[0.001,0.001,0.001,0.001,0.001,0.002,0.005,0.015,0.038,0.076,0.125,0.173,0.209,0.231,0.242,0.247,0.249,0.247,0.243,0.24,0.239,0.235,0.222,0.194,0.158,0.128,0.116,0.128,0.152,0.173,0.175,0.154,0.117,0.079,0.057,0.06,0.088,0.128,0.16,0.177,0.186,0.197,0.215,0.235,0.248,0.254,0.256,0.26,0.263,0.266,0.267,0.27,0.271,0.269,0.261,0.246,0.222,0.195,0.175,0.169,0.18,0.2,0.217,0.226,0.231,0.235,0.24,0.242,0.236,0.22,0.204,0.196,0.201,0.216,0.234,0.247,0.253,0.257,0.262,0.268,0.272,0.271,0.267,0.263,0.256,0.246,0.228,0.204,0.178,0.153,0.133,0.116,0.105,0.1,0.101,0.101,0.096,0.084,0.067,0.05,0.038,0.034,0.042,0.068,0.115,0.177,0.238,0.284,0.31,0.32,0.319,0.31,0.296,0.278,0.267,0.264,0.268,0.267,0.251,0.22,0.186,0.159,0.146,0.143,0.143,0.141,0.136,0.13,0.129,0.131,0.133,0.13,0.123,0.118,0.125,0.147,0.18,0.21,0.23,0.245,0.265,0.29,0.309,0.305,0.276,0.238,0.214,0.218,0.245,0.272,0.276,0.252,0.209,0.167,0.14,0.133,0.137,0.136,0.12,0.094,0.073,0.07,0.088,0.117,0.151,0.188,0.234,0.288,0.335,0.355,0.339,0.295,0.243,0.2,0.176,0.169,0.175,0.192,0.217,0.248,0.278,0.303,0.322,0.337,0.346,0.34,0.313,0.27,0.225,0.189,0.169,0.163,0.163,0.16,0.152,0.143,0.145,0.169,0.209,0.248,0.26,0.233,0.177,0.114,0.063,0.033,0.022,0.027,0.05,0.092,0.148,0.202,0.234,0.235,0.207,0.17,0.143,0.138,0.15,0.166,0.175,0.172,0.158,0.139,0.121,0.111,0.112,0.124,0.146,0.175,0.207,0.233,0.246,0.25,0.255,0.271,0.294,0.308,0.299,0.27,0.238,0.223,0.23,0.247,0.259,0.258,0.249,0.24,0.236,0.238,0.239,0.235,0.225,0.213,0.2,0.191,0.186,0.186,0.191,0.201,0.22,0.247,0.278,0.299,0.302,0.287,0.264,0.242,0.225,0.211,0.198,0.187,0.186,0.203,0.234,0.264,0.273,0.254,0.22,0.186,0.161,0.144,0.131,0.12,0.109,0.097,0.083,0.068,0.054,0.045,0.044,0.061,0.1,0.159,0.219,0.257,0.26,0.233,0.192,0.153,0.128,0.118,0.118,0.127,0.145,0.175,0.212,0.245,0.26,0.255,0.238,0.217,0.199,0.186,0.179,0.175,0.173,0.174,0.18,0.195,0.219,0.246,0.267,0.278,0.282,0.288,0.3,0.315,0.325,0.327,0.325,0.325,0.326,0.323,0.314,0.3,0.289,0.282,0.274,0.258,0.229,0.195,0.167,0.152,0.15,0.155,0.16,0.163,0.169,0.185,0.209,0.236,0.256,0.269,0.28,0.296,0.319,0.343,0.359,0.365,0.361,0.355,0.354,0.361,0.37,0.376,0.377,0.375,0.375,0.374,0.365,0.342,0.306,0.268,0.242,0.235,0.249,0.273,0.294,0.304,0.305,0.301,0.298,0.294,0.287,0.274,0.262,0.259,0.266,0.276,0.278,0.271,0.262,0.26,0.265,0.271,0.271,0.259,0.235,0.204,0.179,0.17,0.182,0.212,0.248,0.274,0.281,0.27,0.255,0.25,0.26,0.28,0.298,0.303,0.29,0.265,0.236,0.215,0.211,0.229,0.267,0.311,0.345,0.356,0.348,0.331,0.315,0.299,0.282,0.264,0.257,0.268,0.294,0.317,0.323,0.307,0.282,0.261,0.254,0.263,0.279,0.29,0.29,0.285,0.288,0.303,0.322,0.33,0.32,0.3,0.285,0.288,0.301,0.313,0.319,0.326,0.339,0.353,0.354,0.336,0.309,0.29,0.293,0.317,0.346,0.367,0.374,0.37,0.363,0.358,0.36,0.366,0.374,0.376,0.374,0.372,0.377,0.386,0.392,0.386,0.37,0.355,0.352,0.363,0.376,0.379,0.369,0.354,0.343,0.34,0.342,0.343,0.343,0.346,0.355,0.367,0.369,0.356,0.331,0.303,0.283,0.275,0.276,0.276,0.269,0.253,0.236,0.23,0.241,0.264,0.283,0.291,0.292,0.295,0.308,0.324,0.338,0.342,0.341,0.338,0.34,0.346,0.353,0.361,0.376,0.408,0.454,0.499,0.521,0.512,0.483,0.454,0.435,0.427,0.427,0.425,0.417,0.404,0.392,0.39,0.398,0.408,0.407,0.392,0.37,0.354,0.346,0.343,0.339,0.333,0.328,0.328,0.33,0.331,0.327,0.322,0.316,0.313,0.31,0.302,0.288,0.27,0.254,0.243,0.238,0.235,0.229,0.221,0.214,0.21,0.207,0.203,0.199,0.195,0.197,0.207,0.23,0.259,0.285,0.295,0.29,0.278,0.265,0.25,0.231,0.208,0.19,0.187,0.202,0.228,0.254,0.27,0.271,0.26,0.242,0.221,0.201,0.186,0.184,0.198,0.229,0.27,0.306,0.326,0.328,0.321,0.317,0.323,0.337,0.35,0.352,0.343,0.327,0.306,0.276,0.232,0.174,0.115,0.066,0.035,0.021,0.019,0.027,0.045,0.07,0.094,0.109,0.108,0.095,0.08,0.073,0.083,0.106,0.135,0.16,0.178,0.19,0.202,0.215,0.231,0.247,0.264,0.277,0.284,0.287,0.286,0.28,0.267,0.249,0.232,0.225,0.228,0.24,0.255,0.267,0.268,0.256,0.237,0.219,0.204,0.191,0.176,0.161,0.151,0.148,0.151,0.158,0.164,0.168,0.169,0.171,0.175,0.181,0.187,0.19,0.192,0.195,0.199,0.202,0.201,0.196,0.19,0.19,0.196,0.203,0.201,0.188,0.166,0.148,0.145,0.16,0.184,0.205,0.213,0.206,0.189,0.171,0.161,0.162,0.17,0.181,0.195,0.214,0.238,0.261,0.272,0.267,0.252,0.236,0.226,0.22,0.215,0.209,0.203,0.202,0.203,0.199,0.187,0.167,0.146,0.127,0.11,0.091,0.069,0.046,0.027,0.015,0.008,0.006,0.005,0.004,0.004,0.007,0.019,0.042,0.076,0.114,0.146,0.167,0.177,0.18,0.179,0.176,0.172,0.172,0.178,0.192,0.209,0.221,0.225,0.219,0.207,0.194,0.184,0.176,0.173,0.174,0.179,0.188,0.196,0.201,0.198,0.185,0.164,0.145,0.139,0.155,0.186,0.216,0.232,0.227,0.206,0.177,0.155,0.15,0.167,0.199,0.237,0.272,0.294,0.297,0.278,0.244,0.21,0.186,0.173,0.164,0.151,0.13,0.107,0.087,0.075,0.072,0.08,0.098,0.127,0.165,0.21,0.256,0.29,0.302,0.285,0.246,0.199,0.159,0.136,0.13,0.137,0.154,0.178,0.21,0.24,0.261,0.267,0.261,0.249,0.236,0.225,0.217,0.211,0.207,0.206,0.21,0.217,0.221,0.215,0.197,0.176,0.166,0.173,0.19,0.202,0.192,0.158,0.113,0.071,0.042,0.032,0.043,0.076,0.128,0.192,0.247,0.278,0.279,0.256,0.221,0.184,0.151,0.125,0.11,0.107,0.112,0.117,0.119,0.116,0.112,0.11,0.114,0.128,0.155,0.193,0.235,0.269,0.289,0.301,0.312,0.324,0.329,0.322,0.305,0.288,0.283,0.29,0.294,0.285,0.264,0.24,0.22,0.209,0.206,0.207,0.207,0.202,0.196,0.194,0.2,0.211,0.22,0.227,0.235,0.249,0.27,0.293,0.307,0.308,0.298,0.284,0.271,0.26,0.251,0.24,0.234,0.238,0.255,0.276,0.284,0.265,0.224,0.175,0.137,0.117,0.106,0.094,0.074,0.05,0.031,0.022,0.025,0.04,0.062,0.09,0.124,0.164,0.208,0.245,0.264,0.264,0.257,0.252,0.251,0.249,0.24,0.226,0.218,0.224,0.245,0.272,0.293,0.301,0.294,0.274,0.245,0.215,0.191,0.178,0.177,0.184,0.192,0.198,0.198,0.196,0.198,0.208,0.229,0.257,0.286,0.312,0.327,0.331,0.322,0.301,0.271,0.238,0.209,0.195,0.198,0.218,0.242,0.258,0.256,0.239,0.215,0.196,0.186,0.188,0.195,0.199,0.197,0.194,0.196,0.203,0.213,0.222,0.228,0.236,0.25,0.27,0.292,0.31,0.323,0.338,0.361,0.39,0.411,0.416,0.409,0.399,0.397,0.402,0.405,0.397,0.377,0.355,0.337,0.328,0.328,0.332,0.34,0.348,0.358,0.37,0.385,0.401,0.417,0.433,0.452,0.474,0.497,0.516,0.521,0.512,0.494,0.478,0.469,0.467,0.464,0.457,0.444,0.428,0.417,0.416,0.427,0.445,0.463,0.47,0.46,0.438,0.418,0.414,0.428,0.451,0.468,0.467,0.447,0.416,0.391,0.381,0.391,0.414,0.444,0.471,0.492,0.505,0.514,0.521,0.529,0.537,0.54,0.532,0.514,0.491,0.465,0.437,0.409,0.39,0.382,0.383,0.384,0.378,0.365,0.352,0.347,0.359,0.39,0.431,0.466,0.485,0.485,0.475,0.466,0.465,0.467,0.469,0.469,0.469,0.474,0.481,0.486,0.479,0.462,0.441,0.422,0.412,0.407,0.406,0.41,0.419,0.433,0.446,0.452,0.453,0.449,0.445,0.442,0.441,0.435,0.424,0.407,0.39,0.379,0.383,0.401,0.432,0.464,0.486,0.491,0.48,0.463,0.448,0.44,0.439,0.442,0.448,0.456,0.464,0.465,0.456,0.436,0.413,0.391,0.372,0.353,0.335,0.319,0.314,0.324,0.346,0.366,0.371,0.36,0.34,0.322,0.316,0.322,0.336,0.35,0.358,0.358,0.353,0.344,0.333,0.321,0.307,0.3,0.309,0.339,0.382,0.421,0.441,0.439,0.422,0.404,0.396,0.399,0.404,0.402,0.392,0.385,0.386,0.394,0.396,0.384,0.358,0.329,0.309,0.302,0.303,0.303,0.299,0.292,0.286,0.281,0.275,0.265,0.255,0.251,0.257,0.271,0.285,0.294,0.297,0.304,0.32,0.346,0.376,0.4,0.415,0.425,0.435,0.452,0.474,0.491,0.49,0.467,0.426,0.383,0.353,0.338,0.327,0.313,0.297,0.285,0.28,0.277,0.267,0.25,0.231,0.22,0.223,0.237,0.254,0.264,0.262,0.25,0.233,0.22,0.216,0.223,0.239,0.262,0.286,0.3,0.298,0.281,0.262,0.251,0.254,0.269,0.291,0.315,0.336,0.35,0.354,0.342,0.311,0.259,0.196,0.135,0.087,0.056,0.042,0.04,0.048,0.062,0.082,0.103,0.123,0.136,0.138,0.134,0.13,0.132,0.141,0.153,0.162,0.164,0.162,0.164,0.18,0.214,0.254,0.279,0.272,0.235,0.188,0.155,0.152,0.177,0.21,0.23,0.222,0.189,0.151,0.131,0.139,0.173,0.213,0.236,0.229,0.201,0.172,0.162,0.179,0.217,0.264,0.308,0.339,0.352,0.347,0.33,0.311,0.293,0.272,0.24,0.196,0.15,0.117,0.11,0.13,0.168,0.202,0.219,0.216,0.205,0.199,0.208,0.224,0.239,0.242,0.233,0.219,0.208,0.203,0.202,0.205,0.216,0.235,0.26,0.28,0.29,0.288,0.282,0.28,0.28,0.273,0.247,0.2,0.142,0.089,0.053,0.036,0.038,0.062,0.111,0.178,0.25,0.313,0.358,0.388,0.402,0.399,0.383,0.365,0.357,0.366,0.391,0.43,0.476,0.511,0.52,0.498,0.453,0.408,0.385,0.395,0.434,0.479,0.504,0.497,0.461,0.413,0.372,0.343,0.327,0.323,0.338,0.377,0.431,0.474,0.486,0.465,0.423,0.375,0.33,0.294,0.272,0.266,0.277,0.301,0.331,0.362,0.39,0.417,0.442,0.461,0.473,0.474,0.46,0.431,0.396,0.374,0.376,0.398,0.427,0.452,0.466,0.473,0.476,0.48,0.484,0.484,0.474,0.457,0.435,0.415,0.4,0.389,0.381,0.376,0.374,0.378,0.386,0.398,0.411,0.426,0.439,0.448,0.449,0.443,0.433,0.42,0.404,0.393,0.388,0.39,0.392,0.389,0.382,0.376,0.371,0.367,0.36,0.353,0.345,0.339,0.332,0.32,0.302,0.28,0.261,0.253,0.258,0.275,0.295,0.306,0.304,0.289,0.271,0.262,0.265,0.272,0.269,0.245,0.207,0.17,0.154,0.167,0.2,0.235,0.26,0.268,0.269,0.269,0.279,0.3,0.33,0.355,0.362,0.349,0.329,0.317,0.324,0.354,0.408,0.473,0.529,0.555,0.544,0.508,0.471,0.451,0.454,0.471,0.486,0.491,0.487,0.479,0.469,0.459,0.452,0.451,0.463,0.487,0.514,0.525,0.507,0.458,0.389,0.319,0.265,0.237,0.236,0.255,0.284,0.316,0.35,0.383,0.416,0.443,0.459,0.46,0.451,0.44,0.435,0.435,0.43,0.418,0.401,0.386,0.381,0.386,0.4,0.421,0.445,0.47,0.489,0.5,0.499,0.485,0.458,0.424,0.398,0.391,0.406,0.431,0.448,0.447,0.428,0.404,0.395,0.413,0.452,0.494,0.517,0.514,0.488,0.45,0.409,0.375,0.353,0.343,0.338,0.331,0.315,0.293,0.275,0.266,0.258,0.233,0.186,0.127,0.074,0.04,0.026,0.027,0.042,0.07,0.108,0.145,0.17,0.172,0.153,0.125,0.11,0.13,0.192,0.278,0.355,0.392,0.384,0.349,0.317,0.306,0.316,0.33,0.333,0.322,0.303,0.277,0.24,0.19,0.138,0.102,0.09,0.094,0.097,0.089,0.068,0.047,0.038,0.049,0.08,0.123,0.166,0.197,0.216,0.231,0.251,0.275,0.289,0.284,0.266,0.247,0.237,0.237,0.237,0.233,0.231,0.237,0.25,0.256,0.24,0.2,0.148,0.103,0.083,0.09,0.12,0.157,0.184,0.187,0.162,0.119,0.076,0.046,0.04,0.057,0.093,0.137,0.176,0.203,0.214,0.216,0.213,0.207,0.198,0.189,0.185,0.194,0.213,0.234,0.246,0.243,0.224,0.198,0.173,0.154,0.14,0.129,0.117,0.105,0.095,0.089,0.085,0.084,0.083,0.084,0.087,0.1,0.124,0.157,0.187,0.202,0.197,0.179,0.156,0.138,0.128,0.125,0.129,0.14,0.158,0.178,0.191,0.192,0.179,0.158,0.14,0.128,0.124,0.122,0.123,0.126,0.131,0.135,0.14,0.149,0.166,0.186,0.193,0.177,0.139,0.093,0.053,0.027,0.014,0.009,0.007,0.008,0.015,0.029,0.049,0.069,0.082,0.088,0.089,0.088,0.084,0.078,0.074,0.075,0.078,0.078,0.07,0.055,0.038,0.023,0.014,0.009,0.011,0.022,0.05,0.095,0.151,0.201,0.228,0.221,0.187,0.143,0.105,0.082,0.078,0.09,0.118,0.157,0.2,0.234,0.248,0.244,0.234,0.225,0.218,0.207,0.191,0.173,0.162,0.163,0.177,0.196,0.214,0.224,0.224,0.208,0.174,0.127,0.081,0.045,0.023,0.014,0.017,0.032,0.06,0.096,0.127,0.141,0.13,0.103,0.074,0.057,0.06,0.077,0.094,0.101,0.097,0.091,0.09,0.091,0.086,0.072,0.053,0.04,0.042,0.062,0.098,0.145,0.196,0.243,0.277,0.288,0.275,0.248,0.222,0.209,0.209,0.217,0.229,0.247,0.272,0.302,0.328,0.342,0.341,0.331,0.317,0.302,0.285,0.263,0.234,0.204,0.179,0.163,0.158,0.159,0.165,0.175,0.188,0.204,0.223,0.241,0.25,0.245,0.225,0.196,0.168,0.145,0.131,0.126,0.132,0.147,0.167,0.18,0.183,0.178,0.173,0.168,0.159,0.147,0.137,0.134,0.136,0.134,0.126,0.112,0.098,0.088,0.086,0.095,0.121,0.167,0.226,0.284,0.327,0.348,0.345,0.332,0.324,0.336,0.364,0.39,0.396,0.387,0.379,0.384,0.402,0.429,0.459,0.488,0.505,0.5,0.468,0.414,0.351,0.297,0.266,0.264,0.283,0.312,0.345,0.376,0.408,0.438,0.464,0.483,0.492,0.49,0.484,0.48,0.484,0.499,0.521,0.542,0.555,0.56,0.562,0.567,0.581,0.601,0.62,0.626,0.61,0.572,0.521,0.471,0.433,0.413,0.407,0.409,0.41,0.403,0.388,0.378,0.386,0.421,0.464,0.493,0.496,0.488,0.491,0.516,0.55,0.576,0.583,0.575,0.561,0.546,0.523,0.481,0.422,0.36,0.317,0.305,0.324,0.359,0.405,0.456,0.512,0.555,0.568,0.545,0.504,0.469,0.45,0.453,0.477,0.52,0.563,0.581,0.561,0.518,0.481,0.467,0.475,0.488,0.495,0.497,0.505,0.528,0.563,0.597,0.615,0.607,0.577,0.538,0.507,0.489,0.479,0.461,0.429,0.392,0.364,0.358,0.372,0.396,0.424,0.456,0.492,0.517,0.52,0.504,0.491,0.499,0.517,0.52,0.49,0.442,0.407,0.41,0.449,0.501,0.544,0.569,0.581,0.582,0.577,0.57,0.569,0.572,0.571,0.565,0.56,0.564,0.579,0.595,0.6,0.59,0.572,0.553,0.541,0.53,0.513,0.481,0.44,0.407,0.397,0.409,0.43,0.446,0.455,0.473,0.508,0.552,0.585,0.587,0.56,0.52,0.487,0.471,0.47,0.47,0.464,0.447,0.423,0.4,0.381,0.37,0.375,0.408,0.474,0.563,0.642,0.686,0.686,0.662,0.638,0.632,0.64,0.657,0.67,0.678,0.681,0.683,0.684,0.683,0.676,0.672,0.676,0.691,0.706,0.707,0.683,0.643,0.606,0.589,0.59,0.599,0.604,0.606,0.606,0.608,0.608,0.598,0.564,0.511,0.453,0.414,0.407,0.43,0.462,0.485,0.489,0.479,0.467,0.459,0.457,0.46,0.469,0.48,0.49,0.494,0.49,0.484,0.483,0.486,0.49,0.49,0.485,0.479,0.477,0.477,0.475,0.467,0.457,0.449,0.448,0.452,0.455,0.451,0.442,0.437,0.442,0.459,0.479,0.49,0.487,0.472,0.454,0.444,0.445,0.454,0.459,0.451,0.428,0.399,0.374,0.354,0.335,0.314,0.292,0.277,0.273,0.279,0.287,0.288,0.282,0.277,0.278,0.285,0.292,0.294,0.293,0.296,0.31,0.33,0.349,0.358,0.358,0.36,0.384,0.443,0.538,0.644,0.726,0.76,0.747,0.711,0.687,0.692,0.721,0.746,0.746,0.718,0.678,0.644,0.622,0.608,0.595,0.584,0.581,0.587,0.597,0.601,0.594,0.581,0.568,0.556,0.546,0.539,0.536,0.54,0.547,0.552,0.547,0.532,0.51,0.484,0.456,0.434,0.428,0.451,0.501,0.561,0.607,0.622,0.609,0.58,0.547,0.517,0.489,0.468,0.461,0.475,0.508,0.546,0.568,0.56,0.521,0.469,0.429,0.418,0.434,0.463,0.488,0.504,0.51,0.512,0.512,0.512,0.512,0.512,0.514,0.515,0.513,0.506,0.495,0.482,0.469,0.456,0.446,0.437,0.432,0.429,0.427,0.426,0.425,0.425,0.427,0.43,0.431,0.432,0.434,0.44,0.449,0.457,0.46,0.449,0.425,0.389,0.349,0.306,0.257,0.201,0.141,0.089,0.052,0.031,0.025,0.034,0.063,0.112,0.174,0.231,0.269,0.284,0.278,0.261,0.236,0.207,0.173,0.138,0.105,0.078,0.063,0.069,0.099,0.153,0.215,0.266,0.292,0.291,0.275,0.252,0.228,0.203,0.177,0.156,0.148,0.157,0.173,0.18,0.166,0.131,0.087,0.049,0.025,0.013,0.008,0.006,0.005,0.005,0.005,0.004,0.004,0.004,0.009,0.023,0.05,0.087,0.122,0.142,0.145,0.137,0.13,0.128,0.128,0.126,0.123,0.126,0.141,0.163,0.175,0.166,0.133,0.09,0.052,0.026,0.014,0.009,0.007,0.006,0.005,0.005,0.007,0.015,0.035,0.071,0.121,0.174,0.211,0.224,0.213,0.187,0.159,0.137,0.122,0.114,0.11,0.108,0.107,0.106,0.104,0.101,0.098,0.094,0.088,0.083,0.078,0.073,0.071,0.069,0.068,0.068,0.068,0.068,0.067,0.068,0.078,0.105,0.152,0.213,0.271,0.313,0.34,0.36,0.37,0.369,0.362,0.376,0.431,0.518,0.602,0.647,0.648,0.618,0.578,0.535,0.488,0.432,0.371,0.313,0.269,0.24,0.215,0.184,0.141,0.096,0.058,0.034,0.022,0.021,0.03,0.045,0.064,0.076,0.077,0.066,0.052,0.038,0.027,0.019,0.013,0.01,0.009,0.009,0.011,0.015,0.024,0.041,0.063,0.085,0.098,0.1,0.094,0.085,0.078,0.074,0.073,0.076,0.079,0.081,0.079,0.076,0.077,0.081,0.089,0.094,0.092,0.084,0.072,0.062,0.056,0.053,0.053,0.052,0.047,0.04,0.034,0.032,0.032,0.032,0.029,0.023,0.017,0.011,0.008,0.006,0.005,0.004,0.004,0.003,0.002,0.001,0.001,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]