[0.012,0.014,0.023,0.04,0.065,0.092,0.113,0.124,0.128,0.133,0.142,0.153,0.156,0.147,0.133,0.123,0.125,0.134,0.14,0.138,0.128,0.12,0.12,0.127,0.135,0.136,0.126,0.108,0.089,0.074,0.066,0.063,0.064,0.064,0.064,0.065,0.067,0.071,0.077,0.088,0.105,0.124,0.138,0.146,0.149,0.151,0.155,0.159,0.161,0.157,0.152,0.152,0.16,0.176,0.19,0.194,0.184,0.163,0.138,0.115,0.097,0.084,0.077,0.074,0.074,0.075,0.078,0.082,0.09,0.105,0.129,0.159,0.192,0.22,0.237,0.241,0.235,0.223,0.21,0.202,0.202,0.21,0.223,0.231,0.225,0.206,0.183,0.168,0.165,0.169,0.172,0.168,0.155,0.138,0.125,0.12,0.123,0.128,0.129,0.126,0.12,0.113,0.104,0.097,0.092,0.091,0.093,0.096,0.102,0.107,0.112,0.117,0.123,0.133,0.142,0.146,0.144,0.142,0.146,0.156,0.165,0.167,0.16,0.148,0.135,0.125,0.122,0.123,0.125,0.123,0.12,0.118,0.12,0.121,0.118,0.109,0.099,0.093,0.095,0.106,0.126,0.15,0.17,0.179,0.176,0.164,0.151,0.145,0.148,0.161,0.179,0.196,0.21,0.221,0.228,0.231,0.228,0.22,0.211,0.205,0.202,0.2,0.196,0.19,0.183,0.179,0.179,0.18,0.176,0.167,0.153,0.139,0.128,0.121,0.115,0.108,0.102,0.097,0.094,0.092,0.091,0.089,0.086,0.084,0.084,0.086,0.094,0.108,0.128,0.154,0.185,0.215,0.236,0.24,0.229,0.209,0.192,0.188,0.197,0.217,0.24,0.259,0.269,0.264,0.247,0.22,0.19,0.166,0.152,0.148,0.147,0.143,0.132,0.116,0.1,0.09,0.091,0.105,0.129,0.155,0.175,0.186,0.191,0.192,0.189,0.185,0.181,0.181,0.189,0.204,0.225,0.248,0.268,0.279,0.275,0.254,0.219,0.177,0.137,0.108,0.092,0.089,0.091,0.095,0.098,0.1,0.102,0.106,0.114,0.126,0.142,0.158,0.172,0.184,0.193,0.195,0.193,0.19,0.192,0.197,0.203,0.204,0.201,0.196,0.195,0.195,0.194,0.189,0.183,0.18,0.184,0.196,0.211,0.221,0.222,0.213,0.198,0.183,0.171,0.164,0.161,0.161,0.16,0.157,0.158,0.165,0.179,0.196,0.21,0.218,0.22,0.216,0.204,0.189,0.177,0.174,0.179,0.184,0.183,0.174,0.164,0.154,0.144,0.132,0.12,0.11,0.108,0.115,0.129,0.149,0.168,0.182,0.189,0.19,0.186,0.182,0.183,0.192,0.209,0.226,0.233,0.222,0.197,0.165,0.141,0.133,0.143,0.166,0.192,0.211,0.221,0.222,0.22,0.218,0.218,0.217,0.215,0.209,0.202,0.196,0.195,0.198,0.2,0.202,0.205,0.213,0.225,0.234,0.235,0.228,0.218,0.208,0.202,0.198,0.199,0.202,0.205,0.205,0.207,0.211,0.22,0.227,0.231,0.23,0.224,0.212,0.195,0.179,0.171,0.174,0.188,0.205,0.221,0.231,0.238,0.243,0.245,0.243,0.238,0.227,0.213,0.193,0.172,0.151,0.133,0.122,0.116,0.114,0.111,0.107,0.102,0.098,0.102,0.116,0.143,0.178,0.213,0.24,0.257,0.266,0.267,0.26,0.245,0.23,0.225,0.231,0.241,0.251,0.261,0.271,0.28,0.284,0.279,0.265,0.248,0.234,0.227,0.228,0.234,0.243,0.252,0.258,0.258,0.251,0.239,0.231,0.235,0.252,0.272,0.28,0.271,0.25,0.225,0.207,0.2,0.203,0.211,0.219,0.221,0.219,0.216,0.214,0.211,0.209,0.21,0.218,0.232,0.245,0.251,0.25,0.244,0.238,0.237,0.243,0.257,0.271,0.276,0.265,0.237,0.202,0.167,0.14,0.123,0.114,0.109,0.107,0.106,0.108,0.113,0.122,0.138,0.163,0.192,0.221,0.24,0.248,0.249,0.247,0.246,0.244,0.239,0.229,0.214,0.2,0.194,0.202,0.217,0.233,0.243,0.248,0.25,0.253,0.255,0.256,0.251,0.239,0.217,0.19,0.164,0.145,0.136,0.134,0.136,0.137,0.138,0.139,0.141,0.144,0.147,0.151,0.155,0.163,0.176,0.195,0.218,0.243,0.265,0.279,0.282,0.277,0.271,0.268,0.266,0.259,0.245,0.233,0.233,0.248,0.271,0.29,0.297,0.291,0.275,0.253,0.234,0.227,0.236,0.253,0.27,0.277,0.273,0.265,0.259,0.256,0.255,0.255,0.253,0.249,0.245,0.241,0.24,0.243,0.25,0.26,0.269,0.272,0.262,0.238,0.206,0.176,0.157,0.151,0.155,0.161,0.159,0.151,0.144,0.146,0.157,0.171,0.179,0.176,0.165,0.152,0.14,0.133,0.129,0.13,0.135,0.145,0.162,0.181,0.195,0.198,0.194,0.19,0.192,0.196,0.196,0.195,0.198,0.208,0.221,0.229,0.227,0.219,0.209,0.204,0.206,0.214,0.223,0.228,0.222,0.207,0.184,0.16,0.139,0.127,0.126,0.133,0.145,0.157,0.166,0.171,0.175,0.178,0.182,0.185,0.186,0.184,0.18,0.178,0.18,0.188,0.197,0.204,0.208,0.209,0.208,0.206,0.202,0.198,0.196,0.196,0.197,0.198,0.201,0.212,0.234,0.265,0.297,0.32,0.332,0.337,0.34,0.342,0.342,0.337,0.329,0.321,0.317,0.325,0.349,0.39,0.437,0.475,0.491,0.482,0.455,0.424,0.4,0.392,0.403,0.422,0.434,0.431,0.414,0.387,0.356,0.327,0.303,0.291,0.292,0.299,0.303,0.3,0.295,0.294,0.303,0.321,0.342,0.356,0.354,0.335,0.303,0.27,0.248,0.251,0.288,0.354,0.43,0.486,0.503,0.479,0.431,0.381,0.348,0.346,0.374,0.414,0.444,0.445,0.416,0.367,0.312,0.263,0.231,0.221,0.231,0.252,0.274,0.288,0.295,0.297,0.301,0.312,0.33,0.347,0.354,0.346,0.328,0.31,0.299,0.301,0.321,0.365,0.429,0.491,0.527,0.519,0.477,0.42,0.374,0.357,0.374,0.413,0.451,0.467,0.449,0.408,0.36,0.327,0.315,0.319,0.325,0.323,0.31,0.291,0.272,0.258,0.256,0.272,0.304,0.338,0.353,0.342,0.314,0.286,0.273,0.284,0.318,0.372,0.434,0.486,0.513,0.506,0.475,0.428,0.379,0.347,0.346,0.38,0.43,0.47,0.479,0.453,0.398,0.332,0.271,0.232,0.221,0.231,0.251,0.27,0.285,0.297,0.31,0.327,0.351,0.381,0.411,0.429,0.428,0.409,0.381,0.358,0.352,0.371,0.409,0.453,0.486,0.501,0.5,0.489,0.476,0.463,0.451,0.44,0.43,0.421,0.415,0.413,0.412,0.409,0.403,0.394,0.386,0.381,0.38,0.381,0.386,0.398,0.414,0.428,0.433,0.427,0.416,0.406,0.398,0.393,0.39,0.391,0.396,0.403,0.413,0.427,0.441,0.454,0.462,0.466,0.469,0.472,0.475,0.477,0.48,0.485,0.491,0.497,0.501,0.497,0.488,0.477,0.466,0.457,0.45,0.448,0.45,0.458,0.465,0.472,0.48,0.49,0.502,0.512,0.516,0.514,0.509,0.506,0.512,0.528,0.552,0.573,0.584,0.585,0.578,0.57,0.56,0.549,0.543,0.546,0.554,0.558,0.554,0.543,0.534,0.526,0.52,0.516,0.517,0.52,0.52,0.515,0.505,0.499,0.497,0.497,0.501,0.508,0.514,0.513,0.505,0.5,0.51,0.533,0.559,0.577,0.584,0.581,0.568,0.551,0.535,0.527,0.522,0.518,0.514,0.517,0.53,0.548,0.565,0.577,0.586,0.588,0.584,0.576,0.572,0.568,0.556,0.534,0.508,0.491,0.486,0.488,0.493,0.504,0.524,0.546,0.564,0.571,0.574,0.578,0.587,0.6,0.608,0.605,0.587,0.559,0.531,0.513,0.514,0.532,0.558,0.578,0.582,0.569,0.552,0.539,0.536,0.542,0.554,0.569,0.585,0.598,0.603,0.598,0.582,0.563,0.553,0.557,0.569,0.578,0.577,0.57,0.566,0.57,0.58,0.59,0.597,0.6,0.597,0.588,0.574,0.561,0.551,0.545,0.542,0.541,0.541,0.54,0.54,0.54,0.541,0.543,0.543,0.54,0.537,0.537,0.54,0.546,0.55,0.549,0.544,0.538,0.54,0.547,0.56,0.571,0.583,0.593,0.601,0.601,0.594,0.585,0.577,0.575,0.575,0.574,0.569,0.563,0.56,0.561,0.562,0.555,0.541,0.521,0.501,0.481,0.461,0.443,0.432,0.431,0.442,0.458,0.471,0.479,0.483,0.491,0.501,0.511,0.518,0.525,0.535,0.539,0.531,0.512,0.492,0.48,0.479,0.484,0.487,0.49,0.497,0.513,0.531,0.543,0.548,0.548,0.548,0.543,0.534,0.522,0.511,0.495,0.472,0.444,0.42,0.415,0.431,0.461,0.488,0.509,0.524,0.541,0.559,0.571,0.572,0.56,0.541,0.526,0.519,0.521,0.526,0.532,0.538,0.543,0.54,0.532,0.524,0.523,0.528,0.534,0.539,0.542,0.543,0.538,0.525,0.507,0.485,0.456,0.419,0.381,0.357,0.358,0.385,0.425,0.461,0.485,0.499,0.512,0.526,0.541,0.556,0.569,0.579,0.579,0.569,0.551,0.537,0.534,0.542,0.554,0.561,0.561,0.558,0.554,0.548,0.538,0.531,0.535,0.548,0.558,0.554,0.537,0.519,0.506,0.503,0.507,0.513,0.516,0.508,0.494,0.483,0.484,0.492,0.499,0.498,0.492,0.493,0.506,0.527,0.545,0.557,0.561,0.567,0.574,0.58,0.576,0.562,0.537,0.504,0.462,0.416,0.37,0.33,0.298,0.277,0.266,0.264,0.267,0.272,0.274,0.272,0.266,0.257,0.248,0.241,0.237,0.237,0.239,0.241,0.24,0.239,0.238,0.24,0.243,0.245,0.242,0.236,0.228,0.221,0.215,0.213,0.214,0.217,0.22,0.223,0.227,0.231,0.234,0.233,0.226,0.215,0.2,0.185,0.168,0.15,0.134,0.12,0.111,0.106,0.105,0.11,0.122,0.146,0.178,0.211,0.236,0.248,0.25,0.245,0.237,0.226,0.217,0.213,0.217,0.226,0.235,0.24,0.238,0.228,0.212,0.191,0.17,0.153,0.145,0.146,0.153,0.161,0.164,0.16,0.15,0.139,0.131,0.125,0.122,0.119,0.116,0.113,0.11,0.111,0.118,0.127,0.135,0.137,0.132,0.125,0.118,0.115,0.116,0.12,0.121,0.118,0.114,0.11,0.11,0.11,0.111,0.112,0.114,0.117,0.119,0.12,0.121,0.124,0.128,0.129,0.126,0.119,0.11,0.102,0.099,0.102,0.113,0.129,0.148,0.168,0.186,0.202,0.213,0.217,0.215,0.213,0.216,0.228,0.243,0.254,0.257,0.252,0.245,0.239,0.239,0.25,0.278,0.326,0.382,0.43,0.463,0.481,0.494,0.499,0.498,0.493,0.493,0.498,0.503,0.506,0.508,0.513,0.516,0.514,0.508,0.505,0.505,0.503,0.497,0.492,0.491,0.49,0.485,0.479,0.48,0.487,0.494,0.494,0.492,0.49,0.485,0.477,0.47,0.474,0.486,0.497,0.504,0.508,0.51,0.505,0.491,0.476,0.468,0.463,0.456,0.446,0.44,0.444,0.446,0.444,0.438,0.437,0.44,0.44,0.439,0.442,0.453,0.462,0.464,0.46,0.455,0.447,0.433,0.418,0.413,0.421,0.429,0.432,0.43,0.431,0.433,0.429,0.423,0.421,0.427,0.435,0.439,0.439,0.443,0.446,0.447,0.446,0.448,0.455,0.458,0.453,0.445,0.441,0.438,0.435,0.431,0.431,0.437,0.44,0.438,0.437,0.443,0.45,0.454,0.451,0.447,0.445,0.438,0.428,0.42,0.42,0.423,0.422,0.419,0.42,0.425,0.426,0.421,0.414,0.411,0.408,0.401,0.393,0.395,0.412,0.433,0.452,0.466,0.478,0.482,0.475,0.464,0.457,0.454,0.448,0.438,0.428,0.427,0.427,0.426,0.424,0.429,0.44,0.45,0.457,0.465,0.48,0.495,0.506,0.51,0.514,0.514,0.51,0.504,0.502,0.509,0.516,0.518,0.515,0.515,0.519,0.523,0.524,0.524,0.525,0.521,0.512,0.502,0.496,0.493,0.487,0.48,0.479,0.488,0.498,0.503,0.502,0.5,0.495,0.482,0.465,0.453,0.451,0.453,0.452,0.45,0.452,0.457,0.461,0.463,0.468,0.479,0.487,0.49,0.49,0.494,0.502,0.51,0.514,0.516,0.515,0.505,0.489,0.475,0.473,0.479,0.488,0.496,0.504,0.514,0.517,0.513,0.5,0.482,0.454,0.418,0.387,0.374,0.383,0.401,0.417,0.426,0.434,0.437,0.434,0.428,0.425,0.426,0.422,0.415,0.409,0.412,0.416,0.418,0.418,0.421,0.429,0.434,0.434,0.432,0.436,0.439,0.438,0.434,0.433,0.434,0.431,0.428,0.429,0.44,0.453,0.46,0.461,0.462,0.462,0.457,0.448,0.439,0.435,0.431,0.424,0.414,0.405,0.393,0.374,0.359,0.36,0.383,0.412,0.434,0.445,0.452,0.456,0.456,0.454,0.458,0.47,0.484,0.493,0.498,0.509,0.521,0.53,0.533,0.535,0.54,0.541,0.537,0.53,0.53,0.536,0.545,0.554,0.565,0.578,0.589,0.595,0.6,0.608,0.615,0.618,0.617,0.618,0.625,0.634,0.643,0.65,0.653,0.649,0.639,0.627,0.62,0.619,0.62,0.622,0.626,0.634,0.638,0.638,0.633,0.629,0.623,0.614,0.602,0.593,0.591,0.588,0.585,0.583,0.588,0.599,0.609,0.615,0.618,0.621,0.621,0.619,0.618,0.622,0.63,0.635,0.636,0.636,0.636,0.632,0.623,0.611,0.604,0.601,0.6,0.599,0.601,0.607,0.613,0.616,0.617,0.62,0.621,0.617,0.607,0.596,0.586,0.574,0.559,0.545,0.538,0.538,0.544,0.554,0.566,0.575,0.574,0.565,0.557,0.559,0.569,0.578,0.582,0.581,0.577,0.569,0.561,0.559,0.567,0.581,0.594,0.601,0.605,0.606,0.598,0.585,0.572,0.566,0.562,0.556,0.549,0.549,0.56,0.574,0.585,0.592,0.596,0.597,0.597,0.6,0.607,0.615,0.617,0.609,0.596,0.588,0.582,0.578,0.578,0.582,0.591,0.598,0.603,0.605,0.606,0.601,0.592,0.581,0.576,0.573,0.57,0.565,0.562,0.562,0.558,0.549,0.54,0.541,0.555,0.579,0.606,0.629,0.646,0.654,0.656,0.656,0.656,0.652,0.641,0.628,0.62,0.62,0.621,0.622,0.623,0.629,0.634,0.636,0.636,0.636,0.638,0.638,0.635,0.631,0.631,0.631,0.629,0.628,0.632,0.639,0.643,0.641,0.634,0.627,0.617,0.605,0.597,0.599,0.611,0.627,0.64,0.648,0.651,0.646,0.634,0.621,0.613,0.614,0.62,0.626,0.633,0.639,0.639,0.631,0.621,0.618,0.623,0.632,0.641,0.649,0.654,0.653,0.646,0.637,0.63,0.626,0.621,0.617,0.617,0.623,0.628,0.629,0.628,0.631,0.636,0.642,0.647,0.651,0.653,0.65,0.646,0.641,0.641,0.641,0.641,0.644,0.653,0.664,0.67,0.667,0.66,0.659,0.662,0.665,0.664,0.659,0.65,0.637,0.625,0.618,0.621,0.628,0.63,0.615,0.579,0.519,0.447,0.378,0.329,0.307,0.305,0.31,0.312,0.308,0.298,0.286,0.275,0.265,0.258,0.252,0.247,0.242,0.234,0.224,0.213,0.204,0.199,0.198,0.198,0.198,0.197,0.196,0.196,0.199,0.204,0.212,0.224,0.239,0.252,0.26,0.26,0.255,0.247,0.238,0.228,0.218,0.21,0.207,0.209,0.212,0.213,0.21,0.206,0.205,0.213,0.229,0.254,0.287,0.325,0.362,0.388,0.393,0.379,0.361,0.355,0.371,0.403,0.439,0.465,0.473,0.46,0.432,0.403,0.39,0.407,0.455,0.521,0.581,0.62,0.639,0.648,0.654,0.656,0.656,0.651,0.644,0.628,0.609,0.596,0.599,0.618,0.638,0.651,0.652,0.645,0.629,0.608,0.589,0.579,0.575,0.569,0.56,0.551,0.546,0.542,0.543,0.551,0.573,0.607,0.642,0.67,0.685,0.685,0.668,0.641,0.617,0.611,0.621,0.638,0.652,0.661,0.662,0.658,0.655,0.661,0.675,0.686,0.685,0.672,0.655,0.639,0.624,0.612,0.602,0.596,0.586,0.569,0.549,0.537,0.533,0.534,0.538,0.552,0.579,0.612,0.641,0.657,0.665,0.667,0.666,0.662,0.658,0.659,0.668,0.682,0.691,0.689,0.675,0.659,0.648,0.648,0.658,0.674,0.69,0.702,0.706,0.698,0.681,0.659,0.646,0.646,0.661,0.681,0.694,0.696,0.692,0.69,0.694,0.701,0.707,0.713,0.719,0.724,0.724,0.719,0.713,0.707,0.703,0.696,0.682,0.663,0.644,0.631,0.623,0.621,0.623,0.627,0.634,0.643,0.655,0.667,0.676,0.674,0.662,0.645,0.635,0.637,0.651,0.667,0.676,0.679,0.678,0.679,0.677,0.671,0.663,0.658,0.657,0.655,0.648,0.635,0.626,0.625,0.632,0.639,0.643,0.645,0.648,0.652,0.653,0.654,0.658,0.663,0.663,0.656,0.645,0.637,0.627,0.617,0.608,0.602,0.598,0.586,0.566,0.543,0.528,0.52,0.517,0.522,0.542,0.577,0.619,0.658,0.685,0.699,0.698,0.687,0.675,0.669,0.668,0.663,0.655,0.647,0.645,0.646,0.649,0.652,0.657,0.661,0.663,0.665,0.666,0.664,0.652,0.633,0.612,0.596,0.58,0.56,0.54,0.531,0.54,0.56,0.58,0.587,0.587,0.586,0.596,0.615,0.638,0.656,0.664,0.663,0.658,0.655,0.655,0.659,0.662,0.66,0.65,0.638,0.63,0.631,0.64,0.654,0.669,0.683,0.692,0.693,0.684,0.667,0.651,0.644,0.651,0.666,0.679,0.683,0.681,0.68,0.683,0.687,0.688,0.685,0.678,0.668,0.658,0.652,0.653,0.661,0.668,0.669,0.661,0.652,0.648,0.652,0.659,0.663,0.657,0.644,0.632,0.629,0.638,0.651,0.66,0.659,0.653,0.647,0.65,0.661,0.674,0.681,0.678,0.671,0.662,0.658,0.654,0.653,0.654,0.659,0.666,0.67,0.664,0.648,0.629,0.615,0.612,0.613,0.613,0.606,0.596,0.587,0.583,0.59,0.606,0.627,0.645,0.658,0.664,0.667,0.67,0.676,0.684,0.687,0.681,0.661,0.639,0.622,0.621,0.629,0.641,0.649,0.655,0.661,0.668,0.677,0.689,0.703,0.714,0.72,0.72,0.722,0.726,0.731,0.734,0.733,0.73,0.725,0.722,0.721,0.724,0.729,0.733,0.736,0.733,0.73,0.726,0.723,0.718,0.711,0.701,0.689,0.68,0.678,0.684,0.693,0.701,0.705,0.705,0.704,0.707,0.716,0.73,0.743,0.751,0.753,0.751,0.748,0.743,0.733,0.721,0.712,0.708,0.709,0.715,0.722,0.728,0.727,0.718,0.703,0.693,0.696,0.714,0.736,0.75,0.752,0.743,0.73,0.715,0.7,0.681,0.664,0.656,0.661,0.679,0.7,0.718,0.73,0.741,0.748,0.756,0.765,0.774,0.78,0.777,0.766,0.749,0.731,0.714,0.698,0.687,0.685,0.694,0.706,0.715,0.714,0.705,0.694,0.685,0.679,0.674,0.666,0.656,0.648,0.647,0.658,0.676,0.697,0.712,0.719,0.72,0.717,0.712,0.704,0.694,0.679,0.663,0.65,0.64,0.626,0.607,0.588,0.581,0.592,0.615,0.643,0.667,0.685,0.692,0.687,0.671,0.653,0.647,0.654,0.67,0.682,0.686,0.68,0.674,0.671,0.674,0.678,0.678,0.674,0.669,0.668,0.668,0.669,0.669,0.672,0.677,0.683,0.689,0.693,0.695,0.692,0.688,0.685,0.685,0.686,0.688,0.696,0.71,0.728,0.74,0.743,0.734,0.724,0.719,0.721,0.726,0.73,0.733,0.738,0.744,0.746,0.742,0.736,0.731,0.73,0.728,0.723,0.71,0.685,0.641,0.572,0.486,0.397,0.325,0.276,0.247,0.231,0.226,0.233,0.251,0.274,0.29,0.294,0.287,0.276,0.267,0.264,0.266,0.269,0.268,0.262,0.254,0.246,0.239,0.233,0.226,0.217,0.211,0.209,0.215,0.231,0.255,0.284,0.31,0.326,0.335,0.341,0.346,0.348,0.342,0.33,0.315,0.304,0.3,0.304,0.314,0.323,0.327,0.322,0.313,0.302,0.294,0.289,0.293,0.304,0.324,0.348,0.374,0.397,0.412,0.419,0.422,0.429,0.441,0.457,0.472,0.487,0.504,0.526,0.557,0.599,0.648,0.698,0.743,0.779,0.804,0.806,0.78,0.726,0.66,0.602,0.563,0.542,0.526,0.499,0.454,0.396,0.341,0.301,0.278,0.27]