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7,888,448,120,1,1,3894,4071,4018,3619,3050,2636,2036,2019,2001,1993,1159,601,587,584,580,573,566,553,551,549,544,539,541,545,544,535,533,531,529,527,524,528,533,542,531,505,492,528,544,534,528,519,526,531,528,533,538,544,544,543,545,547,552,553,563,569,577,581,581,589,599,911,1996,2010,2023,2033,2058,2261,2705,3111,3317,3584,2416,783,1,1,711,999,976,958,906,882,842,805,777,762,741,725,709,698,691,683,675,664,658,649,638,625,612,603,589,574,559,553,542,531,522,514,508,499,493,485,481,476,471,467,463,461,458,456,455,454,455,455,457,461,462,466,471,478,481,488,495,504,515,521,532,543,561,573,590,610,325,171,163,1,1,133,132,132,131,123,105,84,38,1087,1109,1128,1156,1185,1205,22,31,21,31,13,24,3,25,1,1,1,1,1,1,454,4501,4501,4501,2031,2142,2221,2237,2239,2234,2222,2210,2197,2182,2176,2167,2162,2158,2150,2142,768,761,754,763,2131,2144,2148,2154,2164,2174,2176,2183,2191,2204,2212,2218,2228,2240,2256,2270,2013,1760,4501,1082,1071,997,602,281,15,1,1,1,1,1,1,1,25,1,578,1162,1137,1101,1086,1062,1036,1016,1009,1032,124,130,133,133,133,139,162,181,621,610,590,568,558,542,527,517,514,502,493,486,479,477,471,466,462,460,457,455,454,454,454,456,457,460,462,466,471,476,481,484,491,498,507,513,521,531,541,554,558,573,589,604,612,628,640,653,663,668,678,688,696,703,716,730,749,771,788,815,849,888,912,950,964,962,964,987,750,25,4501,4501,4130,3840,2966,2263,2079,2043,2025,2004,1993,1553,618,593,592,592,582,574,561,557,553,553,545,548,547,544,538,537,536,530,531,526,528,535,545,537,504,500,534,546,536,530,525,529,532,533,538,538,545,545,546,544,553,555,560,566,574,588,582,585,588,1485,1983,1997,2006,2021,2040,2368,2290,2822,3237,3375,3418,1752,400,1,63,957,959,963,960,917,890,850,818,789,775,754,736,720,708,702,691,682,671,666,655,644,629,616,606,593,578,560,554,544,532,522,515,509,501,493,486,482,476,471,467,463,461,457,455,454,454,453,454,456,459,461,465,469,475,478,485,491,501,512,518,529,540,556,566,587,610,634,294,166,140,130,130,130,128,93,7,970,989,1008,1029,1051,1072,1105,1141,1163,1207,26,2,16,29,13,30,4,1,4501,1,1,1,25,308,1092,4501,1494,1834,2027,2144,2188,2205,2211,2207,2195,2185,2170,2170,2162,2156,2150,2146,2138,762,755,747,756,2126,2136,2140,2146,2152,2159,2164,2169,2181,2193,2201,2208,2216,2227,2240,2257,4501,1044,1058,1007,1020,1042,557,255,48,16,1,1,1,1,1,27,1,1127,1148,1116,1086,1051,1033,1008,987,965,955,936,919,33,127,127,127,134,1031,670,639,614,587,566,555,539,524,516,511,501,491,483,477,474,469,464,460,458,456,454,454,455,455,456,458,462,463,469,472,476,482,485,493,500,508,513,523,532,543,554,562,576,591,606,614,630,644,659,669,675,684,695,704,708,722,737,755,778,793,817,850,883,913,944,976,1009,1029,1048,642,1,1,4501,4425,4361,3989,2794,2343,2137,2032,2008,1998,1920,1321,596,579,590,585,574,564,562,556,552,547,546,548,547,542,537,538,533,529,528,532,537,547,540,508,501,540,550,539,532,527,530,533,536,536,541,549,549,547,552,556,557,564,560,574,589,587,588,830,1695,1990,2006,2018,2036,2052,2833,2939,3339,3647,4091,2901,1052,1,1,1,1,4501,986,953,908,879,847,814,789,776,756,738,725,712,707,699,687,677,672,661,648,634,619,609,594,581,564,557,545,535,524,515,510,502,494,487,483,477,472,468,464,461,458,456,454,453,453,454,454,457,459,463,468,473,476,481,489,497,509,515,523,536,552,563,582,611,641,677,694,2107,3341,1,1,1,891,913,931,940,959,980,1007,1024,1059,1092,1126,1153,1179,13,1,1,1,1,6,1,1,1,1,4501,971,999,1036,1079,2308,2173,2213,2236,2232,2219,2208,2198,2185,2173,2161,2159,2153,2142,2136,2135,2126,757,744,737,744,2105,2122,2127,2134,2143,2149,2150,2161,2173,2182,2197,2203,2212,2223,2240,2247,2256,2275,4501,1038,1020,1004,925,785,405,88,11,1,1,1,1,1,1,1100,1116,1079,1041,1015,991,969,945,923,912,895,878,855,828,823,785,741,699,675,638,609,584,560,550,535,521,512,507,497,488,481,475,472,466,462,458,457,454,453,452,453,453,456,458,461,463,467,471,477,482,485,492,501,508,514,523,534,544,556,561,575,593,609,619,634,649,662,673,680,689,698,706,712,724,736,752,774,787,814,841,879,899,942,978,1041,792,396,180,32,4501,1,3558,4100,4176,3654,3368,2218,2045,2023,2010,1994,1578,1398,590,579,591,572,569,570,565,557,553,549,552,551,546,539,538,534,533,533,534,540,550,546,515,510,545,556,544,538,534,536,539,543,544,550,554,555,553,551,553,562,565,572,581,584,593,1436,1440,1985,2003,2020,2035,2052,2150,3064,3369,3470,3906,4296,2621,641,1,1,1,1,1055,986,959,906,878,841,811,785,773,754,737,725,713,709,700,690,680,673,663,652,635,620,611,596,581,566,557,547,534,525,515,511,501,494,487,483,478,472,468,464,461,459,455,453,453,452,452,454,456,458,461,465,471,474,480,487,495,504,512,521,532,549,559,578,607,636,667,689,727,767,796,813,836,857,879,897,906,924,947,975,986,1018,1065,1099,1135,1155,1,1,1,11,17,20,1,1,1,1,1000,4501,4501,4501,4501,2279,2269,2250,2237,2222,2206,2190,2180,2168,2159,2146,2141,2134,2127,2122,2119,1904,740,736,728,735,2084,2111,2113,2120,2125,2132,2136,2145,2154,2166,2175,2183,2189,2199,2212,2225,2235,2251,4501,1799,1029,4501,4501,20,35,21,15,1,1,1,1,1,1008,1127,1100,1059,1016,987,960,939,916,893,882,864,845,824,797,783,753,724,688,663,636,604,580,556,547,531,518,508,505,494,485,478,472,469,464,460,456,455,453,452,452,453,454,455,458,461,464,467,472,477,483,487,492,500,509,515,523,535,545,557,563,577,594,611,619,635,652,665,677,682,691,699,708,713,724,736,753,776,788,813,842,880,902,944,982,1032,845,431,207,10,1,1,4501,4501,4258,3472,3338,2742,2061,2040,2027,2013,1869,1423,675,601,592,586,571,564,563,555,556,551,556,555,550,544,542,542,538,535,538,545,558,549,511,512,554,561,549,543,538,542,544,556,558,556,560,564,572,574,559,578,594,589,591,619,616,613,677,651,1996,2050,2019,2068,2088,2117,2131,2481,2537,4501,4501,4501,1,28,12,7,68,997,961,914,885,851,817,789,777,758,742,727,718,711,703,693,684,676,667,653,638,622,612,597,582,566,559,547,534,525,516,511,503,495,487,484,478,473,468,464,462,459,456,454,452,452,452,453,455,456,460,464,470,471,479,485,492,502,511,519,530,547,557,576,603,629,661,678,710,745,770,788,807,831,852,871,881,901,927,956,975,1009,1060,1095,1127,1155,1,1,15,26,14,1,1,1,1,4501,921,1051,2036,2305,4501,2271,2257,2240,2220,2200,2180,2172,2159,2149,2140,2130,2127,2122,2117,2109,2105,2099,729,725,713,721,1487,2091,2097,2104,2110,2116,2118,2127,2135,2148,2158,2165,2174,2185,2198,2203,2210,4501,4501,4501,1574,4501,1,45,41,25,23,1,1,1,1,1,1,1140,1108,1062,1026,981,958,926,899,872,858,838,820,795,771,759,734,705,671,654,625,600,575,554,545,531,516,507,502,493,483,477,471,469,464,459,456,455,453,452,452,453,453,456,459,462,464,468,473,478,483,486,494,501,509,514,524,534,545,557,562,577,596,611,621,638,652,668,679,685,695,704,713,718,729,743,759,784,796,822,854,890,918,954,1004,1053,354,21,18,27,1,4501,4501,4501,4054,3833,3481,3377,2137,2054,2041,2023,2008,1994,1157,645,612,597,582,572,570,568,560,564,565,564,556,550,549,550,542,543,546,551,561,561,534,524,561,566,556,549,544,548,553,557,559,561,564,562,564,569,573,572,581,582,605,614,1379,1983,2003,2014,2033,2052,2066,2081,2491,3046,3217,3454,4501,4501,1,1,1,1,1,1,1071,1022,991,936,907,869,832,806,789,770,751,738,725,718,709,699,687,680,669,655,638,621,612,595,582,564,557,545,534,526,515,511,502,495,488,484,478,473,468,465,461,459,456,454,453,452,451,452,455,456,458,463,468,471,476,484,490,501,507,516,527,545,553,573,598,622,651,663,692,718,744,755,778,799,822,846,857,880,915,952,975,1026,1075,1110,1155,1099,1,1,27,15,4501,1,4501,1,1,4501,4501,4501,4501,4501,2416,2253,2225,2195,2184,2169,2158,2153,2142,2131,2121,2112,2108,2101,2093,2090,2086,795,716,710,698,706,789,2075,2080,2084,2093,2098,2100,2110,2121,2127,2141,2145,2158,2169,2182,2188,2194,2228,2242,2269,4501,1304,4501,81,4501,4,23,25,1,1,1,1,1,56,1121,1082,1036,990,951,919,878,851,835,813,789,767,746,733,712,690,664,647,620,595,574,552,544,529,515,506,501,491,482,475,470,467,462,458,455,454,453,452,452,453,453,455,458,461,464,468,472,477,482,486,493,501,509,515,524,534,543,556,563,577,594,611,621,639,655,672,684,690,701,711,722,727,740,755,774,797,815,844,874,918,942,987,1025,1096,180,23,4501,4501,109,1,4501,4501,3592,3502,3242,3094,2160,2075,2060,2043,2024,2012,1991,1219,612,602,589,587,584,575,573,565,564,569,565,560,559,554,553,544,547,556,570,569,535,535,571,574,559,553,552,558,561,563,565,571,576,573,579,577,576,589,589,603,609,700,1899,2006,2019,2035,2051,2073,2086,2100,2726,2958,3196,4501,4501,1,1,1,1,1,1,4501,1,51,1023,971,936,897,857,827,811,788,767,751,735,728,717,704,693,685,671,655,639,621,612,595,580,563,556,545,532,524,515,510,502,494,488,484,478,473,469,464,462,459,456,454,452,453,452,452,454,456,459,463,468,470,476,483,491,501,507,517,527,545,554,572,595,617,641,654,679,700,719,732,749,768,791,811,829,853,890,928,953,1016,1073,1103,1160,1,1,1,1,4501,1,1,1,4501,4501,4501,4501,4501,2255,2250,2239,2213,2184,2174,2164,2149,2138,2132,2120,2111,2105,2094,2091,2083,2080,2072,2068,758,700,696,685,691,686,2015,2063,2065,2073,2078,2081,2085,2095,2105,2111,2119,2129,2143,2157,2165,2173,2180,2253,4501,4501,2289,4501,1,1,1,1,1,4501,1,1,1,1,756,1088,1049,994,943,908,873,839,808,796,773,755,734,716,707,689,671,649,636,614,594,571,553,543,530,515,506,502,493,482,476,471,468,462,459,456,455,454,453,453,454,454,457,458,462,464,468,472,477,483,486,493,501,509,513,524,533,545,556,562,576,595,610,619,640,657,675,689,696,709,723,735,742,757,775,799,827,842,873,910,953,978,1018,1061,1125,19,2,4501,1,1,1,4501,4501,4501,4024,3813,3628,2466,2096,2087,2065,2047,2036,2018,2006,1329,619,608,601,592,586,582,575,578,584,580,570,568,565,563,556,557,563,580,578,546,542,576,583,570,562,560,566,568,574,576,583,588,585,585,587,598,597,614,613,632,755,2019,2029,2042,2058,2077,2097,2110,2310,2443,2746,4501,4501,4501,105,78,30,22,1,1,1,1,14,1027,996,969,925,881,852,835,811,787,769,751,744,730,716,701,691,676,660,638,622,612,595,579,562,556,544,532,524,515,510,502,494,487,484,478,473,468,465,463,459,456,455,454,453,453,454,456,457,460,463,469,470,477,484,491,502,509,517,527,545,554,570,592,612,635,644,664,682,697,708,722,739,757,776,791,813,850,888,916,966,1029,1065,1106,1158,31,36,26,1,1,1,1,4501,4501,4501,2284,2270,2627,2500,2360,2253,2164,2151,2136,2122,2113,2103,2094,2088,2080,2076,2069,2064,1744,2005,2043,679,686,683,675,680,672,1874,828,1697,2039,2049,1627,1890,2080,2087,2094,2099,2111,2121,2137,2144,2155,2165,2187,2209,2229,2234,4501,4501,4501,1,38,55,56,14,21,21,236,1089,1055,1003,956,899,873,837,804,776,765,746,730,712,699,690,676,659,642,630,611,592,571,554,545,531,516,507,503,494,484,478,471,469,464,460,458,456,455,454,454,455,454,456,459,462,464,468,473,477,483,485,493,500,509,514,523,532,544,555,561,573,593,610,618,639,657,679,694,701,717,732,747,757,772,794,815,851,864,896,933,972,1001,1039,1079,1142,1,1,1,1,1,1,4501,4501,4501,3520,3418,3331,2750,2131,2105,2086,2065,2048,2034,2028,1418,639,627,623,611,602,599,592,591,593,588,581,576,574,571,565,565,573,588,586,551,551,588,590,580,572,572,577,581,587,587,593,595,596,601,607,609,629,745,644,856,2001,2035,2043,2060,2074,2092,2115,2125,2326,2658,2955,4501,4501,4501,1,105,26,64,10,1,4501,1,4,1059,1016,983,948,907,876,858,831,807,786,766,756,741,725,707,696,680,661,640,621,610,594,579,560,554,543,531,522,514,509,501,495,485,483,478,473,469,465,462,460,457,456,455,454,454,455,457,458,461,465,470,473,479,485,492,504,510,519,530,546,555,569,593,608,628,637,656,670,684,691,702,717,731,751,762,782,818,853,875,933,982,1035,1071,1116,47,19,92,7,1,1,1,4501,4501,4501,2263,2265,2360,2485,2347,2183,2136,2128,2116,2104,2094,2090,2078,2070,1992,903,1341,1552,1546,1572,831,665,674,669,662,668,657,777,669,666,1917,1005,1133,1494,2042,2070,2076,2085,2091,2104,2118,2123,2134,2146,2163,2211,2399,2432,2432,4501,4501,4501,1,1,4501,1,1,1,1060,1073,1032,986,926,878,842,810,776,751,741,725,711,696,683,678,665,653,637,626,611,591,574,554,547,531,519,510,505,495,486,479,473,472,466,461,459,458,456,455,455,455,456,457,459,462,464,468,472,477,482,485,492,499,507,512,521,531,541,553,559,574,591,609,617,638,658,681,699,710,728,744,761,771,792,811,835,867,886,913,948,990,1012,1052,1086,1145,1,1,4501,1,1,1,1,4501,4501,4501,4501,3433,3241,2434,2132,2105,2086,2070,2048,2043,2029,1685,1300,1148,638,615,611,601,600,598,597,591,588,584,581,573,571,584,597,597,564,557,599,601,586,579,581,586,590,594,595,602,606,608,612,612,625,1026,901,1513,1855,2035,2054,2063,2080,2096,2120,2137,2156,2376,2700,4501,4501,4501,4501,1,4501,1,1,4501,1,1,1,841,1069,1022,995,960,920,890,873,849,821,801,778,770,752,734,712,701,680,662,640,620,609,591,577,560,552,542,531,521,512,508,500,492,485,482,477,472,468,466,462,460,458,456,456,456,456,457,458,459,463,467,472,474,480,487,495,506,512,521,532,548,558,572,592,610,625,634,648,662,672,679,689,701,717,733,744,764,797,834,862,915,977,1020,1059,1114,72,4501,1,1,12,70,4501,4501,4501,4501,2329,2581,2566,2403,2240,2135,2117,2110,2098,2087,2079,2072,2060,2053,1970,844,1048,685,831,892,649,649,660,656,648,654,646,638,639,646,899,1003,1098,781,1944,2047,2058,2060,2071,2078,2097,2100,2116,2126,2142,2178,2227,2268,2275,4501,4501,4501,837,1,77,29,25,1,1131,1069,1022,973,923,874,837,801,761,738,727,711,697,685,674,669,658,647,632,624,611,592,577,558,550,535,523,512,509,498,489,482,477,473,469,465,461,460,458,456,456,456,457,458,460,462,464,468,472,476,481,485,491,498,506,512,519,529,539,552,557,570,588,607,616,636,658,682,704,715,736,755,776,783,806,826,851,882,900,927,965,999,1022,1060,1094,1145,7,1,2,4501,4501,1,1,4501,4501,4501,4501,4501,2454,2265,2155,2134,2111,2098,2078,2068,2053,2040,1957,2020,1023,713,626,628,619,617,608,601,600,595,594,588,584,590,604,611,577,576,616,613,600,591,592,596,601,606,608,617,620,617,616,682,749,1700,2025,2039,2051,2063,2078,2090,2103,2123,2142,2158,2221,2520,2219,4501,4501,4501,1,1,4501,1,1,1,1,1,1,38,1079,1034,1009,965,932,902,887,859,839,813,793,781,763,742,719,704,684,662,637,620,606,590,574,557,550,539,529,520,512,507,500,492,486,483,477,472,469,465,463,460,458,457,456,456,457,458,461,462,466,470,475,478,484,491,498,509,516,525,535,552,560,576,594,610,625,633,644,657,668,673,683,694,706,723,733,754,790,827,861,918,972,1013,1068,1140,13,72,14,20,29,175,4501,4501,2250,2226,2209,2186,2168,2146,2127,2108,2092,2088,2072,2066,2055,2050,2041,1110,679,653,648,647,640,638,635,636,648,647,639,643,633,628,624,633,638,640,644,651,657,1928,2037,2047,2051,2063,2075,2083,2093,2106,2123,2137,2151,2161,2183,2194,4501,4501,4501,4501,86,28,30,1,4501,963,1023,980,937,870,840,798,763,734,725,708,694,681,672,667,657,648,634,626,611,596,579,562,554,540,527,516,512,503,493,486,480,476,471,467,463,462,459,458,457,457,458,458,460,463,464,467,471,476,481,484,490,497,505,510,518,528,537,549,555,572,587,605,617,636,660,685,710,720,744,764,788,797,819,840,865,896,913,941,975,1013,1036,1074,1107,1155,1,1,1,1,1,4501,1,1,4501,4501,4501,4501,2368,2414,2223,2157,2132,2119,2096,2088,2071,2058,2046,2040,1996,1917,1000,631,627,627,626,617,611,610,606,602,598,602,616,621,594,592,627,625,614,604,607,613,615,622,626,634,633,675,653,1697,1989,2031,2054,2062,2071,2084,2102,2114,2127,2145,2165,2178,2226,4501,4501,4501,4501,1034,771,383,106,18,1,1,1,1,6,1109,1095,1047,1026,987,954,922,9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