1286,
     1493)(1288,1496)(1290,1499)(1292,1502)(1294,1505)(1295,1507)(1297,1510)
     (1299,1513)(1301,1516)(1303,1519)(1304,1521)(1305,1523)(1307,1526)(1311,
     1531)(1313,1534)(1314,1536)(1316,1539)(1318,1542)(1320,1545)(1325,1326)
     (1331,1556)(1332,1557)(1334,1560)(1339,1340)(1345,1570)(1347,1572)(1348,
     1573)(1351,1577)(1352,1578)(1354,1581)(1359,1360)(1365,1561)(1367,1593)
     (1369,1595)(1372,1598)(1374,1600)(1376,1602)(1377,1603)(1380,1605)(1383,
     1608)(1385,1610)(1387,1612)(1389,1614)(1390,1615)(1392,1616)(1393,1617)
     (1395,1620)(1396,1621)(1398,1622)(1399,1623)(1401,1626)(1402,1627)(1404,
     1628)(1405,1629)(1406,1631)(1407,1633)(1408,1464)(1410,1636)(1411,1638)
     (1414,1641)(1415,1642)(1416,1643)(1417,1645)(1418,1647)(1419,1649)(1421,
     1652)(1423,1655)(1425,1658)(1426,1660)(1427,1662)(1428,1664)(1430,1667)
     (1432,1670)(1434,1673)(1436,1676)(1437,1678)(1439,1681)(1441,1684)(1443,
     1687)(1448,1449)(1454,1698)(1455,1699)(1457,1702)(1462,1463)(1466,1711)
     (1468,1714)(1470,1717)(1474,1722)(1475,1723)(1480,1481)(1486,1734)(1488,
     1735)(1490,1737)(1492,1739)(1494,1741)(1495,1742)(1497,1743)(1498,1744)
     (1500,1747)(1501,1748)(1503,1749)(1504,1750)(1506,1752)(1508,1754)(1509,
     1755)(1511,1756)(1512,1757)(1514,1760)(1517,1761)(1518,1762)(1520,1765)
     (1522,1767)(1524,1769)(1525,1770)(1527,1771)(1528,1772)(1529,1773)(1530,
     1774)(1532,1775)(1533,1776)(1535,1779)(1537,1781)(1538,1782)(1540,1783)
     (1541,1784)(1543,1787)(1544,1788)(1546,1789)(1547,1790)(1548,1792)(1549,
     1794)(1550,1796)(1551,1798)(1552,1799)(1553,1801)(1554,1803)(1555,1805)
     (1558,1808)(1559,1809)(1562,1811)(1563,1813)(1564,1815)(1565,1817)(1566,
     1818)(1567,1820)(1568,1822)(1569,1824)(1571,1827)(1574,1831)(1575,1832)
     (1576,1834)(1579,1837)(1580,1838)(1582,1839)(1583,1840)(1584,1842)(1585,
     1844)(1586,1846)(1587,1848)(1588,1849)(1590,1852)(1591,1854)(1592,1856)
     (1594,1859)(1596,1862)(1597,1864)(1599,1867)(1601,1870)(1604,1874)(1606,
     1877)(1607,1879)(1609,1882)(1611,1885)(1613,1888)(1618,1619)(1624,1625)
     (1630,1903)(1632,1905)(1634,1907)(1635,1908)(1637,1909)(1639,1911)(1640,
     1912)(1644,1916)(1646,1918)(1648,1920)(1650,1922)(1651,1923)(1653,1924)
     (1654,1925)(1656,1928)(1657,1929)(1659,1930)(1661,1931)(1663,1933)(1665,
     1935)(1666,1936)(1668,1937)(1669,1938)(1671,1941)(1672,1942)(1674,1943)
     (1675,1944)(1677,1947)(1679,1949)(1680,1950)(1682,1951)(1683,1952)(1685,
     1955)(1686,1956)(1688,1957)(1689,1958)(1690,1960)(1691,1962)(1692,1964)
     (1693,1966)(1694,1967)(1695,1969)(1696,1971)(1697,1973)(1700,1976)(1701,
     1977)(1703,1978)(1704,1979)(1705,1981)(1706,1983)(1707,1985)(1708,1987)
     (1709,1988)(1710,1989)(1712,1990)(1713,1991)(1715,1994)(1716,1995)(1718,
     1996)(1720,1998)(1721,2000)(1724,2003)(1725,2004)(1726,2006)(1727,2008)
     (1728,2010)(1729,2012)(1730,2013)(1731,2015)(1732,2017)(1733,2019)(1736,
     2023)(1738,2025)(1740,2028)(1745,1746)(1753,2039)(1758,1759)(1763,2047)
     (1764,1871)(1766,2050)(1768,2053)(1777,2062)(1778,2063)(1780,2065)(1785,
     1786)(1791,2076)(1793,2078)(1795,2080)(1797,2082)(1800,2084)(1802,2086)
     (1804,1806)(1807,2088)(1810,2090)(1812,2092)(1814,2094)(1816,2096)(1819,
     2099)(1821,2101)(1823,2103)(1825,2105)(1826,2106)(1828,2107)(1829,2108)
     (1830,2109)(1833,2113)(1835,2115)(1836,2116)(1841,2120)(1843,2122)(1845,
     2124)(1847,2126)(1850,2129)(1851,2130)(1853,2132)(1855,2134)(1857,2135)
     (1858,2136)(1860,2137)(1861,2138)(1863,2141)(1865,2143)(1866,2144)(1868,
     2145)(1869,2146)(1872,2149)(1873,2151)(1875,2154)(1876,2155)(1878,2158)
     (1880,2160)(1881,2161)(1883,2162)(1884,2163)(1886,2166)(1887,2167)(1889,
     2168)(1890,2169)(1891,2171)(1892,2173)(1893,2175)(1894,2177)(1895,2178)
     (1896,2180)(1897,2182)(1898,2184)(1899,2185)(1900,2186)(1901,2188)(1902,
     2190)(1904,2192)(1906,2195)(1910,2200)(1913,2204)(1914,2206)(1915,2208)
     (1917,2211)(1919,2214)(1921,2217)(1926,1927)(1932,2226)(1934,2224)(1939,
     1940)(1945,2236)(1946,2237)(1948,2240)(1953,1954)(1959,2251)(1961,2253)
     (1963,2255)(1965,2257)(1968,2260)(1970,2262)(1972,2264)(1974,2266)(1975,
     2267)(1980,2272)(1982,2274)(1984,2276)(1986,2278)(1992,1993)(1997,2288)
     (1999,2290)(2001,2292)(2002,2293)(2005,2297)(2007,2299)(2009,2301)(2011,
     2215)(2014,2305)(2016,2307)(2018,2309)(2020,2311)(2021,2312)(2022,2313)
     (2024,2314)(2026,2317)(2027,2318)(2029,2319)(2030,2320)(2031,2322)(2032,
     2323)(2034,2326)(2035,2327)(2036,2329)(2037,2331)(2038,2332)(2040,2333)
     (2041,2334)(2042,2336)(2043,2338)(2044,2339)(2045,2340)(2046,2342)(2048,
     2345)(2049,2346)(2051,2349)(2052,2350)(2054,2351)(2055,2352)(2056,2354)
     (2057,2356)(2058,2358)(2059,2360)(2060,2362)(2061,2364)(2064,2367)(2066,
     2368)(2067,2369)(2068,2371)(2069,2373)(2070,2375)(2071,2377)(2072,2378)
     (2073,2380)(2074,2382)(2075,2384)(2077,2387)(2079,2390)(2081,2393)(2083,
     2396)(2085,2398)(2087,2401)(2089,2404)(2091,2406)(2093,2409)(2095,2412)
     (2097,2415)(2098,2417)(2100,2419)(2102,2422)(2104,2425)(2110,2431)(2111,
     2432)(2112,2434)(2114,2437)(2117,2441)(2118,2443)(2119,2445)(2121,2448)
     (2123,2451)(2125,2454)(2127,2457)(2128,2459)(2131,2462)(2133,2465)(2139,
     2472)(2140,2473)(2142,2476)(2147,2148)(2150,2481)(2152,2483)(2153,2484)
     (2156,2488)(2157,2489)(2159,2492)(2164,2165)(2170,2503)(2172,2505)(2174,
     2507)(2176,2509)(2179,2512)(2181,2514)(2183,2516)(2187,2520)(2189,2522)
     (2191,2524)(2193,2527)(2194,2528)(2196,2529)(2197,2530)(2198,2532)(2199,
     2533)(2201,2534)(2203,2536)(2205,2539)(2207,2541)(2209,2542)(2210,2543)
     (2212,2544)(2213,2545)(2216,2548)(2218,2549)(2219,2551)(2220,2553)(2221,
     2554)(2222,2555)(2223,2557)(2225,2558)(2228,2561)(2229,2563)(2230,2565)
     (2231,2567)(2232,2568)(2233,2570)(2234,2572)(2235,2574)(2238,2577)(2239,
     2578)(2242,2579)(2243,2581)(2244,2583)(2245,2585)(2246,2587)(2247,2588)
     (2248,2590)(2250,2593)(2252,2596)(2254,2599)(2256,2602)(2258,2605)(2259,
     2607)(2261,2609)(2263,2611)(2265,2614)(2268,2618)(2269,2620)(2270,2622)
     (2271,2624)(2273,2627)(2275,2630)(2277,2633)(2279,2636)(2280,2638)(2281,
     2640)(2282,2642)(2283,2644)(2284,2646)(2285,2647)(2286,2649)(2287,2651)
     (2289,2654)(2291,2657)(2294,2659)(2295,2660)(2296,2662)(2298,2665)(2300,
     2668)(2302,2671)(2303,2673)(2304,2675)(2306,2678)(2308,2681)(2310,2684)
     (2315,2316)(2321,2693)(2324,2695)(2325,2696)(2328,2699)(2330,2701)(2335,
     2706)(2337,2708)(2341,2711)(2343,2713)(2344,2714)(2347,2348)(2353,2721)
     (2355,2723)(2357,2725)(2359,2727)(2361,2728)(2363,2730)(2365,2732)(2366,
     2707)(2370,2735)(2372,2737)(2374,2739)(2376,2741)(2379,2744)(2381,2746)
     (2383,2748)(2385,2750)(2386,2751)(2388,2752)(2389,2753)(2391,2756)(2392,
     2757)(2394,2758)(2395,2759)(2397,2760)(2399,2761)(2400,2762)(2402,2765)
     (2403,2766)(2405,2769)(2407,2770)(2408,2771)(2410,2774)(2411,2775)(2413,
     2776)(2414,2777)(2416,2780)(2418,2690)(2420,2782)(2421,2783)(2423,2786)
     (2424,2787)(2426,2788)(2427,2789)(2428,2791)(2429,2793)(2430,2795)(2433,
     2799)(2435,2446)(2436,2800)(2438,2801)(2439,2802)(2440,2804)(2442,2807)
     (2444,2809)(2447,2811)(2449,2812)(2450,2813)(2452,2816)(2453,2817)(2455,
     2818)(2456,2819)(2458,2822)(2460,2824)(2461,2825)(2463,2826)(2464,2827)
     (2466,2828)(2468,2830)(2469,2832)(2470,2834)(2471,2836)(2474,2839)(2475,
     2840)(2477,2841)(2478,2842)(2479,2844)(2480,2846)(2482,2848)(2485,2852)
     (2486,2853)(2487,2854)(2490,2857)(2491,2858)(2493,2859)(2494,2860)(2495,
     2862)(2496,2864)(2497,2866)(2498,2868)(2499,2869)(2500,2870)(2501,2872)
     (2502,2874)(2504,2877)(2506,2880)(2508,2883)(2510,2886)(2511,2888)(2513,
     2891)(2515,2892)(2517,2895)(2518,2805)(2519,2898)(2521,2901)(2523,2904)
     (2525,2526)(2531,2912)(2535,2916)(2537,2918)(2538,2919)(2540,2922)(2546,
     2547)(2550,2932)(2552,2934)(2556,2938)(2559,2560)(2562,2943)(2564,2945)
     (2566,2947)(2569,2950)(2571,2952)(2573,2954)(2575,2956)(2576,2957)(2580,
     2961)(2582,2963)(2584,2965)(2586,2967)(2589,2970)(2591,2972)(2592,2973)
     (2594,2975)(2595,2976)(2597,2977)(2598,2978)(2600,2981)(2601,2982)(2603,
     2983)(2604,2984)(2606,2987)(2608,2768)(2610,2989)(2612,2992)(2613,2993)
     (2615,2994)(2617,2996)(2619,2999)(2621,3001)(2623,3003)(2625,3005)(2626,
     3006)(2628,3007)(2629,3008)(2631,3011)(2632,3012)(2634,3013)(2635,3014)
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     (7826,7852)(7830,7855)(7832,7856)(7834,7858)(7835,7848)(7836,7859)(7839,
     7861)(7842,7863)(7844,7865)(7854,7868)(7857,7870)(7860,7872)(7862,7873)
     (7864,7875)(7866,7874)(7867,7871);