[0.004,0.009,0.023,0.046,0.079,0.116,0.152,0.181,0.204,0.221,0.236,0.249,0.262,0.274,0.288,0.302,0.318,0.338,0.36,0.381,0.394,0.395,0.384,0.367,0.352,0.343,0.338,0.333,0.323,0.307,0.287,0.269,0.254,0.241,0.227,0.213,0.201,0.192,0.186,0.182,0.179,0.177,0.174,0.166,0.155,0.14,0.127,0.116,0.108,0.101,0.098,0.099,0.102,0.105,0.107,0.109,0.113,0.119,0.124,0.128,0.127,0.123,0.119,0.116,0.115,0.115,0.113,0.11,0.105,0.1,0.097,0.095,0.099,0.109,0.131,0.166,0.213,0.266,0.316,0.354,0.374,0.376,0.367,0.355,0.344,0.336,0.328,0.32,0.312,0.306,0.3,0.292,0.281,0.265,0.244,0.222,0.201,0.185,0.175,0.168,0.161,0.153,0.145,0.141,0.143,0.15,0.157,0.162,0.163,0.161,0.156,0.149,0.14,0.128,0.115,0.103,0.094,0.09,0.088,0.086,0.084,0.081,0.079,0.078,0.079,0.08,0.08,0.078,0.075,0.071,0.067,0.065,0.065,0.067,0.069,0.07,0.068,0.064,0.061,0.06,0.065,0.076,0.091,0.107,0.12,0.131,0.138,0.144,0.151,0.16,0.171,0.184,0.197,0.211,0.224,0.235,0.243,0.244,0.241,0.233,0.223,0.214,0.209,0.208,0.214,0.225,0.237,0.246,0.249,0.246,0.235,0.216,0.194,0.172,0.154,0.143,0.137,0.135,0.136,0.139,0.143,0.147,0.15,0.153,0.155,0.158,0.16,0.162,0.165,0.167,0.169,0.17,0.166,0.159,0.148,0.137,0.128,0.122,0.12,0.12,0.121,0.122,0.121,0.118,0.115,0.112,0.113,0.116,0.121,0.127,0.133,0.136,0.138,0.138,0.137,0.135,0.132,0.126,0.117,0.107,0.1,0.095,0.094,0.095,0.097,0.099,0.1,0.1,0.097,0.092,0.086,0.081,0.079,0.079,0.081,0.085,0.089,0.094,0.1,0.106,0.112,0.116,0.117,0.115,0.112,0.107,0.104,0.103,0.102,0.101,0.1,0.097,0.095,0.092,0.09,0.087,0.085,0.084,0.084,0.085,0.086,0.088,0.091,0.095,0.099,0.103,0.106,0.105,0.102,0.097,0.093,0.088,0.085,0.081,0.079,0.079,0.085,0.099,0.123,0.156,0.193,0.234,0.277,0.323,0.369,0.405,0.425,0.424,0.412,0.397,0.39,0.388,0.389,0.385,0.374,0.357,0.341,0.331,0.328,0.327,0.324,0.319,0.316,0.319,0.325,0.325,0.318,0.306,0.294,0.285,0.277,0.268,0.258,0.249,0.24,0.23,0.218,0.204,0.189,0.175,0.162,0.151,0.14,0.13,0.121,0.114,0.108,0.103,0.099,0.097,0.095,0.092,0.089,0.086,0.084,0.083,0.084,0.084,0.082,0.08,0.077,0.075,0.074,0.079,0.093,0.114,0.139,0.164,0.186,0.203,0.215,0.219,0.216,0.209,0.201,0.202,0.217,0.246,0.284,0.319,0.342,0.347,0.337,0.312,0.277,0.238,0.201,0.174,0.161,0.164,0.179,0.2,0.219,0.23,0.228,0.217,0.199,0.179,0.159,0.144,0.135,0.134,0.14,0.152,0.165,0.178,0.185,0.184,0.172,0.154,0.132,0.111,0.093,0.081,0.072,0.066,0.06,0.054,0.048,0.044,0.043,0.044,0.046,0.048,0.049,0.049,0.048,0.049,0.053,0.06,0.068,0.078,0.09,0.105,0.125,0.148,0.173,0.197,0.219,0.239,0.258,0.278,0.296,0.313,0.325,0.332,0.332,0.332,0.335,0.341,0.343,0.341,0.336,0.334,0.338,0.346,0.35,0.35,0.348,0.351,0.358,0.363,0.361,0.357,0.358,0.366,0.374,0.373,0.365,0.358,0.362,0.373,0.383,0.388,0.388,0.389,0.394,0.4,0.403,0.399,0.391,0.381,0.371,0.362,0.349,0.335,0.32,0.308,0.296,0.279,0.255,0.226,0.202,0.188,0.186,0.193,0.205,0.218,0.234,0.253,0.274,0.292,0.301,0.301,0.296,0.289,0.285,0.281,0.274,0.264,0.253,0.243,0.233,0.22,0.203,0.183,0.167,0.16,0.164,0.176,0.192,0.211,0.231,0.25,0.266,0.277,0.284,0.286,0.285,0.283,0.279,0.275,0.271,0.265,0.256,0.243,0.225,0.204,0.184,0.169,0.162,0.164,0.173,0.185,0.196,0.205,0.214,0.224,0.237,0.249,0.259,0.265,0.268,0.269,0.27,0.268,0.261,0.249,0.232,0.214,0.195,0.18,0.17,0.168,0.17,0.173,0.174,0.174,0.176,0.182,0.195,0.215,0.246,0.286,0.331,0.375,0.41,0.433,0.446,0.451,0.452,0.449,0.445,0.443,0.444,0.449,0.455,0.457,0.454,0.445,0.431,0.415,0.404,0.401,0.405,0.412,0.418,0.417,0.409,0.393,0.373,0.347,0.318,0.286,0.26,0.244,0.241,0.247,0.254,0.257,0.255,0.247,0.233,0.213,0.19,0.167,0.146,0.13,0.12,0.115,0.115,0.116,0.118,0.118,0.116,0.112,0.106,0.1,0.094,0.091,0.09,0.091,0.091,0.086,0.078,0.069,0.063,0.064,0.074,0.092,0.116,0.143,0.168,0.193,0.222,0.257,0.298,0.341,0.387,0.436,0.485,0.532,0.575,0.617,0.658,0.7,0.737,0.767,0.791,0.81,0.823,0.83,0.828,0.816,0.794,0.767,0.738,0.713,0.69,0.665,0.637,0.608,0.579,0.549,0.517,0.48,0.44,0.397,0.351,0.303,0.254,0.21,0.174,0.15,0.137,0.135,0.141,0.152,0.166,0.181,0.195,0.207,0.217,0.225,0.23,0.232,0.229,0.222,0.213,0.204,0.192,0.18,0.167,0.156,0.148,0.144,0.144,0.151,0.168,0.193,0.222,0.247,0.262,0.266,0.267,0.268,0.269,0.267,0.259,0.244,0.228,0.217,0.214,0.217,0.221,0.223,0.222,0.221,0.224,0.23,0.236,0.237,0.234,0.23,0.23,0.236,0.244,0.249,0.249,0.245,0.24,0.238,0.237,0.236,0.234,0.236,0.242,0.247,0.248,0.242,0.232,0.224,0.224,0.23,0.24,0.249,0.255,0.253,0.247,0.243,0.251,0.272,0.298,0.316,0.319,0.313,0.309,0.311,0.314,0.315,0.321,0.336,0.358,0.374,0.371,0.355,0.339,0.339,0.353,0.37,0.379,0.382,0.386,0.393,0.399,0.392,0.371,0.342,0.313,0.286,0.26,0.235,0.213,0.197,0.187,0.177,0.164,0.15,0.141,0.14,0.148,0.158,0.165,0.165,0.161,0.16,0.169,0.187,0.206,0.218,0.219,0.212,0.206,0.207,0.217,0.232,0.245,0.248,0.239,0.221,0.2,0.186,0.182,0.187,0.194,0.205,0.221,0.246,0.274,0.295,0.3,0.287,0.261,0.233,0.212,0.205,0.212,0.227,0.243,0.252,0.25,0.237,0.219,0.202,0.192,0.192,0.204,0.225,0.254,0.291,0.332,0.374,0.407,0.424,0.426,0.416,0.404,0.397,0.397,0.404,0.412,0.416,0.414,0.409,0.405,0.406,0.413,0.424,0.437,0.443,0.439,0.425,0.407,0.39,0.379,0.375,0.375,0.378,0.384,0.393,0.4,0.399,0.39,0.375,0.36,0.346,0.334,0.325,0.322,0.328,0.339,0.348,0.344,0.327,0.305,0.288,0.284,0.289,0.299,0.307,0.312,0.315,0.319,0.324,0.327,0.325,0.322,0.318,0.316,0.317,0.32,0.325,0.329,0.329,0.326,0.319,0.31,0.298,0.282,0.266,0.252,0.243,0.239,0.236,0.229,0.222,0.218,0.222,0.233,0.244,0.25,0.25,0.248,0.251,0.263,0.279,0.288,0.285,0.272,0.258,0.249,0.246,0.244,0.239,0.23,0.22,0.209,0.197,0.185,0.176,0.175,0.187,0.209,0.234,0.252,0.255,0.244,0.222,0.197,0.177,0.17,0.179,0.202,0.233,0.263,0.283,0.286,0.271,0.241,0.208,0.181,0.167,0.169,0.187,0.214,0.242,0.261,0.269,0.263,0.247,0.226,0.203,0.181,0.164,0.154,0.155,0.166,0.184,0.203,0.218,0.227,0.23,0.23,0.229,0.226,0.222,0.219,0.218,0.22,0.224,0.225,0.22,0.209,0.195,0.184,0.182,0.189,0.2,0.212,0.221,0.23,0.238,0.246,0.251,0.253,0.252,0.249,0.245,0.24,0.237,0.235,0.234,0.232,0.228,0.223,0.217,0.209,0.202,0.197,0.196,0.2,0.207,0.215,0.222,0.228,0.233,0.238,0.241,0.24,0.233,0.221,0.207,0.196,0.187,0.183,0.178,0.174,0.168,0.161,0.153,0.145,0.136,0.13,0.127,0.127,0.128,0.13,0.133,0.137,0.143,0.15,0.159,0.169,0.177,0.182,0.182,0.177,0.169,0.161,0.155,0.151,0.147,0.143,0.139,0.135,0.131,0.129,0.128,0.129,0.132,0.135,0.136,0.137,0.138,0.139,0.141,0.143,0.146,0.147,0.146,0.145,0.141,0.137,0.131,0.127,0.124,0.122,0.121,0.12,0.119,0.118,0.116,0.113,0.11,0.108,0.106,0.106,0.108,0.111,0.115,0.122,0.128,0.134,0.139,0.143,0.148,0.157,0.17,0.186,0.201,0.212,0.219,0.227,0.24,0.262,0.288,0.311,0.326,0.339,0.353,0.368,0.379,0.384,0.382,0.378,0.374,0.369,0.356,0.334,0.309,0.29,0.283,0.282,0.279,0.266,0.249,0.237,0.233,0.231,0.224,0.212,0.204,0.205,0.211,0.214,0.206,0.189,0.168,0.149,0.133,0.122,0.115,0.112,0.114,0.119,0.125,0.131,0.137,0.143,0.148,0.151,0.15,0.147,0.144,0.139,0.132,0.126,0.123,0.122,0.121,0.118,0.113,0.108,0.107,0.111,0.122,0.143,0.176,0.22,0.268,0.315,0.352,0.374,0.379,0.371,0.355,0.34,0.329,0.322,0.316,0.309,0.303,0.297,0.292,0.283,0.268,0.246,0.218,0.191,0.17,0.155,0.147,0.142,0.139,0.138,0.143,0.151,0.161,0.168,0.17,0.167,0.162,0.155,0.147,0.138,0.13,0.121,0.112,0.104,0.096,0.089,0.08,0.073,0.067,0.063,0.062,0.063,0.065,0.067,0.068,0.067,0.065,0.064,0.064,0.065,0.067,0.068,0.069,0.069,0.068,0.066,0.065,0.067,0.077,0.093,0.113,0.131,0.141,0.144,0.142,0.141,0.144,0.15,0.159,0.17,0.184,0.202,0.22,0.235,0.242,0.241,0.233,0.223,0.214,0.207,0.202,0.201,0.206,0.215,0.225,0.236,0.243,0.243,0.234,0.218,0.199,0.18,0.167,0.159,0.157,0.158,0.159,0.16,0.163,0.167,0.175,0.185,0.194,0.201,0.205,0.204,0.202,0.198,0.194,0.189,0.184,0.178,0.172,0.166,0.163,0.16,0.159,0.157,0.156,0.157,0.159,0.16,0.159,0.157,0.155,0.156,0.16,0.165,0.17,0.171,0.168,0.163,0.155,0.147,0.14,0.132,0.125,0.118,0.113,0.109,0.107,0.105,0.104,0.102,0.101,0.101,0.103,0.105,0.108,0.113,0.118,0.123,0.126,0.125,0.122,0.117,0.114,0.112,0.112,0.113,0.114,0.116,0.118,0.12,0.122,0.123,0.124,0.124,0.123,0.122,0.121,0.119,0.117,0.116,0.115,0.115,0.117,0.119,0.119,0.119,0.118,0.118,0.119,0.119,0.119,0.117,0.113,0.11,0.107,0.106,0.105,0.106,0.108,0.112,0.12,0.131,0.145,0.16,0.176,0.19,0.2,0.209,0.216,0.222,0.225,0.226,0.223,0.216,0.205,0.194,0.184,0.178,0.174,0.17,0.164,0.156,0.151,0.151,0.155,0.161,0.163,0.161,0.155,0.147,0.141,0.134,0.128,0.125,0.125,0.127,0.127,0.123,0.115,0.106,0.098,0.092,0.087,0.084,0.081,0.08,0.079,0.078,0.077,0.075,0.073,0.071,0.07,0.069,0.07,0.07,0.07,0.069,0.066,0.062,0.058,0.056,0.054,0.054,0.053,0.052,0.053,0.057,0.067,0.084,0.104,0.126,0.143,0.154,0.16,0.162,0.16,0.155,0.149,0.144,0.144,0.149,0.158,0.166,0.17,0.17,0.172,0.179,0.194,0.213,0.233,0.248,0.256,0.257,0.249,0.236,0.218,0.198,0.176,0.155,0.136,0.122,0.112,0.107,0.105,0.104,0.102,0.099,0.093,0.086,0.079,0.075,0.074,0.078,0.086,0.096,0.104,0.111,0.113,0.111,0.105,0.098,0.09,0.082,0.074,0.066,0.058,0.052,0.048,0.048,0.05,0.053,0.054,0.053,0.052,0.052,0.057,0.07,0.094,0.129,0.173,0.221,0.271,0.316,0.352,0.371,0.372,0.357,0.339,0.326,0.32,0.314,0.307,0.297,0.29,0.285,0.282,0.274,0.26,0.239,0.217,0.198,0.183,0.172,0.164,0.162,0.169,0.188,0.218,0.257,0.298,0.34,0.378,0.409,0.429,0.437,0.433,0.418,0.391,0.353,0.309,0.265,0.226,0.198,0.181,0.176,0.181,0.194,0.211,0.227,0.236,0.237,0.23,0.22,0.208,0.199,0.193,0.195,0.203,0.217,0.233,0.246,0.253,0.252,0.248,0.242,0.239,0.235,0.229,0.221,0.216,0.216,0.221,0.228,0.236,0.243,0.249,0.253,0.254,0.254,0.252,0.249,0.243,0.234,0.222,0.211,0.206,0.208,0.216,0.226,0.235,0.242,0.247,0.254,0.261,0.267,0.267,0.263,0.257,0.25,0.244,0.24,0.235,0.228,0.218,0.208,0.203,0.202,0.206,0.214,0.225,0.238,0.255,0.274,0.291,0.305,0.314,0.32,0.322,0.32,0.315,0.305,0.29,0.272,0.252,0.233,0.216,0.201,0.189,0.181,0.179,0.184,0.195,0.208,0.217,0.219,0.216,0.208,0.202,0.198,0.201,0.21,0.224,0.238,0.246,0.248,0.246,0.241,0.234,0.227,0.22,0.215,0.212,0.209,0.208,0.206,0.205,0.205,0.206,0.207,0.207,0.205,0.2,0.193,0.184,0.176,0.169,0.163,0.159,0.158,0.16,0.164,0.168,0.169,0.17,0.172,0.175,0.177,0.174,0.168,0.164,0.168,0.18,0.194,0.206,0.211,0.213,0.211,0.208,0.203,0.195,0.187,0.18,0.175,0.171,0.165,0.157,0.151,0.149,0.152,0.161,0.171,0.182,0.194,0.207,0.219,0.228,0.234,0.24,0.25,0.265,0.281,0.296,0.308,0.317,0.32,0.318,0.314,0.31,0.306,0.303,0.301,0.302,0.305,0.31,0.316,0.32,0.32,0.315,0.305,0.294,0.282,0.271,0.26,0.25,0.24,0.228,0.217,0.211,0.213,0.22,0.23,0.238,0.243,0.246,0.247,0.246,0.244,0.242,0.243,0.248,0.255,0.261,0.265,0.269,0.271,0.273,0.275,0.278,0.282,0.285,0.285,0.282,0.278,0.275,0.271,0.263,0.253,0.245,0.243,0.245,0.249,0.251,0.25,0.246,0.24,0.231,0.221,0.212,0.203,0.197,0.193,0.192,0.193,0.194,0.198,0.205,0.212,0.215,0.211,0.199,0.185,0.173,0.162,0.153,0.146,0.14,0.136,0.134,0.135,0.138,0.141,0.145,0.15,0.159,0.171,0.183,0.19,0.19,0.18,0.163,0.144,0.13,0.123,0.121,0.121,0.119,0.116,0.114,0.116,0.12,0.123,0.124,0.125,0.128,0.134,0.142,0.151,0.158,0.159,0.155,0.146,0.135,0.123,0.114,0.109,0.107,0.11,0.117,0.128,0.139,0.151,0.162,0.173,0.181,0.187,0.191,0.195,0.197,0.197,0.193,0.186,0.18,0.179,0.183,0.189,0.194,0.195,0.194,0.192,0.194,0.197,0.202,0.204,0.202,0.195,0.183,0.168,0.152,0.137,0.128,0.126,0.131,0.141,0.151,0.157,0.16,0.159,0.156,0.152,0.147,0.144,0.144,0.145,0.147,0.15,0.154,0.16,0.165,0.168,0.166,0.158,0.149,0.141,0.138,0.138,0.141,0.143,0.142,0.138,0.132,0.125,0.119,0.115,0.115,0.12,0.131,0.148,0.169,0.192,0.214,0.234,0.25,0.26,0.264,0.264,0.26,0.256,0.25,0.246,0.243,0.244,0.25,0.257,0.262,0.263,0.26,0.254,0.249,0.249,0.255,0.265,0.273,0.279,0.281,0.283,0.286,0.288,0.286,0.278,0.266,0.255,0.25,0.252,0.256,0.257,0.251,0.241,0.23,0.219,0.209,0.2,0.191,0.186,0.187,0.192,0.202,0.211,0.22,0.223,0.218,0.205,0.187,0.168,0.152,0.138,0.127,0.119,0.114,0.112,0.112,0.114,0.118,0.123,0.127,0.132,0.137,0.144,0.151,0.158,0.164,0.169,0.173,0.178,0.184,0.19,0.195,0.199,0.202,0.204,0.208,0.211,0.216,0.221,0.227,0.235,0.243,0.252,0.258,0.261,0.262,0.26,0.257,0.252,0.245,0.236,0.225,0.213,0.203,0.194,0.186,0.179,0.171,0.163,0.155,0.149,0.144,0.141,0.138,0.134,0.131,0.127,0.123,0.12,0.117,0.116,0.115,0.112,0.11,0.106,0.104,0.103,0.102,0.101,0.099,0.098,0.097,0.097,0.097,0.097,0.097,0.1,0.106,0.116,0.128,0.139,0.148,0.154,0.16,0.164,0.165,0.161,0.154,0.145,0.135,0.128,0.123,0.124,0.13,0.141,0.15,0.154,0.151,0.142,0.132,0.123,0.115,0.107,0.099,0.093,0.089,0.089,0.092,0.096,0.101,0.107,0.113,0.121,0.129,0.138,0.144,0.145,0.14,0.129,0.114,0.099,0.088,0.081,0.075,0.07,0.065,0.061,0.059,0.058,0.058,0.058,0.057,0.056,0.056,0.058,0.059,0.061,0.061,0.059,0.057,0.054,0.052,0.049,0.046,0.042,0.039,0.037,0.036,0.035,0.035,0.034,0.033,0.032,0.032,0.032,0.032,0.032,0.03,0.028,0.027,0.026,0.025,0.025,0.025,0.024,0.023,0.022,0.021,0.02,0.02,0.02,0.021,0.021,0.02,0.019,0.018,0.017,0.015,0.014,0.013,0.012,0.011,0.011,0.011,0.012,0.013,0.015,0.015,0.016,0.015,0.015,0.014,0.013,0.012,0.012,0.011,0.011,0.01,0.009,0.009,0.008,0.008,0.008,0.008,0.008,0.008,0.008,0.009,0.009,0.009,0.009,0.009,0.009,0.008,0.008,0.008,0.008,0.008,0.007,0.007,0.007,0.007,0.006,0.006,0.006,0.006,0.006,0.006,0.006,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.005,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.004,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0.001,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]