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3, 2, 2, 2, 2003, 2004, 7, 105, 2, 2, 2004, 2005, 5, 154, 78, 2, 2005, 2009, 7, 12, 2, 2, 2006, 2008, 7, 7, 2, 2, 2007, 2006, 3, 2, 2, 2, 2008, 2011, 3, 2, 2, 2, 2009, 2007, 3, 2, 2, 2, 2009, 2010, 3, 2, 2, 2, 2010, 2013, 3, 2, 2, 2, 2011, 2009, 3, 2, 2, 2, 2012, 2014, 5, 136, 69, 2, 2013, 2012, 3, 2, 2, 2, 2013, 2014, 3, 2, 2, 2, 2014, 143, 3, 2, 2, 2, 2015, 2019, 7, 98, 2, 2, 2016, 2018, 7, 7, 2, 2, 2017, 2016, 3, 2, 2, 2, 2018, 2021, 3, 2, 2, 2, 2019, 2017, 3, 2, 2, 2, 2019, 2020, 3, 2, 2, 2, 2020, 2022, 3, 2, 2, 2, 2021, 2019, 3, 2, 2, 2, 2022, 2023, 7, 11, 2, 2, 2023, 2024, 5, 154, 78, 2, 2024, 2028, 7, 12, 2, 2, 2025, 2027, 7, 7, 2, 2, 2026, 2025, 3, 2, 2, 2, 2027, 2030, 3, 2, 2, 2, 2028, 2026, 3, 2, 2, 2, 2028, 2029, 3, 2, 2, 2, 2029, 2033, 3, 2, 2, 2, 2030, 2028, 3, 2, 2, 2, 2031, 2034, 5, 136, 69, 2, 2032, 2034, 7, 29, 2, 2, 2033, 2031, 3, 2, 2, 2, 2033, 2032, 3, 2, 2, 2, 2034, 145, 3, 2, 2, 2, 2035, 2039, 7, 97, 2, 2, 2036, 2038, 7, 7, 2, 2, 2037, 2036, 3, 2, 2, 2, 2038, 2041, 3, 2, 2, 2, 2039, 2037, 3, 2, 2, 2, 2039, 2040, 3, 2, 2, 2, 2040, 2043, 3, 2, 2, 2, 2041, 2039, 3, 2, 2, 2, 2042, 2044, 5, 136, 69, 2, 2043, 2042, 3, 2, 2, 2, 2043, 2044, 3, 2, 2, 2, 2044, 2048, 3, 2, 2, 2, 2045, 2047, 7, 7, 2, 2, 2046, 2045, 3, 2, 2, 2, 2047, 2050, 3, 2, 2, 2, 2048, 2046, 3, 2, 2, 2, 2048, 2049, 3, 2, 2, 2, 2049, 2051, 3, 2, 2, 2, 2050, 2048, 3, 2, 2, 2, 2051, 2055, 7, 98, 2, 2, 2052, 2054, 7, 7, 2, 2, 2053, 2052, 3, 2, 2, 2, 2054, 2057, 3, 2, 2, 2, 2055, 2053, 3, 2, 2, 2, 2055, 2056, 3, 2, 2, 2, 2056, 2058, 3, 2, 2, 2, 2057, 2055, 3, 2, 2, 2, 2058, 2059, 7, 11, 2, 2, 2059, 2060, 5, 154, 78, 2, 2060, 2061, 7, 12, 2, 2, 2061, 147, 3, 2, 2, 2, 2062, 2063, 5, 190, 96, 2, 2063, 2064, 7, 30, 2, 2, 2064, 2069, 3, 2, 2, 2, 2065, 2066, 5, 194, 98, 2, 2066, 2067, 5, 276, 139, 2, 2067, 2069, 3, 2, 2, 2, 2068, 2062, 3, 2, 2, 2, 2068, 2065, 3, 2, 2, 2, 2069, 2073, 3, 2, 2, 2, 2070, 2072, 7, 7, 2, 2, 2071, 2070, 3, 2, 2, 2, 2072, 2075, 3, 2, 2, 2, 2073, 2071, 3, 2, 2, 2, 2073, 2074, 3, 2, 2, 2, 2074, 2076, 3, 2, 2, 2, 2075, 2073, 3, 2, 2, 2, 2076, 2077, 5, 154, 78, 2, 2077, 149, 3, 2, 2, 2, 2078, 2082, 9, 7, 2, 2, 2079, 2081, 7, 7, 2, 2, 2080, 2079, 3, 2, 2, 2, 2081, 2084, 3, 2, 2, 2, 2082, 2080, 3, 2, 2, 2, 2082, 2083, 3, 2, 2, 2, 2083, 151, 3, 2, 2, 2, 2084, 2082, 3, 2, 2, 2, 2085, 2087, 9, 7, 2, 2, 2086, 2085, 3, 2, 2, 2, 2087, 2088, 3, 2, 2, 2, 2088, 2086, 3, 2, 2, 2, 2088, 2089, 3, 2, 2, 2, 2089, 153, 3, 2, 2, 2, 2090, 2091, 5, 156, 79, 2, 2091, 155, 3, 2, 2, 2, 2092, 2109, 5, 158, 80, 2, 2093, 2095, 7, 7, 2, 2, 2094, 2093, 3, 2, 2, 2, 2095, 2098, 3, 2, 2, 2, 2096, 2094, 3, 2, 2, 2, 2096, 2097, 3, 2, 2, 2, 2097, 2099, 3, 2, 2, 2, 2098, 2096, 3, 2, 2, 2, 2099, 2103, 7, 25, 2, 2, 2100, 2102, 7, 7, 2, 2, 2101, 2100, 3, 2, 2, 2, 2102, 2105, 3, 2, 2, 2, 2103, 2101, 3, 2, 2, 2, 2103, 2104, 3, 2, 2, 2, 2104, 2106, 3, 2, 2, 2, 2105, 2103, 3, 2, 2, 2, 2106, 2108, 5, 158, 80, 2, 2107, 2096, 3, 2, 2, 2, 2108, 2111, 3, 2, 2, 2, 2109, 2107, 3, 2, 2, 2, 2109, 2110, 3, 2, 2, 2, 2110, 157, 3, 2, 2, 2, 2111, 2109, 3, 2, 2, 2, 2112, 2129, 5, 160, 81, 2, 2113, 2115, 7, 7, 2, 2, 2114, 2113, 3, 2, 2, 2, 2115, 2118, 3, 2, 2, 2, 2116, 2114, 3, 2, 2, 2, 2116, 2117, 3, 2, 2, 2, 2117, 2119, 3, 2, 2, 2, 2118, 2116, 3, 2, 2, 2, 2119, 2123, 7, 24, 2, 2, 2120, 2122, 7, 7, 2, 2, 2121, 2120, 3, 2, 2, 2, 2122, 2125, 3, 2, 2, 2, 2123, 2121, 3, 2, 2, 2, 2123, 2124, 3, 2, 2, 2, 2124, 2126, 3, 2, 2, 2, 2125, 2123, 3, 2, 2, 2, 2126, 2128, 5, 160, 81, 2, 2127, 2116, 3, 2, 2, 2, 2128, 2131, 3, 2, 2, 2, 2129, 2127, 3, 2, 2, 2, 2129, 2130, 3, 2, 2, 2, 2130, 159, 3, 2, 2, 2, 2131, 2129, 3, 2, 2, 2, 2132, 2144, 5, 162, 82, 2, 2133, 2137, 5, 278, 140, 2, 2134, 2136, 7, 7, 2, 2, 2135, 2134, 3, 2, 2, 2, 2136, 2139, 3, 2, 2, 2, 2137, 2135, 3, 2, 2, 2, 2137, 2138, 3, 2, 2, 2, 2138, 2140, 3, 2, 2, 2, 2139, 2137, 3, 2, 2, 2, 2140, 2141, 5, 162, 82, 2, 2141, 2143, 3, 2, 2, 2, 2142, 2133, 3, 2, 2, 2, 2143, 2146, 3, 2, 2, 2, 2144, 2142, 3, 2, 2, 2, 2144, 2145, 3, 2, 2, 2, 2145, 161, 3, 2, 2, 2, 2146, 2144, 3, 2, 2, 2, 2147, 2159, 5, 164, 83, 2, 2148, 2152, 5, 280, 141, 2, 2149, 2151, 7, 7, 2, 2, 2150, 2149, 3, 2, 2, 2, 2151, 2154, 3, 2, 2, 2, 2152, 2150, 3, 2, 2, 2, 2152, 2153, 3, 2, 2, 2, 2153, 2155, 3, 2, 2, 2, 2154, 2152, 3, 2, 2, 2, 2155, 2156, 5, 164, 83, 2, 2156, 2158, 3, 2, 2, 2, 2157, 2148, 3, 2, 2, 2, 2158, 2161, 3, 2, 2, 2, 2159, 2157, 3, 2, 2, 2, 2159, 2160, 3, 2, 2, 2, 2160, 163, 3, 2, 2, 2, 2161, 2159, 3, 2, 2, 2, 2162, 2166, 5, 166, 84, 2, 2163, 2165, 5, 204, 103, 2, 2164, 2163, 3, 2, 2, 2, 2165, 2168, 3, 2, 2, 2, 2166, 2164, 3, 2, 2, 2, 2166, 2167, 3, 2, 2, 2, 2167, 165, 3, 2, 2, 2, 2168, 2166, 3, 2, 2, 2, 2169, 2190, 5, 168, 85, 2, 2170, 2174, 5, 282, 142, 2, 2171, 2173, 7, 7, 2, 2, 2172, 2171, 3, 2, 2, 2, 2173, 2176, 3, 2, 2, 2, 2174, 2172, 3, 2, 2, 2, 2174, 2175, 3, 2, 2, 2, 2175, 2177, 3, 2, 2, 2, 2176, 2174, 3, 2, 2, 2, 2177, 2178, 5, 168, 85, 2, 2178, 2189, 3, 2, 2, 2, 2179, 2183, 5, 284, 143, 2, 2180, 2182, 7, 7, 2, 2, 2181, 2180, 3, 2, 2, 2, 2182, 2185, 3, 2, 2, 2, 2183, 2181, 3, 2, 2, 2, 2183, 2184, 3, 2, 2, 2, 2184, 2186, 3, 2, 2, 2, 2185, 2183, 3, 2, 2, 2, 2186, 2187, 5, 100, 51, 2, 2187, 2189, 3, 2, 2, 2, 2188, 2170, 3, 2, 2, 2, 2188, 2179, 3, 2, 2, 2, 2189, 2192, 3, 2, 2, 2, 2190, 2188, 3, 2, 2, 2, 2190, 2191, 3, 2, 2, 2, 2191, 167, 3, 2, 2, 2, 2192, 2190, 3, 2, 2, 2, 2193, 2211, 5, 172, 87, 2, 2194, 2196, 7, 7, 2, 2, 2195, 2194, 3, 2, 2, 2, 2196, 2199, 3, 2, 2, 2, 2197, 2195, 3, 2, 2, 2, 2197, 2198, 3, 2, 2, 2, 2198, 2200, 3, 2, 2, 2, 2199, 2197, 3, 2, 2, 2, 2200, 2204, 5, 170, 86, 2, 2201, 2203, 7, 7, 2, 2, 2202, 2201, 3, 2, 2, 2, 2203, 2206, 3, 2, 2, 2, 2204, 2202, 3, 2, 2, 2, 2204, 2205, 3, 2, 2, 2, 2205, 2207, 3, 2, 2, 2, 2206, 2204, 3, 2, 2, 2, 2207, 2208, 5, 172, 87, 2, 2208, 2210, 3, 2, 2, 2, 2209, 2197, 3, 2, 2, 2, 2210, 2213, 3, 2, 2, 2, 2211, 2209, 3, 2, 2, 2, 2211, 2212, 3, 2, 2, 2, 2212, 169, 3, 2, 2, 2, 2213, 2211, 3, 2, 2, 2, 2214, 2215, 7, 47, 2, 2, 2215, 2216, 7, 28, 2, 2, 2216, 171, 3, 2, 2, 2, 2217, 2229, 5, 174, 88, 2, 2218, 2222, 5, 346, 174, 2, 2219, 2221, 7, 7, 2, 2, 2220, 2219, 3, 2, 2, 2, 2221, 2224, 3, 2, 2, 2, 2222, 2220, 3, 2, 2, 2, 2222, 2223, 3, 2, 2, 2, 2223, 2225, 3, 2, 2, 2, 2224, 2222, 3, 2, 2, 2, 2225, 2226, 5, 174, 88, 2, 2226, 2228, 3, 2, 2, 2, 2227, 2218, 3, 2, 2, 2, 2228, 2231, 3, 2, 2, 2, 2229, 2227, 3, 2, 2, 2, 2229, 2230, 3, 2, 2, 2, 2230, 173, 3, 2, 2, 2, 2231, 2229, 3, 2, 2, 2, 2232, 2243, 5, 176, 89, 2, 2233, 2237, 7, 38, 2, 2, 2234, 2236, 7, 7, 2, 2, 2235, 2234, 3, 2, 2, 2, 2236, 2239, 3, 2, 2, 2, 2237, 2235, 3, 2, 2, 2, 2237, 2238, 3, 2, 2, 2, 2238, 2240, 3, 2, 2, 2, 2239, 2237, 3, 2, 2, 2, 2240, 2242, 5, 176, 89, 2, 2241, 2233, 3, 2, 2, 2, 2242, 2245, 3, 2, 2, 2, 2243, 2241, 3, 2, 2, 2, 2243, 2244, 3, 2, 2, 2, 2244, 175, 3, 2, 2, 2, 2245, 2243, 3, 2, 2, 2, 2246, 2258, 5, 178, 90, 2, 2247, 2251, 5, 286, 144, 2, 2248, 2250, 7, 7, 2, 2, 2249, 2248, 3, 2, 2, 2, 2250, 2253, 3, 2, 2, 2, 2251, 2249, 3, 2, 2, 2, 2251, 2252, 3, 2, 2, 2, 2252, 2254, 3, 2, 2, 2, 2253, 2251, 3, 2, 2, 2, 2254, 2255, 5, 178, 90, 2, 2255, 2257, 3, 2, 2, 2, 2256, 2247, 3, 2, 2, 2, 2257, 2260, 3, 2, 2, 2, 2258, 2256, 3, 2, 2, 2, 2258, 2259, 3, 2, 2, 2, 2259, 177, 3, 2, 2, 2, 2260, 2258, 3, 2, 2, 2, 2261, 2273, 5, 180, 91, 2, 2262, 2266, 5, 288, 145, 2, 2263, 2265, 7, 7, 2, 2, 2264, 2263, 3, 2, 2, 2, 2265, 2268, 3, 2, 2, 2, 2266, 2264, 3, 2, 2, 2, 2266, 2267, 3, 2, 2, 2, 2267, 2269, 3, 2, 2, 2, 2268, 2266, 3, 2, 2, 2, 2269, 2270, 5, 180, 91, 2, 2270, 2272, 3, 2, 2, 2, 2271, 2262, 3, 2, 2, 2, 2272, 2275, 3, 2, 2, 2, 2273, 2271, 3, 2, 2, 2, 2273, 2274, 3, 2, 2, 2, 2274, 179, 3, 2, 2, 2, 2275, 2273, 3, 2, 2, 2, 2276, 2294, 5, 182, 92, 2, 2277, 2279, 7, 7, 2, 2, 2278, 2277, 3, 2, 2, 2, 2279, 2282, 3, 2, 2, 2, 2280, 2278, 3, 2, 2, 2, 2280, 2281, 3, 2, 2, 2, 2281, 2283, 3, 2, 2, 2, 2282, 2280, 3, 2, 2, 2, 2283, 2287, 5, 290, 146, 2, 2284, 2286, 7, 7, 2, 2, 2285, 2284, 3, 2, 2, 2, 2286, 2289, 3, 2, 2, 2, 2287, 2285, 3, 2, 2, 2, 2287, 2288, 3, 2, 2, 2, 2288, 2290, 3, 2, 2, 2, 2289, 2287, 3, 2, 2, 2, 2290, 2291, 5, 100, 51, 2, 2291, 2293, 3, 2, 2, 2, 2292, 2280, 3, 2, 2, 2, 2293, 2296, 3, 2, 2, 2, 2294, 2292, 3, 2, 2, 2, 2294, 2295, 3, 2, 2, 2, 2295, 181, 3, 2, 2, 2, 2296, 2294, 3, 2, 2, 2, 2297, 2299, 5, 184, 93, 2, 2298, 2297, 3, 2, 2, 2, 2299, 2302, 3, 2, 2, 2, 2300, 2298, 3, 2, 2, 2, 2300, 2301, 3, 2, 2, 2, 2301, 2303, 3, 2, 2, 2, 2302, 2300, 3, 2, 2, 2, 2303, 2304, 5, 186, 94, 2, 2304, 183, 3, 2, 2, 2, 2305, 2315, 5, 336, 169, 2, 2306, 2315, 5, 134, 68, 2, 2307, 2311, 5, 292, 147, 2, 2308, 2310, 7, 7, 2, 2, 2309, 2308, 3, 2, 2, 2, 2310, 2313, 3, 2, 2, 2, 2311, 2309, 3, 2, 2, 2, 2311, 2312, 3, 2, 2, 2, 2312, 2315, 3, 2, 2, 2, 2313, 2311, 3, 2, 2, 2, 2314, 2305, 3, 2, 2, 2, 2314, 2306, 3, 2, 2, 2, 2314, 2307, 3, 2, 2, 2, 2315, 185, 3, 2, 2, 2, 2316, 2320, 5, 214, 108, 2, 2317, 2319, 5, 188, 95, 2, 2318, 2317, 3, 2, 2, 2, 2319, 2322, 3, 2, 2, 2, 2320, 2318, 3, 2, 2, 2, 2320, 2321, 3, 2, 2, 2, 2321, 187, 3, 2, 2, 2, 2322, 2320, 3, 2, 2, 2, 2323, 2329, 5, 294, 148, 2, 2324, 2329, 5, 208, 105, 2, 2325, 2329, 5, 204, 103, 2, 2326, 2329, 5, 200, 101, 2, 2327, 2329, 5, 202, 102, 2, 2328, 2323, 3, 2, 2, 2, 2328, 2324, 3, 2, 2, 2, 2328, 2325, 3, 2, 2, 2, 2328, 2326, 3, 2, 2, 2, 2328, 2327, 3, 2, 2, 2, 2329, 189, 3, 2, 2, 2, 2330, 2331, 5, 186, 94, 2, 2331, 2332, 5, 198, 100, 2, 2332, 2336, 3, 2, 2, 2, 2333, 2336, 5, 346, 174, 2, 2334, 2336, 5, 192, 97, 2, 2335, 2330, 3, 2, 2, 2, 2335, 2333, 3, 2, 2, 2, 2335, 2334, 3, 2, 2, 2, 2336, 191, 3, 2, 2, 2, 2337, 2341, 7, 11, 2, 2, 2338, 2340, 7, 7, 2, 2, 2339, 2338, 3, 2, 2, 2, 2340, 2343, 3, 2, 2, 2, 2341, 2339, 3, 2, 2, 2, 2341, 2342, 3, 2, 2, 2, 2342, 2344, 3, 2, 2, 2, 2343, 2341, 3, 2, 2, 2, 2344, 2348, 5, 190, 96, 2, 2345, 2347, 7, 7, 2, 2, 2346, 2345, 3, 2, 2, 2, 2347, 2350, 3, 2, 2, 2, 2348, 2346, 3, 2, 2, 2, 2348, 2349, 3, 2, 2, 2, 2349, 2351, 3, 2, 2, 2, 2350, 2348, 3, 2, 2, 2, 2351, 2352, 7, 12, 2, 2, 2352, 193, 3, 2, 2, 2, 2353, 2356, 5, 182, 92, 2, 2354, 2356, 5, 196, 99, 2, 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