[0.422,0.436,0.453,0.456,0.444,0.439,0.45,0.468,0.478,0.476,0.463,0.44,0.412,0.39,0.387,0.402,0.425,0.437,0.435,0.426,0.428,0.448,0.48,0.499,0.488,0.441,0.384,0.349,0.364,0.422,0.498,0.559,0.583,0.564,0.516,0.462,0.425,0.411,0.415,0.424,0.43,0.424,0.401,0.365,0.332,0.318,0.329,0.356,0.377,0.373,0.343,0.305,0.276,0.263,0.257,0.25,0.249,0.261,0.278,0.282,0.264,0.244,0.254,0.31,0.387,0.44,0.43,0.362,0.266,0.181,0.126,0.099,0.093,0.108,0.146,0.203,0.262,0.303,0.308,0.282,0.238,0.197,0.172,0.167,0.175,0.183,0.178,0.161,0.14,0.128,0.131,0.144,0.153,0.157,0.164,0.186,0.226,0.266,0.288,0.289,0.281,0.277,0.278,0.271,0.247,0.212,0.181,0.168,0.179,0.211,0.257,0.3,0.322,0.312,0.275,0.232,0.2,0.188,0.183,0.174,0.152,0.126,0.11,0.115,0.148,0.199,0.254,0.294,0.313,0.312,0.298,0.276,0.256,0.244,0.238,0.227,0.202,0.167,0.141,0.139,0.161,0.191,0.211,0.219,0.219,0.219,0.21,0.187,0.154,0.13,0.131,0.161,0.207,0.247,0.26,0.241,0.207,0.183,0.186,0.206,0.223,0.223,0.212,0.214,0.248,0.314,0.381,0.412,0.384,0.31,0.223,0.158,0.128,0.125,0.135,0.146,0.157,0.172,0.195,0.221,0.237,0.234,0.209,0.168,0.126,0.096,0.087,0.102,0.136,0.175,0.205,0.216,0.21,0.195,0.178,0.165,0.162,0.166,0.17,0.164,0.146,0.124,0.104,0.095,0.099,0.119,0.151,0.18,0.191,0.174,0.14,0.102,0.075,0.062,0.064,0.083,0.121,0.177,0.246,0.314,0.36,0.369,0.343,0.308,0.292,0.31,0.341,0.362,0.358,0.34,0.316,0.289,0.247,0.195,0.141,0.104,0.093,0.114,0.159,0.216,0.263,0.294,0.306,0.303,0.28,0.235,0.178,0.126,0.09,0.071,0.067,0.077,0.104,0.146,0.199,0.256,0.314,0.364,0.404,0.421,0.409,0.366,0.301,0.24,0.213,0.239,0.307,0.376,0.405,0.376,0.303,0.222,0.157,0.121,0.109,0.118,0.142,0.175,0.214,0.253,0.293,0.332,0.361,0.37,0.36,0.345,0.331,0.31,0.269,0.21,0.152,0.119,0.118,0.14,0.171,0.2,0.231,0.272,0.318,0.354,0.357,0.318,0.252,0.182,0.129,0.099,0.086,0.079,0.075,0.074,0.08,0.094,0.11,0.124,0.138,0.162,0.206,0.259,0.292,0.284,0.239,0.185,0.152,0.154,0.177,0.201,0.216,0.233,0.271,0.33,0.394,0.443,0.467,0.47,0.454,0.43,0.404,0.373,0.328,0.263,0.19,0.131,0.094,0.075,0.066,0.061,0.06,0.062,0.067,0.071,0.069,0.062,0.053,0.046,0.042,0.04,0.042,0.047,0.055,0.065,0.076,0.091,0.123,0.181,0.258,0.334,0.38,0.382,0.34,0.278,0.227,0.218,0.256,0.32,0.375,0.401,0.396,0.371,0.331,0.277,0.216,0.16,0.121,0.1,0.092,0.094,0.101,0.113,0.129,0.153,0.182,0.209,0.217,0.201,0.169,0.145,0.149,0.182,0.229,0.27,0.288,0.274,0.237,0.194,0.173,0.189,0.24,0.303,0.344,0.341,0.294,0.223,0.155,0.111,0.093,0.092,0.097,0.101,0.106,0.116,0.126,0.132,0.137,0.149,0.18,0.223,0.263,0.275,0.255,0.215,0.183,0.173,0.178,0.179,0.164,0.134,0.102,0.076,0.061,0.058,0.075,0.12,0.186,0.254,0.293,0.292,0.257,0.214,0.185,0.187,0.22,0.267,0.305,0.323,0.322,0.313,0.295,0.261,0.21,0.161,0.134,0.137,0.163,0.189,0.196,0.18,0.157,0.146,0.156,0.173,0.175,0.153,0.116,0.082,0.06,0.051,0.046,0.043,0.04,0.039,0.046,0.068,0.113,0.178,0.249,0.301,0.319,0.298,0.251,0.2,0.17,0.168,0.19,0.228,0.286,0.365,0.451,0.509,0.508,0.451,0.368,0.302,0.273,0.269,0.259,0.223,0.166,0.111,0.076,0.067,0.084,0.128,0.197,0.271,0.316,0.311,0.267,0.218,0.197,0.207,0.227,0.232,0.212,0.171,0.125,0.086,0.062,0.052,0.05,0.051,0.06,0.088,0.145,0.223,0.291,0.319,0.293,0.23,0.159,0.105,0.072,0.056,0.052,0.061,0.088,0.134,0.19,0.243,0.274,0.278,0.263,0.255,0.27,0.304,0.334,0.348,0.343,0.33,0.303,0.258,0.195,0.135,0.099,0.102,0.14,0.196,0.241,0.253,0.231,0.196,0.165,0.142,0.121,0.096,0.072,0.053,0.041,0.035,0.033,0.032,0.032,0.031,0.03,0.037,0.062,0.11,0.172,0.221,0.232,0.205,0.165,0.137,0.127,0.122,0.114,0.105,0.106,0.12,0.134,0.134,0.114,0.085,0.06,0.045,0.04,0.037,0.036,0.034,0.037,0.054,0.092,0.155,0.23,0.307,0.374,0.429,0.468,0.485,0.465,0.404,0.311,0.213,0.134,0.087,0.07,0.073,0.089,0.114,0.146,0.179,0.204,0.212,0.199,0.167,0.127,0.091,0.065,0.05,0.046,0.054,0.081,0.13,0.196,0.256,0.288,0.277,0.231,0.17,0.12,0.093,0.094,0.116,0.15,0.183,0.2,0.192,0.162,0.123,0.089,0.066,0.054,0.051,0.06,0.091,0.153,0.243,0.339,0.406,0.416,0.368,0.285,0.201,0.14,0.111,0.113,0.135,0.16,0.167,0.152,0.123,0.1,0.103,0.136,0.184,0.218,0.214,0.174,0.122,0.084,0.074,0.09,0.122,0.163,0.211,0.269,0.335,0.39,0.407,0.368,0.285,0.19,0.115,0.072,0.056,0.057,0.075,0.113,0.166,0.216,0.243,0.243,0.227,0.211,0.197,0.177,0.147,0.117,0.102,0.105,0.118,0.13,0.138,0.156,0.199,0.278,0.368,0.433,0.435,0.371,0.268,0.168,0.096,0.057,0.041,0.036,0.04,0.063,0.11,0.171,0.219,0.226,0.187,0.126,0.073,0.044,0.039,0.046,0.058,0.074,0.097,0.129,0.166,0.189,0.185,0.152,0.108,0.071,0.054,0.06,0.087,0.127,0.176,0.23,0.291,0.347,0.379,0.373,0.332,0.269,0.202,0.142,0.095,0.064,0.053,0.061,0.084,0.109,0.119,0.109,0.084,0.058,0.04,0.032,0.03,0.036,0.055,0.096,0.156,0.219,0.255,0.247,0.198,0.135,0.08,0.047,0.034,0.032,0.034,0.036,0.035,0.034,0.036,0.046,0.064,0.088,0.113,0.136,0.158,0.173,0.172,0.151,0.114,0.081,0.068,0.082,0.115,0.152,0.183,0.21,0.233,0.247,0.234,0.192,0.132,0.08,0.048,0.035,0.032,0.031,0.029,0.029,0.031,0.042,0.067,0.106,0.144,0.164,0.156,0.129,0.108,0.122,0.176,0.247,0.295,0.295,0.251,0.199,0.169,0.168,0.189,0.218,0.242,0.246,0.22,0.171,0.117,0.078,0.064,0.075,0.105,0.147,0.185,0.205,0.195,0.16,0.116,0.085,0.079,0.094,0.119,0.137,0.138,0.122,0.1,0.084,0.086,0.107,0.144,0.179,0.196,0.183,0.148,0.104,0.069,0.052,0.062,0.093,0.138,0.175,0.19,0.175,0.139,0.096,0.063,0.045,0.046,0.067,0.108,0.163,0.222,0.272,0.297,0.282,0.229,0.157,0.093,0.058,0.059,0.09,0.133,0.165,0.168,0.141,0.1,0.065,0.049,0.054,0.085,0.134,0.186,0.216,0.211,0.179,0.141,0.115,0.106,0.114,0.141,0.189,0.253,0.309,0.33,0.299,0.231,0.159,0.111,0.096,0.102,0.112,0.114,0.104,0.085,0.064,0.045,0.033,0.034,0.057,0.114,0.199,0.295,0.365,0.389,0.359,0.294,0.214,0.144,0.092,0.06,0.043,0.035,0.034,0.043,0.066,0.103,0.142,0.165,0.158,0.124,0.084,0.056,0.047,0.056,0.072,0.084,0.086,0.077,0.062,0.047,0.036,0.03,0.032,0.043,0.063,0.09,0.124,0.159,0.185,0.188,0.165,0.123,0.082,0.052,0.036,0.032,0.039,0.065,0.116,0.189,0.262,0.313,0.327,0.31,0.274,0.241,0.213,0.194,0.182,0.18,0.184,0.188,0.177,0.151,0.115,0.086,0.074,0.081,0.098,0.116,0.126,0.129,0.131,0.14,0.154,0.171,0.188,0.203,0.211,0.202,0.173,0.133,0.097,0.073,0.058,0.05,0.044,0.041,0.04,0.041,0.049,0.071,0.109,0.154,0.191,0.204,0.194,0.17,0.142,0.113,0.084,0.063,0.058,0.071,0.095,0.114,0.116,0.1,0.085,0.091,0.123,0.165,0.187,0.174,0.132,0.09,0.068,0.073,0.096,0.127,0.158,0.178,0.18,0.16,0.129,0.098,0.085,0.093,0.117,0.141,0.151,0.141,0.12,0.102,0.099,0.108,0.116,0.114,0.108,0.116,0.145,0.184,0.207,0.198,0.16,0.115,0.084,0.081,0.101,0.13,0.153,0.166,0.169,0.166,0.153,0.129,0.097,0.069,0.05,0.042,0.038,0.036,0.035,0.037,0.04,0.042,0.043,0.051,0.081,0.14,0.22,0.29,0.333,0.344,0.344,0.347,0.353,0.343,0.302,0.231,0.151,0.087,0.05,0.038,0.046,0.072,0.11,0.154,0.186,0.195,0.177,0.142,0.102,0.071,0.053,0.05,0.061,0.087,0.126,0.167,0.194,0.194,0.166,0.126,0.088,0.066,0.069,0.1,0.147,0.186,0.197,0.177,0.148,0.135,0.151,0.189,0.229,0.252,0.246,0.211,0.162,0.115,0.085,0.076,0.083,0.102,0.126,0.149,0.164,0.162,0.144,0.123,0.116,0.132,0.161,0.184,0.191,0.193,0.206,0.231,0.244,0.229,0.184,0.129,0.084,0.058,0.047,0.045,0.047,0.055,0.068,0.087,0.104,0.111,0.103,0.09,0.089,0.108,0.143,0.175,0.19,0.185,0.165,0.139,0.117,0.114,0.141,0.197,0.264,0.32,0.351,0.352,0.322,0.264,0.19,0.12,0.071,0.051,0.062,0.106,0.178,0.261,0.326,0.357,0.359,0.351,0.344,0.336,0.314,0.271,0.216,0.173,0.168,0.208,0.281,0.358,0.409,0.419,0.388,0.336,0.283,0.241,0.206,0.173,0.141,0.113,0.092,0.076,0.061,0.05,0.044,0.049,0.071,0.121,0.197,0.281,0.341,0.352,0.316,0.255,0.197,0.153,0.132,0.138,0.176,0.234,0.287,0.304,0.275,0.211,0.145,0.099,0.079,0.077,0.082,0.088,0.097,0.111,0.127,0.135,0.133,0.12,0.111,0.117,0.146,0.19,0.235,0.271,0.288,0.284,0.252,0.199,0.138,0.1,0.105,0.155,0.226,0.276,0.279,0.237,0.186,0.159,0.166,0.189,0.203,0.194,0.171,0.155,0.154,0.16,0.16,0.152,0.151,0.163,0.185,0.195,0.18,0.143,0.1,0.068,0.054,0.058,0.076,0.102,0.121,0.126,0.116,0.098,0.079,0.063,0.05,0.04,0.033,0.03,0.03,0.03,0.031,0.036,0.055,0.096,0.163,0.245,0.322,0.366,0.359,0.302,0.219,0.143,0.104,0.108,0.148,0.2,0.245,0.274,0.291,0.304,0.307,0.296,0.268,0.238,0.219,0.211,0.195,0.161,0.113,0.071,0.049,0.054,0.078,0.106,0.122,0.119,0.1,0.081,0.073,0.077,0.083,0.08,0.068,0.051,0.039,0.035,0.039,0.051,0.073,0.101,0.126,0.137,0.129,0.105,0.077,0.056,0.043,0.036,0.032,0.03,0.029,0.03,0.03,0.03,0.029,0.027,0.031,0.05,0.089,0.141,0.186,0.203,0.198,0.201,0.244,0.328,0.413,0.458,0.441,0.382,0.309,0.242,0.181,0.126,0.081,0.056,0.055,0.082,0.128,0.18,0.214,0.214,0.181,0.133,0.092,0.074,0.079,0.096,0.109,0.106,0.087,0.069,0.074,0.115,0.184,0.251,0.28,0.257,0.2,0.144,0.112,0.113,0.13,0.145,0.148,0.145,0.152,0.174,0.205,0.231,0.243,0.242,0.229,0.204,0.166,0.123,0.083,0.057,0.044,0.043,0.056,0.084,0.132,0.191,0.244,0.269,0.253,0.201,0.137,0.091,0.086,0.134,0.228,0.335,0.409,0.409,0.336,0.228,0.14,0.101,0.115,0.159,0.205,0.226,0.216,0.179,0.132,0.088,0.057,0.038,0.03,0.032,0.049,0.085,0.135,0.184,0.216,0.225,0.215,0.194,0.165,0.134,0.11,0.105,0.123,0.155,0.188,0.208,0.216,0.218,0.225,0.242,0.267,0.289,0.295,0.275,0.234,0.189,0.158,0.15,0.158,0.166,0.16,0.137,0.107,0.081,0.063,0.056,0.061,0.077,0.101,0.123,0.138,0.152,0.172,0.197,0.21,0.198,0.162,0.121,0.1,0.11,0.152,0.211,0.264,0.284,0.261,0.205,0.145,0.104,0.098,0.13,0.197,0.28,0.346,0.366,0.331,0.26,0.186,0.129,0.096,0.081,0.077,0.074,0.069,0.064,0.065,0.076,0.094,0.11,0.116,0.111,0.1,0.088,0.077,0.066,0.055,0.048,0.054,0.078,0.116,0.154,0.17,0.154,0.119,0.091,0.095,0.138,0.201,0.256,0.284,0.28,0.255,0.225,0.211,0.229,0.279,0.343,0.399,0.433,0.448,0.444,0.413,0.351,0.267,0.188,0.139,0.126,0.139,0.163,0.189,0.212,0.224,0.216,0.187,0.146,0.104,0.073,0.061,0.074,0.115,0.171,0.216,0.226,0.196,0.147,0.109,0.098,0.114,0.137,0.148,0.137,0.111,0.08,0.057,0.044,0.04,0.04,0.04,0.039,0.042,0.053,0.082,0.134,0.196,0.245,0.264,0.254,0.237,0.223,0.211,0.191,0.166,0.156,0.177,0.226,0.276,0.301,0.298,0.281,0.263,0.241,0.21,0.17,0.134,0.114,0.118,0.141,0.169,0.182,0.171,0.14,0.105,0.077,0.061,0.054,0.049,0.044,0.037,0.031,0.029,0.036,0.06,0.099,0.141,0.166,0.16,0.129,0.09,0.059,0.043,0.039,0.048,0.069,0.095,0.115,0.119,0.105,0.083,0.061,0.05,0.056,0.094,0.169,0.269,0.363,0.421,0.424,0.388,0.334,0.282,0.233,0.185,0.142,0.12,0.13,0.175,0.239,0.307,0.361,0.394,0.405,0.403,0.396,0.388,0.373,0.34,0.286,0.221,0.164,0.14,0.154,0.196,0.236,0.254,0.244,0.222,0.2,0.188,0.187,0.189,0.185,0.172,0.157,0.15,0.156,0.163,0.156,0.135,0.113,0.115,0.148,0.197,0.232,0.235,0.214,0.192,0.189,0.199,0.215,0.233,0.254,0.274,0.276,0.249,0.198,0.139,0.091,0.061,0.047,0.042,0.039,0.037,0.037,0.046,0.07,0.111,0.155,0.185,0.184,0.158,0.126,0.116,0.141,0.195,0.261,0.324,0.377,0.417,0.432,0.408,0.344,0.265,0.207,0.195,0.22,0.249,0.251,0.217,0.163,0.12,0.112,0.143,0.197,0.246,0.27,0.279,0.3,0.359,0.451,0.542,0.587,0.563,0.471,0.348,0.232,0.151,0.105,0.084,0.083,0.107,0.153,0.202,0.231,0.234,0.23,0.239,0.261,0.272,0.249,0.2,0.153,0.138,0.156,0.187,0.201,0.188,0.154,0.117,0.09,0.076,0.071,0.068,0.069,0.082,0.12,0.181,0.249,0.294,0.293,0.247,0.177,0.112,0.069,0.05,0.048,0.053,0.058,0.061,0.065,0.075,0.094,0.117,0.138,0.151,0.151,0.137,0.119,0.114,0.14,0.199,0.267,0.308,0.299,0.255,0.217,0.228,0.299,0.399,0.476,0.488,0.429,0.327,0.221,0.139,0.092,0.077,0.09,0.125,0.179,0.239,0.286,0.3,0.273,0.215,0.151,0.101,0.074,0.067,0.079,0.112,0.166,0.225,0.265,0.272,0.253,0.23,0.213,0.2,0.183,0.161,0.139,0.119,0.099,0.079,0.06,0.052,0.065,0.108,0.177,0.248,0.293,0.304,0.302,0.314,0.339,0.347,0.313,0.239,0.157,0.099,0.076,0.084,0.111,0.146,0.177,0.193,0.192,0.19,0.201,0.228,0.255,0.265,0.254,0.236,0.226,0.228,0.229,0.219,0.191,0.155,0.123,0.108,0.116,0.141,0.173,0.194,0.19,0.164,0.129,0.101,0.089,0.094,0.112,0.137,0.16,0.182,0.204,0.228,0.238,0.226,0.19,0.15,0.123,0.117,0.124,0.137,0.154,0.172,0.189,0.194,0.184,0.167,0.161,0.177,0.213,0.248,0.267,0.257,0.225,0.183,0.146,0.124,0.125,0.148,0.187,0.224,0.238,0.221,0.181,0.137,0.107,0.096,0.112,0.156,0.224,0.291,0.328,0.317,0.267,0.2,0.139,0.099,0.086,0.107,0.162,0.238,0.306,0.338,0.328,0.301,0.289,0.304,0.331,0.34,0.317,0.273,0.236,0.227,0.243,0.26,0.256,0.222,0.171,0.122,0.091,0.086,0.103,0.133,0.163,0.185,0.198,0.207,0.215,0.227,0.24,0.247,0.241,0.222,0.206,0.213,0.25,0.297,0.328,0.323,0.288,0.241,0.196,0.159,0.129,0.103,0.087,0.09,0.12,0.177,0.253,0.33,0.384,0.395,0.364,0.309,0.256,0.219,0.194,0.169,0.141,0.118,0.109,0.117,0.139,0.166,0.196,0.232,0.275,0.316,0.34,0.339,0.316,0.282,0.246,0.211,0.179,0.149,0.12,0.093,0.079,0.091,0.137,0.211,0.291,0.342,0.343,0.298,0.234,0.181,0.156,0.153,0.161,0.174,0.203,0.255,0.322,0.38,0.404,0.387,0.338,0.277,0.217,0.168,0.132,0.108,0.094,0.084,0.078,0.074,0.075,0.083,0.102,0.132,0.163,0.18,0.174,0.152,0.129,0.117,0.122,0.142,0.167,0.184,0.183,0.165,0.143,0.129,0.125,0.127,0.126,0.122,0.116,0.112,0.118,0.135,0.156,0.171,0.172,0.168,0.17,0.187,0.212,0.24,0.265,0.284,0.288,0.278,0.261,0.249,0.244,0.238,0.221,0.199,0.181,0.181,0.201,0.233,0.264,0.277,0.267,0.238,0.206,0.189,0.199,0.234,0.275,0.294,0.279,0.237,0.195,0.172,0.169,0.171,0.161,0.138,0.115,0.108,0.127,0.168,0.213,0.242,0.24,0.209,0.164,0.125,0.099,0.087,0.079,0.072,0.062,0.052,0.045,0.045,0.054,0.075,0.104,0.135,0.159,0.178,0.204,0.249,0.313,0.376,0.412,0.41,0.383,0.353,0.335,0.331,0.34,0.356,0.369,0.373,0.382,0.418,0.493,0.574,0.615,0.586,0.504,0.407,0.329,0.284,0.268,0.271,0.278,0.281,0.273,0.256,0.234,0.219,0.213,0.215,0.215,0.209,0.197,0.188,0.182,0.181,0.184,0.197,0.222,0.256,0.286,0.304,0.308,0.303,0.296,0.291,0.289,0.289,0.294,0.313,0.353,0.405,0.443,0.441,0.394,0.319,0.248,0.201,0.183,0.195,0.229,0.271,0.303,0.312,0.296,0.268,0.24,0.217,0.197,0.177,0.156,0.14,0.135,0.142,0.154,0.161,0.157,0.142,0.125,0.112,0.104,0.095,0.084,0.073,0.068,0.067,0.067,0.062,0.052,0.045,0.045,0.054,0.07,0.084,0.092,0.093,0.09,0.089,0.097,0.118,0.146,0.17,0.179,0.175,0.177,0.201,0.251,0.302,0.32,0.289,0.224,0.162,0.13,0.135,0.158,0.175,0.168,0.139,0.102,0.072,0.056,0.054,0.061,0.073,0.09,0.104,0.114,0.116,0.114,0.111,0.106,0.101,0.093,0.083,0.073,0.066,0.06,0.057,0.056,0.056,0.057,0.065,0.085,0.123,0.175,0.228,0.267,0.283,0.277,0.251,0.214,0.173,0.134,0.105,0.091,0.094,0.112,0.143,0.177,0.21,0.236,0.255,0.263,0.256,0.235,0.214,0.21,0.231,0.26,0.271,0.247,0.198,0.144,0.102,0.076,0.06,0.051,0.047,0.054,0.076,0.113,0.154,0.186,0.201,0.202,0.2,0.2,0.204,0.201,0.188,0.168,0.152,0.149,0.166,0.196,0.226,0.242,0.24,0.229,0.217,0.207,0.198,0.188,0.182,0.177,0.17,0.153,0.131,0.119,0.131,0.169,0.214,0.245,0.249,0.231,0.205,0.179,0.154,0.129,0.106,0.09,0.085,0.087,0.093,0.1,0.105,0.109,0.117,0.131,0.151,0.165,0.164,0.147,0.128,0.119,0.123,0.133,0.136,0.126,0.106,0.085,0.074,0.081,0.103,0.137,0.172,0.199,0.211,0.205,0.184,0.151,0.115,0.083,0.06,0.044,0.034,0.028,0.024,0.023,0.027,0.037,0.048,0.054,0.05,0.037,0.023,0.015]