[0.039,0.036,0.032,0.031,0.039,0.058,0.084,0.11,0.128,0.136,0.137,0.134,0.131,0.129,0.129,0.128,0.126,0.123,0.12,0.118,0.117,0.117,0.116,0.115,0.114,0.115,0.117,0.115,0.107,0.093,0.078,0.069,0.066,0.066,0.063,0.054,0.047,0.048,0.058,0.071,0.078,0.072,0.06,0.051,0.053,0.066,0.079,0.083,0.075,0.063,0.055,0.059,0.07,0.078,0.076,0.067,0.06,0.066,0.082,0.103,0.118,0.122,0.119,0.114,0.112,0.115,0.118,0.119,0.119,0.117,0.117,0.118,0.119,0.119,0.117,0.114,0.111,0.111,0.112,0.112,0.109,0.101,0.093,0.086,0.082,0.078,0.069,0.057,0.048,0.048,0.058,0.07,0.075,0.069,0.056,0.046,0.047,0.056,0.067,0.071,0.065,0.056,0.052,0.057,0.067,0.074,0.072,0.064,0.059,0.065,0.079,0.096,0.108,0.113,0.114,0.115,0.12,0.126,0.129,0.129,0.126,0.122,0.12,0.121,0.122,0.123,0.122,0.12,0.117,0.117,0.119,0.121,0.122,0.12,0.117,0.112,0.107,0.1,0.09,0.076,0.063,0.058,0.064,0.077,0.087,0.086,0.076,0.066,0.063,0.072,0.084,0.09,0.084,0.073,0.066,0.069,0.08,0.091,0.095,0.09,0.084,0.081,0.085,0.092,0.1,0.104,0.105,0.103,0.103,0.102,0.099,0.094,0.089,0.089,0.095,0.105,0.112,0.114,0.112,0.108,0.104,0.101,0.099,0.097,0.096,0.096,0.097,0.099,0.102,0.105,0.104,0.101,0.094,0.086,0.078,0.069,0.06,0.05,0.04,0.033,0.03,0.03,0.03,0.028,0.025,0.024,0.025,0.028,0.03,0.03,0.027,0.025,0.025,0.031,0.042,0.059,0.082,0.113,0.145,0.172,0.191,0.208,0.236,0.275,0.315,0.341,0.35,0.355,0.374,0.414,0.47,0.53,0.583,0.612,0.604,0.557,0.484,0.412,0.353,0.303,0.253,0.201,0.153,0.122,0.112,0.118,0.128,0.131,0.121,0.106,0.094,0.093,0.1,0.108,0.112,0.113,0.12,0.135,0.158,0.181,0.196,0.201,0.195,0.181,0.163,0.147,0.135,0.127,0.122,0.124,0.137,0.161,0.187,0.202,0.203,0.195,0.189,0.189,0.191,0.195,0.209,0.242,0.302,0.38,0.46,0.517,0.532,0.505,0.448,0.384,0.328,0.279,0.23,0.179,0.133,0.101,0.09,0.097,0.11,0.116,0.109,0.093,0.079,0.076,0.088,0.113,0.141,0.164,0.176,0.179,0.177,0.172,0.166,0.16,0.151,0.14,0.126,0.116,0.116,0.13,0.153,0.179,0.2,0.215,0.222,0.221,0.215,0.205,0.194,0.181,0.168,0.156,0.149,0.158,0.191,0.257,0.348,0.437,0.492,0.494,0.457,0.411,0.374,0.346,0.315,0.272,0.225,0.187,0.167,0.161,0.159,0.151,0.133,0.112,0.098,0.096,0.107,0.126,0.146,0.162,0.17,0.171,0.169,0.169,0.173,0.179,0.181,0.179,0.173,0.17,0.173,0.182,0.193,0.204,0.214,0.223,0.228,0.227,0.218,0.203,0.185,0.169,0.162,0.17,0.198,0.251,0.326,0.415,0.498,0.556,0.568,0.535,0.473,0.408,0.353,0.305,0.256,0.204,0.158,0.127,0.117,0.121,0.127,0.122,0.102,0.075,0.051,0.038,0.037,0.048,0.078,0.134,0.218,0.319,0.414,0.469,0.461,0.398,0.316,0.269,0.285,0.348,0.404,0.409,0.357,0.284,0.227,0.204,0.201,0.201,0.194,0.192,0.214,0.27,0.342,0.39,0.382,0.328,0.276,0.278,0.342,0.429,0.485,0.482,0.428,0.357,0.292,0.242,0.205,0.18,0.167,0.164,0.169,0.179,0.186,0.186,0.175,0.158,0.142,0.137,0.141,0.148,0.155,0.161,0.17,0.181,0.19,0.191,0.184,0.172,0.165,0.165,0.168,0.17,0.167,0.159,0.153,0.155,0.166,0.187,0.209,0.224,0.226,0.215,0.196,0.175,0.16,0.157,0.173,0.215,0.286,0.375,0.464,0.525,0.54,0.509,0.45,0.386,0.333,0.29,0.252,0.216,0.183,0.159,0.15,0.155,0.167,0.172,0.165,0.149,0.136,0.134,0.141,0.149,0.148,0.137,0.12,0.109,0.109,0.123,0.141,0.155,0.161,0.161,0.161,0.163,0.164,0.16,0.153,0.147,0.149,0.158,0.168,0.171,0.167,0.161,0.16,0.167,0.178,0.189,0.2,0.216,0.248,0.305,0.383,0.456,0.494,0.483,0.438,0.387,0.348,0.32,0.294,0.262,0.224,0.189,0.165,0.159,0.165,0.173,0.176,0.174,0.172,0.174,0.175,0.173,0.165,0.155,0.145,0.138,0.132,0.128,0.123,0.117,0.11,0.109,0.114,0.126,0.139,0.149,0.157,0.165,0.176,0.189,0.197,0.194,0.181,0.163,0.148,0.143,0.151,0.172,0.207,0.256,0.319,0.39,0.456,0.499,0.505,0.474,0.423,0.372,0.332,0.302,0.271,0.234,0.195,0.163,0.149,0.155,0.169,0.18,0.179,0.168,0.153,0.14,0.131,0.13,0.147,0.189,0.258,0.341,0.415,0.447,0.42,0.343,0.257,0.211,0.231,0.295,0.345,0.338,0.271,0.187,0.127,0.108,0.114,0.122,0.124,0.131,0.166,0.237,0.323,0.38,0.379,0.331,0.287,0.288,0.341,0.409,0.449,0.441,0.398,0.349,0.316,0.307,0.313,0.324,0.331,0.331,0.329,0.327,0.327,0.327,0.323,0.314,0.304,0.294,0.287,0.285,0.289,0.296,0.302,0.306,0.308,0.31,0.313,0.316,0.319,0.321,0.321,0.317,0.31,0.301,0.292,0.286,0.28,0.275,0.271,0.272,0.279,0.288,0.292,0.286,0.275,0.266,0.269,0.279,0.288,0.288,0.279,0.271,0.274,0.29,0.31,0.325,0.331,0.327,0.317,0.303,0.288,0.28,0.28,0.289,0.297,0.3,0.293,0.279,0.266,0.26,0.268,0.288,0.315,0.335,0.342,0.335,0.322,0.31,0.301,0.294,0.285,0.274,0.264,0.258,0.257,0.259,0.26,0.259,0.257,0.255,0.253,0.25,0.243,0.237,0.233,0.232,0.232,0.232,0.232,0.234,0.24,0.249,0.26,0.269,0.272,0.272,0.266,0.26,0.255,0.256,0.265,0.28,0.294,0.303,0.306,0.302,0.295,0.287,0.282,0.282,0.286,0.295,0.306,0.319,0.331,0.335,0.329,0.317,0.307,0.307,0.319,0.335,0.344,0.341,0.328,0.312,0.3,0.295,0.296,0.303,0.311,0.319,0.322,0.318,0.305,0.287,0.267,0.254,0.251,0.257,0.265,0.267,0.264,0.261,0.265,0.276,0.291,0.306,0.319,0.327,0.329,0.32,0.302,0.28,0.26,0.25,0.249,0.255,0.261,0.263,0.262,0.257,0.252,0.248,0.247,0.251,0.258,0.264,0.268,0.269,0.268,0.264,0.259,0.254,0.251,0.251,0.253,0.253,0.25,0.244,0.237,0.233,0.233,0.235,0.236,0.235,0.232,0.229,0.229,0.231,0.234,0.235,0.235,0.234,0.234,0.237,0.243,0.253,0.265,0.275,0.282,0.285,0.285,0.282,0.275,0.268,0.264,0.27,0.283,0.297,0.304,0.302,0.292,0.282,0.276,0.275,0.276,0.274,0.271,0.266,0.262,0.26,0.261,0.265,0.268,0.27,0.267,0.262,0.257,0.254,0.252,0.253,0.254,0.258,0.265,0.272,0.274,0.269,0.261,0.255,0.255,0.259,0.263,0.265,0.264,0.263,0.263,0.265,0.266,0.264,0.258,0.252,0.25,0.253,0.259,0.263,0.262,0.26,0.259,0.263,0.271,0.279,0.284,0.283,0.277,0.27,0.262,0.258,0.259,0.264,0.27,0.274,0.275,0.272,0.269,0.266,0.262,0.256,0.25,0.245,0.242,0.243,0.247,0.252,0.255,0.258,0.26,0.263,0.265,0.265,0.261,0.254,0.247,0.241,0.238,0.236,0.234,0.23,0.226,0.226,0.231,0.24,0.253,0.263,0.272,0.279,0.287,0.296,0.304,0.307,0.303,0.295,0.288,0.284,0.281,0.275,0.264,0.253,0.244,0.241,0.243,0.245,0.245,0.241,0.234,0.228,0.226,0.231,0.241,0.252,0.258,0.258,0.256,0.252,0.248,0.244,0.242,0.247,0.262,0.285,0.305,0.315,0.311,0.298,0.28,0.264,0.253,0.247,0.241,0.233,0.219,0.201,0.185,0.176,0.175,0.182,0.19,0.195,0.195,0.191,0.185,0.179,0.172,0.162,0.152,0.147,0.15,0.161,0.173,0.18,0.178,0.165,0.147,0.128,0.112,0.103,0.101,0.106,0.117,0.135,0.156,0.173,0.179,0.171,0.154,0.135,0.122,0.115,0.112,0.113,0.121,0.133,0.147,0.158,0.166,0.171,0.177,0.182,0.184,0.182,0.178,0.174,0.169,0.164,0.158,0.152,0.144,0.135,0.124,0.114,0.105,0.098,0.093,0.088,0.082,0.074,0.062,0.049,0.035,0.022,0.013,0.007,0.004,0.003,0.003,0.003,0.004,0.004,0.005,0.006,0.007,0.007,0.008,0.009,0.01,0.011,0.011,0.012,0.013,0.015,0.021,0.037,0.063,0.096,0.13,0.174,0.235,0.308,0.358,0.351,0.28,0.179,0.093,0.055,0.079,0.16,0.276,0.381,0.434,0.425,0.381,0.34,0.325,0.335,0.358,0.379,0.389,0.388,0.376,0.358,0.334,0.306,0.278,0.259,0.254,0.262,0.274,0.284,0.296,0.319,0.361,0.417,0.469,0.488,0.46,0.395,0.33,0.303,0.326,0.371,0.392,0.363,0.299,0.239,0.21,0.215,0.232,0.247,0.257,0.271,0.293,0.32,0.346,0.369,0.391,0.419,0.454,0.493,0.527,0.543,0.532,0.503,0.471,0.45,0.443,0.444,0.445,0.442,0.435,0.424,0.407,0.381,0.346,0.307,0.271,0.244,0.226,0.213,0.203,0.197,0.203,0.229,0.28,0.349,0.415,0.448,0.431,0.374,0.318,0.305,0.348,0.421,0.483,0.508,0.499,0.474,0.442,0.406,0.363,0.324,0.306,0.324,0.375,0.435,0.476,0.482,0.461,0.438,0.437,0.461,0.495,0.515,0.505,0.469,0.427,0.394,0.376,0.37,0.369,0.369,0.368,0.368,0.366,0.354,0.326,0.279,0.222,0.168,0.132,0.12,0.133,0.163,0.205,0.254,0.313,0.376,0.432,0.459,0.447,0.4,0.35,0.33,0.353,0.399,0.436,0.443,0.423,0.392,0.364,0.341,0.319,0.302,0.297,0.312,0.341,0.374,0.397,0.409,0.413,0.421,0.441,0.474,0.51,0.531,0.526,0.5,0.471,0.452,0.445,0.447,0.448,0.447,0.444,0.437,0.422,0.391,0.345,0.289,0.238,0.204,0.191,0.195,0.209,0.228,0.253,0.287,0.333,0.39,0.447,0.479,0.468,0.416,0.355,0.324,0.345,0.399,0.45,0.473,0.467,0.446,0.419,0.387,0.347,0.31,0.294,0.317,0.377,0.452,0.511,0.535,0.524,0.5,0.483,0.483,0.493,0.496,0.484,0.454,0.42,0.391,0.372,0.363,0.362,0.364,0.365,0.36,0.349,0.332,0.307,0.276,0.242,0.213,0.193,0.185,0.185,0.194,0.212,0.242,0.286,0.34,0.388,0.409,0.391,0.346,0.307,0.301,0.333,0.375,0.396,0.382,0.346,0.31,0.288,0.281,0.282,0.291,0.309,0.338,0.371,0.4,0.418,0.424,0.426,0.435,0.458,0.492,0.526,0.542,0.532,0.499,0.46,0.429,0.411,0.403,0.4,0.398,0.395,0.392,0.382,0.362,0.331,0.294,0.261,0.239,0.227,0.221,0.218,0.221,0.239,0.274,0.326,0.385,0.436,0.455,0.429,0.369,0.312,0.296,0.334,0.401,0.46,0.487,0.481,0.458,0.422,0.374,0.315,0.262,0.242,0.275,0.347,0.427,0.476,0.479,0.45,0.421,0.418,0.444,0.482,0.502,0.49,0.448,0.4,0.363,0.346,0.343,0.346,0.349,0.353,0.358,0.36,0.351,0.325,0.287,0.244,0.211,0.192,0.186,0.19,0.203,0.228,0.268,0.323,0.386,0.44,0.463,0.446,0.397,0.352,0.341,0.369,0.412,0.437,0.429,0.397,0.362,0.336,0.316,0.294,0.274,0.268,0.284,0.315,0.348,0.37,0.382,0.393,0.41,0.439,0.478,0.516,0.538,0.535,0.51,0.478,0.451,0.435,0.426,0.422,0.421,0.421,0.418,0.407,0.381,0.34,0.292,0.253,0.237,0.253,0.303,0.376,0.451,0.51,0.548,0.569,0.583,0.591,0.586,0.564,0.527,0.492,0.476,0.485,0.511,0.533,0.531,0.502,0.457,0.417,0.396,0.396,0.404,0.412,0.419,0.432,0.454,0.474,0.477,0.453,0.408,0.354,0.302,0.259,0.225,0.2,0.179,0.159,0.139,0.121,0.108,0.098,0.089,0.078,0.07,0.071,0.08,0.091,0.094,0.086,0.071,0.059,0.056,0.063,0.073,0.077,0.072,0.061,0.052,0.052,0.058,0.066,0.067,0.062,0.054,0.05,0.055,0.065,0.075,0.081,0.086,0.091,0.097,0.101,0.099,0.093,0.086,0.083,0.087,0.096,0.105,0.11,0.111,0.109,0.106,0.101,0.096,0.09,0.086,0.081,0.076,0.071,0.067,0.063,0.059,0.054,0.052,0.053,0.057,0.058,0.054,0.044,0.034,0.029,0.03,0.036,0.041,0.043,0.04,0.035,0.033,0.033,0.035,0.036,0.036,0.038,0.051,0.076,0.109,0.14,0.163,0.175,0.182,0.188,0.193,0.197,0.198,0.197,0.2,0.209,0.225,0.243,0.258,0.27,0.286,0.319,0.372,0.435,0.481,0.495,0.476,0.444,0.414,0.39,0.362,0.327,0.286,0.248,0.222,0.208,0.197,0.178,0.149,0.117,0.095,0.09,0.1,0.112,0.12,0.121,0.123,0.13,0.144,0.162,0.18,0.194,0.202,0.202,0.198,0.192,0.188,0.183,0.176,0.174,0.181,0.198,0.216,0.219,0.208,0.192,0.187,0.196,0.213,0.228,0.241,0.26,0.297,0.353,0.419,0.477,0.506,0.502,0.471,0.433,0.398,0.365,0.323,0.271,0.213,0.164,0.137,0.135,0.147,0.156,0.151,0.132,0.113,0.106,0.117,0.142,0.171,0.192,0.198,0.192,0.181,0.175,0.177,0.183,0.185,0.178,0.165,0.156,0.159,0.174,0.192,0.209,0.222,0.232,0.24,0.243,0.242,0.236,0.228,0.219,0.207,0.194,0.184,0.187,0.211,0.264,0.344,0.432,0.498,0.523,0.509,0.477,0.446,0.42,0.394,0.361,0.322,0.284,0.254,0.235,0.222,0.206,0.182,0.155,0.134,0.126,0.132,0.147,0.163,0.175,0.182,0.184,0.187,0.194,0.203,0.212,0.214,0.207,0.195,0.186,0.187,0.199,0.218,0.237,0.253,0.266,0.274,0.274,0.264,0.246,0.224,0.204,0.194,0.197,0.217,0.253,0.304,0.366,0.431,0.482,0.503,0.488,0.451,0.411,0.384,0.371,0.363,0.351,0.332,0.309,0.289,0.272,0.256,0.231,0.195,0.155,0.121,0.102,0.1,0.115,0.153,0.22,0.315,0.416,0.497,0.528,0.502,0.431,0.352,0.306,0.316,0.369,0.423,0.434,0.392,0.324,0.271,0.249,0.252,0.257,0.254,0.249,0.261,0.302,0.361,0.406,0.411,0.374,0.319,0.278,0.259,0.255,0.251,0.241,0.225,0.208,0.192,0.182,0.177,0.178,0.18,0.182,0.181,0.178,0.175,0.172,0.168,0.164,0.162,0.161,0.159,0.15,0.136,0.125,0.127,0.145,0.167,0.182,0.182,0.171,0.162,0.162,0.168,0.175,0.174,0.167,0.158,0.153,0.155,0.163,0.175,0.186,0.195,0.198,0.194,0.185,0.173,0.161,0.151,0.142,0.138,0.145,0.161,0.183,0.201,0.209,0.204,0.186,0.162,0.138,0.123,0.118,0.117,0.115,0.11,0.106,0.104,0.103,0.101,0.098,0.101,0.114,0.135,0.156,0.167,0.166,0.155,0.142,0.135,0.137,0.146,0.157,0.164,0.169,0.173,0.176,0.175,0.167,0.153,0.14,0.133,0.135,0.144,0.157,0.172,0.185,0.194,0.199,0.202,0.204,0.207,0.208,0.208,0.207,0.203,0.199,0.194,0.188,0.182,0.175,0.168,0.162,0.159,0.157,0.151,0.137,0.121,0.11,0.111,0.121,0.133,0.143,0.15,0.155,0.161,0.166,0.167,0.165,0.159,0.153,0.148,0.144,0.14,0.135,0.131,0.131,0.138,0.151,0.163,0.17,0.174,0.175,0.179,0.182,0.184,0.179,0.168,0.155,0.145,0.143,0.151,0.168,0.184,0.192,0.188,0.178,0.167,0.162,0.159,0.158,0.158,0.158,0.158,0.154,0.146,0.134,0.122,0.112,0.107,0.109,0.118,0.133,0.15,0.16,0.16,0.151,0.138,0.126,0.117,0.111,0.107,0.102,0.094,0.085,0.074,0.063,0.053,0.046,0.041,0.037,0.034,0.032,0.036,0.051,0.079,0.119,0.159,0.196,0.237,0.287,0.333,0.345,0.305,0.224,0.139,0.085,0.083,0.136,0.234,0.345,0.432,0.473,0.475,0.465,0.46,0.463,0.466,0.467,0.466,0.464,0.458,0.442,0.411,0.368,0.323,0.286,0.266,0.262,0.267,0.276,0.29,0.314,0.353,0.407,0.461,0.496,0.491,0.444,0.379,0.336,0.339,0.385,0.438,0.468,0.464,0.441,0.411,0.382,0.352,0.325,0.311,0.32,0.349,0.385,0.416,0.437,0.45,0.464,0.486,0.517,0.548,0.565,0.554,0.521,0.482,0.456,0.45,0.456,0.466,0.471,0.47,0.462,0.446,0.419,0.383,0.343,0.307,0.281,0.265,0.257,0.251,0.246,0.247,0.263,0.302,0.363,0.432,0.482,0.49,0.452,0.393,0.355,0.367,0.423,0.484,0.519,0.518,0.497,0.472,0.444,0.408,0.366,0.332,0.324,0.351,0.402,0.453,0.477,0.468,0.441,0.426,0.442,0.485,0.531,0.555,0.549,0.521,0.491,0.468,0.456,0.45,0.445,0.44,0.434,0.424,0.408,0.377,0.331,0.275,0.219,0.177,0.156,0.157,0.175,0.208,0.254,0.316,0.388,0.459,0.511,0.522,0.491,0.435,0.394,0.4,0.451,0.516,0.557,0.559,0.534,0.499,0.461,0.422,0.385,0.36,0.356,0.371,0.394,0.415,0.43,0.442,0.457,0.479,0.507,0.533,0.544,0.529,0.493,0.45,0.421,0.409,0.411,0.417,0.423,0.427,0.428,0.421,0.404,0.374,0.337,0.298,0.268,0.251,0.247,0.252,0.262,0.277,0.302,0.342,0.396,0.452,0.488,0.484,0.438,0.376,0.338,0.351,0.408,0.469,0.504,0.503,0.483,0.456,0.425,0.388,0.351,0.33,0.343,0.391,0.459,0.52,0.55,0.547,0.525,0.51,0.514,0.531,0.54,0.527,0.496,0.461,0.437,0.425,0.422,0.422,0.42,0.414,0.406,0.394,0.377,0.353,0.326,0.3,0.281,0.268,0.259,0.252,0.249,0.256,0.277,0.317,0.372,0.43,0.467,0.464,0.422,0.368,0.34,0.357,0.408,0.459,0.481,0.469,0.439,0.407,0.377,0.347,0.321,0.31,0.322,0.353,0.389,0.418,0.432,0.439,0.45,0.476,0.516,0.556,0.573,0.554,0.505,0.447,0.404,0.383,0.379,0.381,0.384,0.388,0.393,0.394,0.387,0.365,0.33,0.29,0.254,0.228,0.215,0.212,0.219,0.24,0.279,0.339,0.413,0.484,0.528,0.527,0.486,0.43,0.399,0.411,0.457,0.501,0.515,0.495,0.459,0.421,0.382,0.333,0.278,0.238,0.239,0.292,0.38,0.469,0.523,0.529,0.503,0.48,0.484,0.514,0.543,0.548,0.523,0.483,0.449,0.429,0.421,0.418,0.417,0.416,0.415,0.409,0.395,0.367,0.329,0.289,0.257,0.239,0.232,0.232,0.236,0.247,0.275,0.326,0.395,0.464,0.507,0.504,0.461,0.406,0.378,0.394,0.444,0.492,0.511,0.497,0.47,0.441,0.416,0.385,0.352,0.324,0.314,0.326,0.351,0.376,0.397,0.413,0.432,0.461,0.5,0.538,0.558,0.546,0.508,0.461,0.426,0.408,0.405,0.409,0.414,0.419,0.424,0.423,0.409,0.378,0.333,0.285,0.251,0.242,0.26,0.3,0.351,0.402,0.447,0.488,0.527,0.561,0.58,0.576,0.548,0.513,0.489,0.488,0.508,0.529,0.532,0.51,0.472,0.437,0.419,0.421,0.434,0.444,0.447,0.45,0.465,0.496,0.526,0.537,0.515,0.465,0.397,0.328,0.27,0.227,0.198,0.176,0.154,0.132,0.109,0.089,0.071,0.057,0.047,0.041,0.037,0.036,0.036,0.036,0.037,0.037,0.037,0.037,0.037,0.036,0.035,0.034,0.033,0.031,0.03,0.028,0.025,0.022,0.02,0.019]