bin1 := (2,3)(4,6)(7,10)(8,12)(9,14)(11,17)(13,20)(16,24)(18,27)(21,31)(22,33)
     (26,38)(28,41)(34,46)(35,48)(36,49)(37,51)(39,53)(42,54)(43,56)(44,58)
     (47,62)(50,66)(55,72)(57,75)(59,78)(60,80)(61,82)(63,85)(64,73)(65,88)
     (67,91)(68,76)(69,94)(70,79)(77,97)(83,104)(84,106)(86,109)(87,110)(90,
     113)(92,116)(95,120)(98,123)(100,126)(101,128)(102,130)(103,131)(107,136)
     (111,139)(112,141)(115,145)(118,148)(119,149)(121,151)(122,153)(125,156)
     (129,161)(132,165)(133,167)(140,174)(142,177)(143,178)(144,180)(146,183)
     (147,184)(150,188)(154,192)(155,193)(157,196)(158,198)(160,200)(164,205)
     (166,208)(169,212)(170,214)(171,216)(172,218)(173,220)(175,223)(179,228)
     (182,232)(186,237)(187,239)(189,242)(190,244)(191,246)(195,249)(197,252)
     (199,255)(201,258)(202,260)(203,262)(204,235)(206,266)(207,268)(209,271)
     (213,273)(217,278)(222,284)(224,287)(227,291)(229,294)(230,296)(231,298)
     (233,301)(236,304)(240,309)(241,311)(247,318)(248,320)(250,323)(251,325)
     (257,330)(259,333)(261,336)(263,339)(264,341)(265,343)(270,348)(272,351)
     (274,354)(275,356)(276,358)(277,360)(279,363)(280,364)(281,366)(282,368)
     (286,373)(288,376)(289,378)(290,315)(292,382)(295,384)(297,387)(299,390)
     (305,393)(306,395)(307,397)(310,401)(312,404)(313,406)(314,407)(317,334)
     (319,413)(322,416)(324,419)(326,421)(327,423)(328,425)(329,427)(331,429)
     (332,431)(335,433)(337,436)(338,438)(340,441)(342,443)(344,445)(345,447)
     (346,448)(350,453)(352,456)(353,457)(355,460)(359,465)(361,468)(365,472)
     (369,476)(370,474)(371,479)(372,481)(374,484)(377,486)(379,487)(383,490)
     (386,494)(388,497)(391,500)(396,506)(398,509)(399,511)(400,513)(403,515)
     (405,518)(408,522)(409,524)(410,526)(411,527)(412,478)(414,531)(415,533)
     (417,536)(420,540)(424,545)(426,548)(428,550)(430,553)(434,557)(437,561)
     (439,564)(440,455)(444,570)(446,572)(449,576)(450,578)(451,580)(454,584)
     (458,589)(459,591)(461,507)(462,593)(464,596)(466,473)(469,566)(470,587)
     (471,603)(477,610)(480,614)(482,617)(485,621)(488,625)(489,626)(491,628)
     (492,629)(493,529)(496,633)(499,623)(502,638)(503,639)(504,590)(505,641)
     (508,643)(512,646)(514,648)(516,650)(519,654)(520,655)(523,630)(525,659)
     (528,663)(534,666)(537,670)(542,674)(547,675)(549,676)(551,679)(554,683)
     (559,688)(560,690)(562,604)(563,583)(568,699)(569,701)(574,707)(577,711)
     (581,716)(588,724)(592,728)(594,731)(595,733)(597,691)(598,737)(600,739)
     (601,741)(602,743)(605,747)(606,749)(607,750)(608,752)(609,754)(611,757)
     (613,759)(618,672)(619,766)(620,768)(622,771)(624,774)(631,781)(632,783)
     (634,786)(635,788)(637,790)(640,794)(642,796)(644,673)(647,800)(651,804)
     (652,806)(653,808)(656,812)(657,751)(658,815)(664,820)(665,742)(667,824)
     (668,826)(669,828)(671,830)(677,836)(680,840)(681,842)(682,844)(684,847)
     (685,848)(686,850)(692,856)(693,858)(694,859)(695,861)(696,863)(697,865)
     (702,870)(703,872)(704,874)(705,876)(708,879)(712,884)(713,886)(714,888)
     (717,891)(718,893)(719,895)(720,897)(722,900)(723,902)(725,905)(727,878)
     (729,909)(734,914)(735,916)(736,918)(738,921)(744,928)(745,929)(748,933)
     (753,938)(755,941)(758,945)(760,947)(761,949)(762,951)(765,955)(767,957)
     (770,961)(773,964)(775,967)(776,969)(778,972)(779,974)(780,935)(782,978)
     (785,982)(789,986)(791,988)(792,990)(793,992)(795,968)(797,997)(802,1002)
     (803,1004)(807,1009)(809,1012)(810,1014)(811,1016)(816,1022)(817,1024)
     (818,1026)(819,996)(821,1030)(822,1032)(823,835)(827,1036)(831,1041)(838,
     1046)(839,1048)(843,1053)(845,1056)(846,1058)(849,1061)(851,1064)(852,
     1066)(853,1068)(854,1070)(857,1073)(864,1080)(866,1083)(867,1084)(868,
     1085)(869,1087)(873,931)(875,1094)(877,1097)(880,1101)(881,1103)(885,
     1108)(887,1111)(889,1113)(890,1115)(892,1118)(894,1121)(896,1123)(898,
     1126)(903,1132)(906,1136)(907,1138)(910,1141)(911,1142)(912,1144)(917,
     1147)(919,1086)(920,1150)(922,1153)(923,1155)(924,1157)(926,1159)(927,
     1161)(930,1165)(934,1008)(936,1001)(937,1172)(939,1175)(943,1180)(944,
     1182)(946,1184)(948,1187)(953,1193)(958,1197)(959,1199)(960,1201)(962,
     1204)(963,1206)(965,1208)(966,1210)(970,1043)(971,1215)(973,1218)(975,
     1221)(977,1224)(979,1227)(980,1229)(983,1233)(985,1235)(987,1220)(991,
     1069)(993,1243)(994,1245)(998,1249)(999,1162)(1000,1251)(1003,1255)(1005,
     1047)(1006,1259)(1011,1265)(1013,1268)(1015,1271)(1017,1274)(1018,1276)
     (1019,1278)(1020,1280)(1021,1282)(1023,1285)(1028,1289)(1031,1293)(1033,
     1295)(1034,1297)(1035,1299)(1037,1302)(1042,1308)(1044,1310)(1049,1315)
     (1050,1317)(1052,1320)(1055,1324)(1057,1327)(1059,1329)(1060,1331)(1062,
     1334)(1067,1339)(1071,1344)(1074,1348)(1075,1350)(1076,1352)(1077,1354)
     (1078,1356)(1081,1360)(1082,1361)(1088,1365)(1089,1367)(1090,1368)(1092,
     1371)(1093,1373)(1098,1377)(1100,1380)(1102,1383)(1104,1385)(1105,1386)
     (1106,1388)(1107,1389)(1109,1391)(1110,1392)(1112,1304)(1116,1399)(1120,
     1403)(1122,1405)(1124,1408)(1127,1412)(1128,1414)(1129,1415)(1131,1417)
     (1139,1422)(1140,1424)(1143,1428)(1145,1341)(1148,1434)(1152,1438)(1156,
     1443)(1158,1446)(1164,1453)(1166,1456)(1168,1393)(1169,1460)(1170,1462)
     (1171,1200)(1173,1466)(1174,1468)(1176,1471)(1177,1473)(1178,1475)(1183,
     1480)(1185,1483)(1188,1487)(1189,1489)(1190,1491)(1191,1493)(1192,1495)
     (1194,1497)(1195,1499)(1196,1501)(1202,1508)(1203,1510)(1205,1513)(1207,
     1516)(1209,1519)(1211,1463)(1212,1523)(1214,1526)(1216,1514)(1219,1531)
     (1225,1538)(1228,1542)(1230,1545)(1234,1548)(1237,1552)(1238,1554)(1239,
     1556)(1240,1430)(1242,1559)(1244,1562)(1246,1564)(1248,1566)(1252,1570)
     (1253,1572)(1254,1574)(1256,1577)(1257,1579)(1258,1581)(1260,1584)(1261,
     1287)(1262,1586)(1263,1587)(1267,1591)(1269,1529)(1270,1569)(1272,1597)
     (1273,1599)(1275,1601)(1279,1606)(1283,1610)(1284,1612)(1286,1509)(1288,
     1616)(1290,1619)(1294,1623)(1296,1625)(1298,1418)(1301,1629)(1303,1632)
     (1305,1634)(1309,1637)(1311,1639)(1312,1641)(1313,1643)(1314,1645)(1316,
     1648)(1318,1651)(1319,1337)(1321,1654)(1322,1656)(1323,1658)(1326,1662)
     (1328,1665)(1332,1670)(1333,1672)(1335,1675)(1336,1677)(1338,1678)(1340,
     1681)(1342,1683)(1343,1684)(1345,1687)(1346,1689)(1347,1691)(1351,1696)
     (1353,1699)(1355,1701)(1357,1704)(1358,1705)(1359,1706)(1363,1710)(1364,
     1712)(1366,1715)(1372,1721)(1375,1724)(1376,1726)(1378,1729)(1379,1731)
     (1382,1735)(1395,1746)(1396,1747)(1397,1749)(1400,1752)(1401,1753)(1402,
     1755)(1404,1742)(1407,1759)(1410,1762)(1411,1666)(1413,1766)(1416,1768)
     (1419,1770)(1420,1772)(1421,1774)(1423,1777)(1426,1781)(1429,1783)(1432,
     1787)(1433,1789)(1435,1792)(1436,1794)(1437,1795)(1439,1798)(1440,1800)
     (1441,1802)(1442,1804)(1444,1565)(1445,1615)(1447,1810)(1448,1622)(1449,
     1813)(1451,1816)(1452,1818)(1455,1822)(1457,1825)(1459,1827)(1464,1613)
     (1465,1832)(1469,1837)(1474,1841)(1476,1844)(1478,1847)(1479,1849)(1481,
     1852)(1484,1856)(1488,1861)(1490,1864)(1496,1871)(1500,1875)(1502,1877)
     (1503,1879)(1504,1881)(1505,1882)(1506,1884)(1507,1886)(1511,1891)(1512,
     1893)(1515,1870)(1518,1899)(1520,1901)(1521,1902)(1524,1906)(1525,1907)
     (1527,1909)(1528,1911)(1530,1914)(1532,1917)(1533,1918)(1534,1920)(1536,
     1923)(1539,1926)(1540,1928)(1541,1930)(1543,1933)(1549,1939)(1557,1624)
     (1558,1707)(1560,1949)(1563,1952)(1567,1956)(1571,1961)(1573,1887)(1575,
     1966)(1576,1968)(1580,1972)(1582,1974)(1585,1978)(1588,1982)(1589,1983)
     (1590,1985)(1592,1988)(1594,1991)(1596,1994)(1598,1997)(1602,2002)(1603,
     2004)(1604,2006)(1608,2009)(1609,2010)(1611,2012)(1614,2016)(1617,2019)
     (1618,2021)(1626,2027)(1627,2029)(1628,2031)(1631,2035)(1633,2037)(1635,
     2039)(1642,2046)(1644,2048)(1646,2050)(1647,2052)(1652,2056)(1653,2058)
     (1659,2065)(1660,2066)(1661,2068)(1664,2072)(1667,2076)(1668,2078)(1669,
     2080)(1674,2001)(1676,1935)(1680,2089)(1682,2092)(1686,2096)(1688,2099)
     (1690,2102)(1692,2105)(1693,2107)(1694,2109)(1695,2111)(1697,1929)(1700,
     2116)(1703,2120)(1709,2126)(1711,2129)(1713,2132)(1716,2136)(1717,1723)
     (1718,1958)(1722,2139)(1725,2143)(1727,2146)(1730,2150)(1732,2153)(1733,
     2154)(1734,2156)(1736,2159)(1737,2161)(1738,1922)(1740,1946)(1745,2167)
     (1748,2170)(1750,2173)(1751,1932)(1757,2178)(1758,2180)(1760,2007)(1761,
     2183)(1764,2186)(1771,2189)(1773,2191)(1776,2195)(1778,2198)(1779,2200)
     (1784,2137)(1785,2206)(1786,2208)(1788,2210)(1790,2213)(1791,2215)(1793,
     2218)(1796,2221)(1797,2223)(1801,1812)(1803,2228)(1805,2230)(1808,2233)
     (1817,2202)(1819,2130)(1820,2242)(1824,2247)(1826,2250)(1828,2253)(1829,
     2255)(1830,2256)(1831,2258)(1833,2260)(1834,2262)(1835,2264)(1838,2268)
     (1839,1868)(1840,2271)(1842,2274)(1845,2277)(1850,2282)(1851,2284)(1853,
     2090)(1854,2288)(1855,2290)(1857,2293)(1858,2295)(1863,2299)(1865,2241)
     (1866,2303)(1867,2305)(1869,2308)(1873,2313)(1874,2314)(1876,2317)(1883,
     2323)(1885,1904)(1888,2329)(1890,2331)(1895,2337)(1897,2340)(1903,2345)
     (1912,2352)(1915,2355)(1919,2360)(1921,2363)(1927,2369)(1934,2003)(1940,
     2378)(1941,2379)(1943,2382)(1945,2384)(1950,2388)(1951,2390)(1953,2393)
     (1954,2395)(1955,2396)(1957,2398)(1959,2400)(1962,2403)(1963,2405)(1965,
     2407)(1967,2410)(1969,2412)(1970,2008)(1971,2414)(1973,2417)(1975,2141)
     (1976,2421)(1977,2423)(1979,2425)(1980,2427)(1984,2432)(1993,2440)(1996,
     2444)(1998,2447)(2000,2084)(2005,2453)(2011,2459)(2013,2462)(2014,2251)
     (2017,2467)(2020,2471)(2022,2474)(2023,2476)(2025,2478)(2030,2483)(2032,
     2486)(2033,2488)(2034,2489)(2036,2491)(2040,2496)(2041,2498)(2042,2493)
     (2043,2499)(2044,2500)(2045,2502)(2047,2505)(2049,2507)(2051,2510)(2053,
     2511)(2057,2515)(2059,2518)(2060,2520)(2062,2522)(2063,2524)(2064,2525)
     (2067,2527)(2070,2531)(2074,2536)(2079,2541)(2081,2544)(2082,2546)(2083,
     2548)(2087,2553)(2091,2557)(2093,2374)(2094,2560)(2095,2562)(2097,2565)
     (2098,2567)(2100,2570)(2101,2572)(2103,2575)(2104,2576)(2106,2579)(2108,
     2582)(2110,2585)(2113,2588)(2117,2592)(2118,2594)(2121,2558)(2122,2599)
     (2123,2601)(2125,2603)(2127,2606)(2128,2608)(2138,2618)(2140,2621)(2142,
     2623)(2147,2629)(2148,2631)(2149,2633)(2155,2638)(2158,2642)(2160,2342)
     (2164,2646)(2165,2648)(2166,2650)(2169,2653)(2175,2659)(2177,2662)(2179,
     2665)(2182,2669)(2185,2673)(2190,2676)(2192,2679)(2193,2680)(2197,2685)
     (2199,2688)(2201,2690)(2204,2419)(2207,2695)(2211,2700)(2212,2702)(2214,
     2705)(2216,2708)(2219,2712)(2222,2714)(2224,2716)(2225,2718)(2226,2720)
     (2227,2721)(2231,2726)(2232,2728)(2235,2731)(2236,2732)(2237,2734)(2238,
     2735)(2240,2738)(2243,2742)(2244,2744)(2245,2746)(2248,2750)(2249,2752)
     (2252,2754)(2254,2757)(2257,2761)(2259,2764)(2261,2767)(2263,2770)(2265,
     2773)(2269,2778)(2270,2780)(2273,2784)(2275,2787)(2276,2789)(2278,2791)
     (2279,2792)(2280,2794)(2281,2796)(2283,2799)(2285,2801)(2286,2803)(2287,
     2805)(2289,2808)(2292,2812)(2294,2815)(2296,2818)(2297,2820)(2298,2320)
     (2300,2824)(2301,2826)(2304,2829)(2306,2832)(2309,2835)(2310,2837)(2311,
     2839)(2312,2841)(2316,2845)(2318,2848)(2319,2850)(2322,2854)(2324,2857)
     (2326,2860)(2327,2753)(2328,2350)(2330,2864)(2332,2867)(2333,2869)(2334,
     2871)(2335,2873)(2336,2875)(2339,2879)(2341,2882)(2344,2884)(2346,2887)
     (2347,2889)(2348,2890)(2349,2512)(2351,2893)(2353,2896)(2359,2900)(2361,
     2902)(2364,2906)(2366,2908)(2370,2912)(2371,2914)(2372,2916)(2375,2919)
     (2380,2924)(2389,2931)(2391,2934)(2392,2936)(2401,2943)(2402,2945)(2406,
     2950)(2409,2954)(2411,2957)(2413,2960)(2416,2964)(2418,2966)(2422,2969)
     (2426,2974)(2428,2977)(2430,2457)(2431,2980)(2433,2983)(2434,2985)(2435,
     2497)(2436,2987)(2437,2989)(2438,2991)(2439,2992)(2442,2995)(2446,3000)
     (2448,3003)(2449,3004)(2452,3006)(2454,2758)(2455,2816)(2458,3011)(2460,
     2513)(2463,3015)(2464,2763)(2469,3020)(2473,3025)(2475,3028)(2479,3032)
     (2480,3034)(2481,3036)(2482,3038)(2485,3042)(2487,3045)(2490,3048)(2492,
     3051)(2494,3053)(2495,3055)(2501,3061)(2503,3064)(2506,3068)(2508,3071)
     (2514,3075)(2516,3078)(2517,3080)(2519,3083)(2521,3086)(2526,3090)(2528,
     3093)(2529,3095)(2530,3097)(2532,3100)(2533,3102)(2534,3103)(2535,3105)
     (2537,3107)(2538,3108)(2540,3111)(2542,3114)(2543,3115)(2545,3118)(2550,
     3124)(2552,2939)(2554,2674)(2555,2595)(2556,3129)(2559,3133)(2561,3136)
     (2563,3139)(2564,3140)(2568,3145)(2571,3147)(2573,3149)(2577,3154)(2580,
     3158)(2581,3160)(2586,3165)(2590,3170)(2591,3172)(2593,3175)(2596,3179)
     (2597,3181)(2598,3183)(2600,3186)(2602,3187)(2604,3190)(2605,3191)(2607,
     3163)(2610,3197)(2611,3199)(2612,3200)(2613,3202)(2614,2625)(2616,3205)
     (2617,3207)(2622,3213)(2624,3216)(2626,3219)(2627,3221)(2628,3223)(2630,
     3225)(2632,3228)(2634,3230)(2637,3234)(2639,3237)(2640,3239)(2641,3240)
     (2643,3242)(2645,3231)(2654,3250)(2655,3252)(2656,2671)(2657,3255)(2658,
     3209)(2660,3259)(2661,3261)(2663,3264)(2664,3266)(2666,3269)(2667,3271)
     (2670,3275)(2677,2932)(2681,3284)(2683,3286)(2684,3288)(2687,3282)(2691,
     3293)(2692,3295)(2693,3079)(2694,3297)(2696,3279)(2697,3300)(2699,3302)
     (2701,2745)(2703,3306)(2704,3308)(2706,3311)(2713,3318)(2719,3324)(2723,
     3317)(2730,3335)(2736,3338)(2737,3340)(2739,3343)(2740,3211)(2743,3348)
     (2747,3353)(2748,3355)(2749,3357)(2751,3360)(2755,3364)(2756,3365)(2759,
     2918)(2762,3371)(2765,3375)(2768,3379)(2769,3381)(2771,3384)(2772,3350)
     (2774,3388)(2776,3390)(2777,3392)(2779,3395)(2781,3398)(2782,3400)(2786,
     3404)(2788,3007)(2795,3411)(2797,3413)(2800,3416)(2807,3422)(2810,3426)
     (2811,3428)(2813,3431)(2817,3433)(2821,3438)(2823,3441)(2825,3444)(2827,
     3447)(2828,3449)(2830,3451)(2834,3455)(2840,3461)(2842,3464)(2843,3466)
     (2846,3468)(2847,3470)(2849,3473)(2851,3475)(2852,3477)(2853,3479)(2855,
     3482)(2856,3484)(2858,3462)(2859,3487)(2861,3490)(2862,3491)(2865,3495)
     (2866,3497)(2874,3505)(2876,3508)(2877,3509)(2878,3511)(2880,3513)(2883,
     3516)(2886,3520)(2888,2999)(2891,3524)(2892,3526)(2894,3039)(2895,3530)
     (2897,3532)(2898,3534)(2901,3536)(2903,3515)(2907,3541)(2920,3550)(2921,
     3552)(2922,3486)(2925,3557)(2928,3499)(2929,3298)(2933,3561)(2935,3564)
     (2937,3566)(2938,3546)(2940,3570)(2941,3572)(2942,3574)(2944,3577)(2946,
     3157)(2947,3581)(2949,3073)(2952,3586)(2956,3591)(2958,3594)(2962,3599)
     (2963,3601)(2967,3606)(2968,3607)(2970,3610)(2975,3616)(2976,3617)(2978,
     3620)(2979,3622)(2981,3625)(2982,3627)(2986,3631)(2990,3636)(2993,3214)
     (2994,3640)(2996,3643)(2997,3645)(2998,3646)(3001,3649)(3005,3652)(3008,
     3351)(3009,3453)(3010,3638)(3012,3658)(3014,3087)(3016,3662)(3017,3664)
     (3018,3666)(3019,3229)(3021,3669)(3022,3671)(3023,3673)(3024,3675)(3027,
     3678)(3029,3681)(3031,3595)(3033,3684)(3037,3062)(3040,3690)(3041,3435)
     (3043,3694)(3046,3696)(3047,3437)(3049,3700)(3052,3703)(3056,3707)(3058,
     3708)(3059,3710)(3060,3474)(3069,3719)(3072,3721)(3074,3724)(3076,3727)
     (3081,3732)(3082,3734)(3084,3736)(3088,3741)(3089,3743)(3091,3745)(3096,
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