bin1 := (1,2)(3,5)(4,7)(6,10)(8,13)(11,17)(12,19)(14,22)(15,24)(16,26)(18,29)
     (20,32)(21,34)(23,37)(25,40)(27,43)(28,45)(30,48)(31,50)(33,53)(35,56)
     (36,58)(38,61)(39,63)(41,66)(42,68)(44,71)(46,74)(47,76)(49,79)(51,82)
     (52,84)(54,87)(55,89)(57,92)(59,95)(60,97)(62,100)(64,103)(65,105)(67,
     108)(69,111)(70,113)(72,116)(73,118)(75,121)(77,124)(78,126)(80,129)(81,
     131)(83,134)(85,137)(86,139)(88,142)(90,145)(91,147)(93,150)(94,152)(96,
     155)(98,158)(99,160)(101,163)(102,165)(104,168)(106,171)(107,173)(109,
     176)(110,178)(112,181)(114,184)(115,186)(117,189)(120,193)(122,196)(123,
     198)(125,201)(127,204)(128,206)(130,209)(132,212)(133,214)(135,217)(136,
     219)(138,222)(140,225)(141,227)(143,230)(144,232)(146,235)(148,238)(149,
     240)(151,243)(153,246)(154,248)(156,251)(157,253)(159,256)(161,259)(162,
     261)(164,264)(166,267)(167,269)(169,272)(170,274)(172,277)(174,280)(175,
     282)(177,285)(179,288)(180,290)(182,293)(183,295)(185,298)(187,301)(188,
     303)(190,306)(191,308)(192,310)(194,313)(195,315)(197,318)(199,321)(202,
     325)(203,327)(205,330)(207,333)(208,335)(210,338)(211,340)(213,343)(215,
     346)(216,348)(218,351)(220,354)(221,356)(223,359)(224,361)(226,364)(228,
     367)(229,369)(231,372)(233,375)(234,377)(236,380)(237,382)(239,385)(241,
     388)(242,390)(244,393)(245,395)(247,398)(249,401)(250,403)(252,406)(254,
     409)(255,411)(257,414)(258,416)(260,419)(262,422)(263,424)(265,427)(266,
     429)(268,432)(270,435)(271,437)(273,440)(275,443)(276,445)(278,448)(279,
     450)(281,453)(283,456)(284,458)(286,461)(287,463)(289,466)(291,469)(292,
     471)(294,474)(296,477)(297,479)(299,482)(300,484)(302,487)(304,490)(305,
     492)(307,495)(309,498)(311,501)(312,503)(314,506)(316,509)(317,511)(319,
     514)(320,516)(322,519)(323,521)(324,523)(326,526)(328,529)(329,531)(331,
     534)(332,536)(334,539)(336,542)(337,544)(339,547)(341,550)(342,552)(344,
     555)(345,557)(347,560)(349,563)(350,565)(352,568)(353,570)(355,573)(357,
     576)(358,578)(360,581)(362,584)(363,586)(365,589)(366,591)(368,594)(370,
     597)(371,599)(373,602)(374,604)(376,607)(378,610)(379,612)(381,615)(383,
     618)(384,620)(386,623)(387,625)(389,628)(391,631)(392,633)(394,636)(396,
     639)(397,641)(399,644)(400,646)(402,649)(404,652)(405,654)(407,657)(408,
     659)(410,662)(412,665)(413,667)(415,670)(417,673)(418,675)(420,678)(421,
     680)(423,683)(425,686)(426,688)(428,691)(430,694)(431,696)(433,699)(434,
     701)(436,704)(438,707)(439,709)(441,712)(442,714)(444,717)(446,720)(447,
     722)(449,725)(451,728)(452,730)(454,733)(455,735)(457,738)(459,741)(460,
     743)(462,746)(464,749)(465,751)(467,754)(468,756)(470,759)(472,762)(473,
     764)(475,767)(476,769)(478,772)(480,775)(481,777)(483,780)(485,783)(486,
     785)(488,788)(489,790)(491,793)(493,796)(494,798)(496,801)(497,803)(499,
     805)(500,807)(502,810)(504,813)(505,815)(507,818)(508,820)(510,823)(512,
     826)(513,828)(515,831)(517,834)(518,836)(520,839)(522,842)(524,845)(525,
     847)(527,850)(528,852)(530,855)(532,858)(533,860)(535,863)(537,866)(538,
     868)(540,871)(541,873)(543,876)(545,879)(546,881)(548,884)(549,885)(551,
     888)(553,891)(554,893)(556,896)(558,899)(559,901)(561,904)(562,906)(564,
     909)(566,912)(567,914)(569,917)(571,920)(572,922)(574,925)(575,927)(577,
     930)(579,933)(580,935)(582,938)(583,940)(585,943)(587,946)(588,948)(590,
     951)(592,954)(593,956)(595,959)(596,961)(598,964)(600,967)(601,969)(603,
     972)(605,975)(606,977)(608,980)(609,982)(611,985)(613,988)(614,990)(616,
     993)(617,995)(619,998)(621,1001)(622,1003)(624,1006)(626,1009)(627,1011)
     (629,1014)(630,1016)(632,1019)(634,1022)(635,1024)(637,1027)(638,1029)
     (640,1032)(642,1035)(643,1037)(645,1040)(647,1043)(648,1045)(650,1048)
     (651,1050)(653,1053)(655,1056)(656,1058)(658,1061)(660,1064)(661,1066)
     (663,1069)(664,1071)(668,1076)(669,1078)(671,1081)(672,1083)(674,1086)
     (676,1089)(677,1091)(679,1094)(681,1097)(682,1099)(684,1102)(685,1104)
     (687,1107)(689,1110)(690,1112)(692,1115)(693,1117)(695,1120)(697,1123)
     (698,1125)(700,1128)(702,1131)(703,1133)(705,1136)(706,1138)(708,1141)
     (710,1144)(711,1146)(713,1149)(715,1152)(716,1154)(718,1157)(719,1159)
     (721,1162)(723,1165)(724,1167)(726,1170)(727,1172)(729,1175)(731,1178)
     (732,1180)(734,1183)(736,1185)(737,1187)(739,1190)(740,1192)(742,1195)
     (744,1198)(745,1200)(747,1203)(748,1205)(750,1208)(752,1211)(753,1213)
     (755,1216)(757,1218)(758,1220)(760,1223)(761,1225)(763,1228)(765,1231)
     (766,1232)(768,1235)(770,1238)(771,1240)(773,1243)(774,1245)(776,1248)
     (778,1251)(779,1253)(781,1256)(782,1258)(784,1261)(786,1264)(787,1266)
     (789,1269)(791,1272)(792,1274)(794,1277)(795,1279)(797,1282)(799,1285)
     (800,1287)(802,1290)(804,1293)(806,1296)(808,1299)(809,1301)(811,1304)
     (812,1306)(814,1309)(816,1312)(817,1314)(819,1317)(821,1320)(822,1322)
     (824,1325)(825,1327)(827,1330)(829,1333)(830,1335)(832,1338)(833,1340)
     (835,1343)(837,1346)(838,1348)(840,1351)(841,1353)(843,1356)(844,1358)
     (846,1361)(848,1364)(849,1366)(851,1369)(853,1372)(854,1374)(856,1377)
     (857,1379)(861,1384)(862,1386)(864,1389)(865,1391)(867,1394)(869,1397)
     (870,1399)(872,1402)(874,1405)(875,1407)(877,1410)(878,1412)(880,1415)
     (882,1418)(883,1420)(886,1424)(887,1426)(889,1429)(890,1431)(892,1434)
     (894,1437)(895,1439)(897,1442)(898,1444)(900,1447)(902,1450)(903,1452)
     (905,1455)(907,1458)(908,1460)(910,1463)(911,1465)(913,1468)(915,1471)
     (916,1473)(918,1476)(919,1478)(921,1481)(923,1484)(924,1486)(926,1489)
     (928,1492)(929,1494)(931,1497)(932,1499)(934,1502)(936,1505)(937,1507)
     (939,1510)(941,1513)(942,1515)(944,1518)(945,1520)(947,1523)(949,1526)
     (950,1528)(952,1531)(953,1533)(955,1536)(957,1539)(958,1541)(960,1544)
     (962,1547)(963,1549)(965,1552)(966,1554)(968,1557)(970,1560)(971,1562)
     (973,1565)(974,1445)(976,1569)(978,1572)(979,1574)(981,1577)(983,1580)
     (984,1582)(986,1585)(987,1587)(989,1590)(991,1593)(992,1595)(994,1598)
     (996,1601)(997,1603)(999,1606)(1000,1608)(1002,1611)(1004,1614)(1005,
     1616)(1007,1619)(1008,1621)(1010,1624)(1012,1627)(1013,1629)(1015,1632)
     (1017,1635)(1018,1637)(1020,1640)(1021,1642)(1023,1645)(1025,1648)(1026,
     1650)(1028,1653)(1030,1656)(1031,1658)(1033,1661)(1034,1663)(1036,1666)
     (1038,1669)(1039,1671)(1041,1674)(1042,1676)(1044,1679)(1046,1682)(1047,
     1684)(1049,1687)(1051,1690)(1052,1692)(1054,1695)(1055,1697)(1057,1700)
     (1059,1703)(1060,1705)(1062,1708)(1063,1710)(1065,1713)(1067,1716)(1068,
     1718)(1070,1721)(1072,1724)(1073,1726)(1074,1728)(1075,1730)(1077,1733)
     (1079,1736)(1080,1738)(1082,1741)(1084,1744)(1085,1746)(1087,1749)(1088,
     1751)(1090,1754)(1092,1757)(1093,1759)(1095,1762)(1096,1764)(1098,1767)
     (1100,1770)(1101,1772)(1103,1775)(1105,1778)(1106,1780)(1108,1783)(1109,
     1785)(1111,1788)(1113,1791)(1114,1793)(1116,1796)(1118,1799)(1119,1801)
     (1121,1804)(1122,1806)(1124,1809)(1126,1812)(1127,1814)(1129,1817)(1130,
     1819)(1132,1822)(1134,1825)(1135,1827)(1137,1830)(1139,1833)(1140,1835)
     (1142,1838)(1143,1840)(1145,1843)(1147,1846)(1148,1848)(1150,1851)(1151,
     1852)(1153,1855)(1155,1858)(1156,1860)(1158,1863)(1160,1866)(1161,1868)
     (1163,1871)(1164,1873)(1166,1876)(1168,1879)(1169,1881)(1171,1884)(1173,
     1887)(1174,1889)(1176,1892)(1177,1894)(1179,1897)(1181,1900)(1182,1902)
     (1184,1905)(1186,1908)(1188,1911)(1189,1913)(1191,1916)(1193,1919)(1194,
     1921)(1196,1924)(1197,1926)(1199,1929)(1201,1932)(1202,1934)(1204,1937)
     (1206,1938)(1207,1940)(1209,1943)(1210,1945)(1212,1948)(1214,1951)(1215,
     1953)(1217,1956)(1219,1959)(1221,1962)(1222,1964)(1224,1967)(1226,1970)
     (1227,1972)(1229,1975)(1230,1977)(1233,1981)(1234,1982)(1236,1985)(1237,
     1987)(1239,1990)(1241,1993)(1242,1995)(1244,1998)(1246,2000)(1247,2002)
     (1249,2005)(1250,2007)(1252,2010)(1254,2013)(1255,2015)(1257,2018)(1259,
     2021)(1260,2023)(1262,2026)(1263,2028)(1265,2031)(1267,2034)(1268,2036)
     (1270,2039)(1271,2041)(1273,2044)(1275,2047)(1276,2049)(1278,2052)(1280,
     2055)(1281,2057)(1283,2060)(1284,2062)(1286,2065)(1288,2068)(1289,2070)
     (1291,2073)(1292,2075)(1294,2077)(1295,2079)(1297,2082)(1298,2084)(1300,
     2087)(1302,2090)(1303,2092)(1305,2095)(1307,2098)(1308,2100)(1310,2103)
     (1311,2105)(1313,2108)(1315,2110)(1316,2112)(1318,2115)(1319,2117)(1321,
     2120)(1323,2123)(1324,2125)(1326,2128)(1328,2131)(1329,2133)(1331,2136)
     (1332,2138)(1334,2141)(1336,2144)(1337,2146)(1339,2149)(1341,2152)(1342,
     2154)(1344,2157)(1345,2159)(1347,2162)(1349,2165)(1350,2167)(1352,2170)
     (1354,2173)(1355,2175)(1357,2178)(1359,2181)(1360,2183)(1362,2186)(1363,
     2188)(1365,2191)(1367,2194)(1368,2196)(1370,2199)(1371,2201)(1373,2204)
     (1375,2207)(1376,2209)(1378,2212)(1380,2215)(1381,2217)(1382,2219)(1383,
     2221)(1385,2224)(1387,2227)(1388,2229)(1390,2232)(1392,2235)(1393,2237)
     (1395,2240)(1396,2242)(1398,2245)(1400,2248)(1401,2250)(1403,2253)(1404,
     2255)(1406,2258)(1408,2261)(1409,2263)(1411,2266)(1413,2269)(1414,2271)
     (1416,2274)(1417,2276)(1419,2279)(1421,2282)(1422,2284)(1423,2286)(1425,
     2289)(1427,2292)(1428,2294)(1430,2297)(1432,2300)(1433,2302)(1435,2305)
     (1436,2307)(1438,2310)(1440,2313)(1441,2315)(1443,2318)(1446,2322)(1448,
     2325)(1449,2327)(1451,2330)(1453,2333)(1454,2335)(1456,2338)(1457,2340)
     (1459,2343)(1461,2346)(1462,2348)(1464,2351)(1466,1870)(1467,2355)(1469,
     2358)(1470,2360)(1472,2363)(1474,2366)(1475,2368)(1477,2371)(1479,2374)
     (1480,2376)(1482,2379)(1483,2381)(1485,2384)(1487,2387)(1488,2389)(1490,
     2392)(1491,2394)(1493,2397)(1495,2400)(1496,2402)(1498,2405)(1500,2407)
     (1501,2409)(1503,2412)(1504,2414)(1506,2417)(1508,2420)(1509,2422)(1511,
     2425)(1512,2427)(1514,2430)(1516,2433)(1517,2435)(1519,2438)(1521,2441)
     (1522,2443)(1524,2446)(1525,2448)(1527,2451)(1529,2454)(1530,2456)(1532,
     2459)(1534,2462)(1535,2464)(1537,2467)(1538,2469)(1540,2472)(1542,2475)
     (1543,2477)(1545,2479)(1546,2481)(1548,2484)(1550,2487)(1551,2489)(1553,
     2491)(1555,2494)(1556,2496)(1558,2499)(1559,2501)(1561,2504)(1563,2507)
     (1564,2509)(1566,2512)(1567,2514)(1568,2516)(1570,2519)(1571,2521)(1573,
     2524)(1575,2527)(1576,2529)(1578,2532)(1579,2534)(1581,2537)(1583,2540)
     (1584,2542)(1586,2545)(1588,2548)(1589,2550)(1591,2553)(1592,2555)(1594,
     2558)(1596,2561)(1597,2563)(1599,2566)(1600,2568)(1602,2571)(1604,2574)
     (1605,2576)(1607,2579)(1609,2582)(1610,2584)(1612,2587)(1613,2589)(1615,
     2592)(1617,2595)(1618,2597)(1620,2600)(1622,2603)(1623,2605)(1625,2608)
     (1626,2610)(1628,2613)(1630,2616)(1631,2618)(1633,2621)(1634,2623)(1636,
     2626)(1638,2628)(1639,2630)(1641,2633)(1643,2636)(1644,2638)(1646,2641)
     (1647,2643)(1649,2646)(1651,2649)(1652,2651)(1654,2654)(1655,2656)(1657,
     2659)(1659,2662)(1660,2664)(1662,2667)(1664,2670)(1665,2672)(1667,2675)
     (1668,2677)(1670,2680)(1672,2683)(1673,2684)(1675,2687)(1677,2690)(1678,
     2692)(1680,2695)(1681,2697)(1683,2700)(1685,2703)(1686,2705)(1688,2708)
     (1689,2710)(1691,2713)(1693,2716)(1694,2718)(1696,2721)(1698,2724)(1699,
     2726)(1701,2729)(1702,2730)(1704,2732)(1706,2735)(1707,2737)(1709,2740)
     (1711,2743)(1712,2745)(1714,2748)(1715,2750)(1717,2752)(1719,2755)(1720,
     2757)(1722,2760)(1723,2762)(1725,2765)(1727,2768)(1729,2771)(1731,2774)
     (1732,2776)(1734,2779)(1735,2781)(1737,2784)(1739,2786)(1740,2788)(1742,
     2791)(1743,2793)(1745,2796)(1747,2799)(1748,2801)(1750,2804)(1752,2807)
     (1753,2809)(1755,2812)(1756,2814)(1758,2817)(1760,2820)(1761,2822)(1763,
     2825)(1765,2828)(1766,2830)(1768,2833)(1769,2835)(1771,2838)(1773,2841)
     (1774,2843)(1776,2846)(1777,2848)(1779,2851)(1781,2854)(1782,2856)(1784,
     2859)(1786,2862)(1787,2864)(1789,2867)(1790,2869)(1792,2872)(1794,2875)
     (1795,2877)(1797,2880)(1798,2882)(1800,2885)(1802,2888)(1803,2890)(1805,
     2893)(1807,2896)(1808,2898)(1810,2901)(1811,2903)(1813,2906)(1815,2909)
     (1816,2910)(1818,2913)(1820,2916)(1821,2918)(1823,2921)(1824,2923)(1826,
     2926)(1828,2929)(1829,2931)(1831,2934)(1832,2936)(1834,2939)(1836,2942)
     (1837,2944)(1839,2947)(1841,2950)(1842,2952)(1844,2955)(1845,2957)(1847,
     2960)(1849,2963)(1850,2965)(1853,2969)(1854,2894)(1856,2973)(1857,2975)
     (1859,2978)(1861,2981)(1862,2983)(1864,2986)(1865,2988)(1867,2991)(1869,
     2994)(1872,2998)(1874,3001)(1875,3003)(1877,3006)(1878,3008)(1880,3011)
     (1882,3014)(1883,3016)(1885,3019)(1886,3021)(1888,3024)(1890,3027)(1891,
     3029)(1893,3032)(1895,3035)(1896,3037)(1898,3040)(1899,3042)(1901,3045)
     (1903,3048)(1904,3050)(1906,3053)(1907,3055)(1909,3058)(1910,3060)(1912,
     3063)(1914,3066)(1915,3068)(1917,3071)(1918,3073)(1920,3076)(1922,3079)
     (1923,3081)(1925,3084)(1927,3087)(1928,3089)(1930,3092)(1931,3094)(1933,
     3097)(1935,3100)(1936,3102)(1939,3106)(1941,3109)(1942,3111)(1944,3114)
     (1946,3117)(1947,3119)(1949,3122)(1950,3124)(1952,3127)(1954,3130)(1955,
     3132)(1957,3135)(1958,3137)(1960,3140)(1961,3142)(1963,3145)(1965,3148)
     (1966,3150)(1968,3153)(1969,3155)(1971,3158)(1973,3161)(1974,3163)(1976,
     3166)(1978,3168)(1979,3170)(1980,3172)(1983,3176)(1984,3178)(1986,3181)
     (1988,3184)(1989,3186)(1991,3189)(1992,3191)(1994,3194)(1996,3197)(1997,
     3199)(1999,3202)(2001,3205)(2003,3208)(2004,3210)(2006,3213)(2008,3216)
     (2009,3218)(2011,3221)(2012,3223)(2014,3226)(2016,3229)(2017,3231)(2019,
     3233)(2020,3235)(2022,3238)(2024,3241)(2025,3243)(2027,3246)(2029,3249)
     (2030,3251)(2032,3254)(2033,3256)(2035,3259)(2037,3262)(2038,3264)(2040,
     3267)(2042,3270)(2043,3272)(2045,3275)(2046,3277)(2048,3280)(2050,3283)
     (2051,3285)(2053,3288)(2054,3290)(2056,3293)(2058,3296)(2059,3298)(2061,
     3301)(2063,3304)(2064,3306)(2066,3309)(2067,3311)(2069,3314)(2071,3317)
     (2072,3318)(2074,3321)(2076,3324)(2078,3327)(2080,3330)(2081,3332)(2083,
     3335)(2085,3338)(2086,3340)(2088,3343)(2089,3345)(2091,3348)(2093,3351)
     (2094,3353)(2096,3356)(2097,3358)(2099,3361)(2101,3364)(2102,3366)(2104,
     3368)(2106,3371)(2107,3373)(2109,3376)(2111,3379)(2113,3382)(2114,3384)
     (2116,3387)(2118,3390)(2119,3392)(2121,3395)(2122,3397)(2124,3400)(2126,
     3403)(2127,3405)(2129,3408)(2130,3410)(2132,3413)(2134,3416)(2135,3418)
     (2137,3421)(2139,3424)(2140,3426)(2142,3429)(2143,3431)(2145,3434)(2147,
     3437)(2148,3439)(2150,3442)(2151,3444)(2153,3447)(2155,3450)(2156,3452)
     (2158,3455)(2160,3458)(2161,3460)(2163,3463)(2164,3465)(2166,3468)(2168,
     2777)(2169,3472)(2171,3475)(2172,3477)(2174,3480)(2176,3483)(2177,3485)
     (2179,3488)(2180,3490)(2182,3493)(2184,2758)(2185,3497)(2187,3500)(2189,
     3503)(2190,3505)(2192,3508)(2193,3509)(2195,3512)(2197,3515)(2198,3517)
     (2200,3520)(2202,3523)(2203,3525)(2205,3528)(2206,3530)(2208,3533)(2210,
     3536)(2211,3538)(2213,3541)(2214,3542)(2216,3545)(2218,3548)(2220,3551)
     (2222,3554)(2223,3555)(2225,3558)(2226,3560)(2228,3563)(2230,3566)(2231,
     3568)(2233,3570)(2234,3572)(2236,3575)(2238,3578)(2239,3580)(2241,3583)
     (2243,3586)(2244,3588)(2246,3590)(2247,3592)(2249,3595)(2251,3598)(2252,
     3600)(2254,3603)(2256,3606)(2257,3608)(2259,3611)(2260,3613)(2262,3616)
     (2264,3618)(2265,3620)(2267,3623)(2268,3625)(2270,3628)(2272,3631)(2273,
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