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3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,2,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,6,6,5,4,3,3,3,3,3,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,3,3,3,4,4,5,5,5,5,4,4,5,4,4,3,3,3,3,3,3,3,3,3,4,4,5,5,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,6,6,6,6,5,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,3,2,2,2,2,3,3,2,2,2,3,3,2,2,2,2,2,2,2,2,2,3,3,3,3,2,2,2,2,2,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,6,5,4,3,4,3,3,3,3,3,3,4,4,3,3,3,4,4,3,3,3,3,3,3,3,3,3,4,4,4,4,3,3,2,2,3,4,5,5,5,5,4,4,4,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,4,3,3,4,4,3,3,3,3,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,3,3,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,6,6,6,6,5,3,2,2,2,2,2,2,3,3,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,3,3,3,2,2,2,2,3,3,3,3,3,3,3,3,2,2,2,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,6,5,4,3,3,3,3,3,3,3,3,3,4,4,3,3,4,4,3,3,3,3,3,3,3,3,4,4,4,3,3,3,3,3,3,3,3,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,6,6,5,4,3,3,3,3,3,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,6,6,6,6,4,3,3,2,2,2,2,3,3,2,2,2,2,2,2,2,2,2,2,2,2,3,2,3,3,3,3,4,3,3,3,2,2,3,3,2,2,3,3,3,3,3,3,2,2,2,2,2,3,4,4,4,4,4,4,4,3,4,4,5,5,5,5,5,6,5,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,3,3,4,4,3,3,3,3,3,3,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,5,5,6,6,5,4,4,4,3,3,3,3,3,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,2,3,3,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,6,6,5,2,2,2,2,2,2,3,2,2,3,2,2,3,2,2,2,2,3,2,3,3,3,3,3,3,4,4,3,3,3,3,2,3,3,2,2,2,2,3,3,3,3,2,2,2,2,2,3,3,4,4,4,4,4,4,3,4,4,4,5,5,5,6,5,4,3,3,3,3,3,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,3,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,5,5,5,5,4,3,3,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,4,3,3,2,2,3,3,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,4,3,2,2,2,2,3,3,3,2,2,3,3,3,2,2,2,3,3,3,3,3,3,3,4,4,4,3,3,3,3,2,2,3,3,2,3,3,3,3,3,3,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,3,3,4,5,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,3,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,3,2,2,2,2,2,2,3,3,3,2,2,2,2,3,3,3,4,4,3,3,4,4,4,4,3,3,2,2,3,3,3,2,3,3,3,3,2,2,2,2,2,2,3,2,2,2,3,4,3,3,4,4,3,4,4,4,5,5,5,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1,2,2,2,2,3,2,2,2,3,3,3,3,4,3,3,3,3,4,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,3,3,3,4,4,4,5,5,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,3,3,3,3,3,3,3,3,3,3,4,3,4,4,4,4,4,4,4,4,4,5,4,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,5,5,4,4,4,4,5,5,5,5,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,4,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,5,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,6,6,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5,4,4,4,3,3,4,4,5,5,5,5,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,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1482,1376,1397,1422,1317,1263,1278,1159,575,413,173,68,99,165,412,374,583,786,715,536,301,211,2,52,281,328,382,302,289,352,180,2,0,0,0,0,0,0,0,0,8,29,362,473,859,997,681,573,404,173,32,1,0,0,0,0,0,0,5,405,339,333,357,237,144,80,8,8,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20,17,10,8,8,9,14,10,6,6,11,10,3,3,19,32,54,108,166,154,124,111,106,94,92,85,84,94,133,158,170,150,127,117,154,182,188,201,203,221,208,207,184,158,134,136,117,103,80,69,45,34,30,26,27,20,10,5,4,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,159,315,209,145,257,441,558,652,1023,1401,1829,2187,2373,2154,1988,2075,2106,1906,1977,2194,2489,2448,2439,2762,2861,2523,2370,2349,2401,2305,2288,2370,2336,2189,2345,2317,2240,2341,2431,1771,1705,1753,1839,1746,1700,1584,888,521,644,1225,1134,1212,1306,1479,1473,1428,1314,1338,1305,1064,744,574,618,700,508,385,254,8,0,0,0,1276,1403,1686,2330,2455,2258,2198,2073,1945,1935,1866,1823,1721,1431,1375,1612,1635,1541,1439,1452,1618,1727,1666,1502,1319,1191,711,332,189,119,104,353,162,282,625,628,445,375,338,147,139,368,406,408,332,272,371,334,240,66,0,0,0,0,0,0,0,0,0,0,43,383,674,687,637,499,278,157,34,1,0,0,0,0,0,0,0,29,248,301,308,289,215,115,22,34,64,36,24,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10,10,9,8,11,18,20,9,3,5,11,9,3,11,17,39,95,175,238,190,138,138,126,90,73,41,50,56,57,37,73,100,130,119,96,122,139,160,179,215,231,226,204,186,175,163,137,114,94,82,68,42,29,30,23,25,14,12,9,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,243,484,474,692,661,926,1230,1595,2046,2227,2142,2144,2205,2197,2159,2094,2034,1992,2187,2675,2703,2938,3041,2749,2511,2471,2342,2359,2375,2331,2390,2410,2362,2325,2324,2313,2266,2124,1986,2011,2056,2053,1983,1951,1894,1830,1716,1554,1525,1481,1506,1530,1533,1523,1487,1432,1424,1184,1150,972,723,356,41,0,0,1,0,0,0,128,1302,1416,1772,2276,2408,2435,2456,2301,2081,1984,1953,1888,1796,1662,1632,1705,1692,1615,1620,1740,1843,1893,1864,1679,1336,864,661,392,139,123,92,393,152,377,719,458,209,376,343,81,225,452,439,399,230,389,234,123,18,0,0,0,0,0,0,0,0,0,0,0,0,95,461,567,558,295,7,6,22,2,0,0,0,0,0,0,0,0,0,408,461,308,257,159,132,142,108,165,97,45,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,6,8,13,14,7,1,0,0,0,6,10,10,10,16,52,82,93,168,193,152,130,95,44,35,29,22,23,16,3,5,6,28,55,80,88,94,104,122,148,162,174,180,186,188,185,150,148,139,103,73,57,38,26,24,24,21,19,18,14,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,526,725,723,1430,1609,1751,1990,2286,2317,2277,2388,2464,2493,2463,2557,2598,2545,2403,2479,2885,2812,2885,2885,2785,2726,2565,2351,2404,2405,2401,2395,2357,2239,2188,2161,2201,2223,2153,2153,2130,2152,2184,2189,2158,2124,2073,1986,1902,1816,1780,1789,1741,1636,1563,1623,1565,1404,1415,1235,763,776,368,0,10,23,0,0,0,0,0,210,1222,991,1393,2019,2248,2322,2261,2127,2018,1885,1829,1778,1730,1776,1823,1745,1660,1730,1848,1929,1962,1340,1112,1299,423,316,393,107,126,5,113,622,1037,221,1,377,178,127,148,546,494,450,526,393,230,30,70,118,0,0,0,0,0,0,0,0,0,0,0,0,0,64,165,25,40,2,0,7,0,0,0,0,0,0,0,0,0,0,0,25,438,498,375,291,120,103,107,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,7,9,13,10,2,1,2,6,5,5,5,7,5,6,28,44,59,69,137,170,109,102,82,50,33,24,11,1,0,2,2,2,3,31,69,78,84,93,93,129,159,159,157,158,155,170,154,149,155,114,78,50,38,27,28,30,31,27,22,21,17,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,460,1158,1487,1838,1985,2089,2243,2496,2500,2581,2644,2730,2822,2876,2849,2788,2752,2493,2795,2622,2680,2812,2848,2575,2600,2388,2317,2319,2383,2391,2311,2246,2268,2298,2279,2347,2266,2275,2223,2222,2252,2324,2319,2266,2224,2163,2154,2181,2161,2086,1990,1926,1838,1786,1780,1603,1649,1722,1426,869,878,950,542,587,374,425,211,109,3,0,119,875,294,7,934,1751,1841,1919,2051,1957,1913,1834,1877,1754,1796,1892,1865,1787,1739,1730,1777,1390,1099,1489,1319,477,140,47,219,211,404,320,874,289,28,0,15,3,266,665,606,477,512,301,533,109,66,36,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,37,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,28,104,235,58,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,14,9,0,6,11,13,8,11,14,16,17,7,3,33,55,33,44,49,64,97,79,41,27,19,12,0,0,0,0,3,10,11,19,52,86,90,88,85,90,111,179,178,163,153,157,151,145,125,88,61,45,29,19,24,42,41,36,36,27,17,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,558,1880,1828,1843,1452,1324,1562,1934,2136,2137,2074,2303,2701,2903,2950,2670,2633,2582,2757,2486,2682,2648,2659,2413,2438,2461,2429,2350,2402,2345,2218,2181,2231,2310,2428,2414,2397,2343,2303,2318,2346,2337,2260,2194,2165,2183,2248,2299,2265,2204,2162,2120,2059,1936,1791,1811,1832,1762,1617,1601,1722,1635,1707,1601,1450,1528,1495,1369,1433,1263,1575,1378,1007,1,35,772,1247,1456,1645,1917,2125,2123,1988,1881,1864,1937,1971,1944,1764,1622,1596,1122,969,1341,1191,1118,439,42,261,686,388,164,9,0,0,0,0,589,803,651,557,513,489,39,505,53,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,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