[0.081,0.082,0.086,0.089,0.091,0.094,0.098,0.103,0.107,0.108,0.107,0.109,0.115,0.125,0.133,0.134,0.128,0.124,0.127,0.137,0.148,0.152,0.15,0.146,0.144,0.142,0.138,0.129,0.12,0.117,0.121,0.128,0.131,0.128,0.124,0.121,0.123,0.126,0.128,0.126,0.124,0.125,0.133,0.144,0.15,0.151,0.147,0.147,0.154,0.165,0.174,0.177,0.174,0.172,0.173,0.173,0.168,0.155,0.142,0.134,0.133,0.136,0.139,0.138,0.134,0.131,0.129,0.131,0.134,0.136,0.135,0.135,0.137,0.14,0.14,0.136,0.135,0.144,0.161,0.181,0.194,0.193,0.183,0.172,0.164,0.156,0.144,0.13,0.117,0.11,0.109,0.109,0.105,0.097,0.087,0.076,0.066,0.057,0.049,0.043,0.038,0.034,0.031,0.029,0.028,0.027,0.026,0.025,0.025,0.026,0.029,0.033,0.04,0.053,0.078,0.122,0.184,0.254,0.315,0.357,0.377,0.378,0.367,0.35,0.33,0.315,0.31,0.317,0.332,0.349,0.365,0.379,0.392,0.404,0.412,0.413,0.406,0.395,0.389,0.394,0.408,0.425,0.436,0.435,0.421,0.396,0.366,0.339,0.315,0.292,0.267,0.246,0.236,0.239,0.249,0.252,0.239,0.213,0.185,0.167,0.164,0.175,0.198,0.232,0.274,0.312,0.335,0.338,0.33,0.322,0.329,0.35,0.379,0.407,0.421,0.418,0.399,0.374,0.352,0.34,0.339,0.342,0.342,0.332,0.311,0.28,0.245,0.208,0.172,0.141,0.12,0.109,0.105,0.103,0.099,0.097,0.099,0.107,0.116,0.122,0.125,0.127,0.13,0.133,0.132,0.128,0.123,0.122,0.126,0.129,0.129,0.125,0.121,0.119,0.123,0.131,0.139,0.144,0.142,0.138,0.137,0.139,0.14,0.138,0.13,0.123,0.121,0.125,0.13,0.133,0.134,0.134,0.135,0.138,0.15,0.178,0.227,0.293,0.361,0.414,0.446,0.46,0.461,0.454,0.435,0.405,0.368,0.336,0.316,0.309,0.31,0.313,0.321,0.336,0.355,0.371,0.379,0.375,0.363,0.345,0.325,0.308,0.303,0.316,0.344,0.379,0.41,0.428,0.432,0.423,0.404,0.381,0.355,0.331,0.309,0.29,0.277,0.271,0.28,0.302,0.328,0.344,0.339,0.317,0.291,0.275,0.274,0.28,0.283,0.277,0.266,0.258,0.262,0.279,0.311,0.348,0.378,0.39,0.379,0.35,0.315,0.283,0.263,0.256,0.261,0.269,0.276,0.278,0.276,0.275,0.275,0.276,0.276,0.274,0.273,0.273,0.275,0.278,0.28,0.282,0.288,0.298,0.309,0.318,0.325,0.328,0.331,0.333,0.332,0.326,0.316,0.304,0.292,0.282,0.274,0.266,0.258,0.25,0.245,0.245,0.248,0.25,0.25,0.248,0.251,0.258,0.268,0.276,0.279,0.278,0.276,0.274,0.277,0.289,0.318,0.367,0.429,0.485,0.516,0.519,0.502,0.483,0.473,0.475,0.481,0.482,0.473,0.456,0.443,0.445,0.462,0.486,0.507,0.52,0.527,0.532,0.531,0.521,0.5,0.47,0.433,0.399,0.381,0.39,0.427,0.476,0.518,0.535,0.526,0.503,0.484,0.48,0.489,0.502,0.509,0.507,0.498,0.491,0.49,0.498,0.509,0.517,0.513,0.504,0.501,0.513,0.533,0.548,0.544,0.521,0.483,0.446,0.421,0.414,0.426,0.449,0.473,0.482,0.469,0.438,0.405,0.384,0.379,0.379,0.374,0.36,0.345,0.344,0.366,0.406,0.444,0.464,0.461,0.448,0.437,0.432,0.424,0.407,0.382,0.353,0.325,0.298,0.28,0.279,0.301,0.338,0.373,0.382,0.359,0.318,0.282,0.267,0.272,0.284,0.288,0.277,0.258,0.25,0.266,0.307,0.351,0.381,0.389,0.39,0.399,0.419,0.442,0.456,0.46,0.454,0.44,0.417,0.394,0.383,0.397,0.431,0.467,0.481,0.463,0.425,0.386,0.363,0.361,0.376,0.396,0.412,0.422,0.43,0.443,0.462,0.483,0.496,0.503,0.506,0.509,0.506,0.492,0.462,0.422,0.377,0.334,0.302,0.289,0.304,0.348,0.41,0.464,0.489,0.476,0.443,0.412,0.396,0.395,0.397,0.396,0.393,0.399,0.419,0.451,0.482,0.503,0.508,0.503,0.496,0.493,0.485,0.466,0.432,0.389,0.35,0.326,0.324,0.346,0.387,0.431,0.461,0.464,0.441,0.403,0.371,0.355,0.356,0.363,0.361,0.347,0.328,0.318,0.331,0.366,0.407,0.436,0.443,0.437,0.429,0.421,0.409,0.39,0.369,0.349,0.332,0.315,0.302,0.302,0.32,0.347,0.368,0.367,0.342,0.307,0.283,0.281,0.296,0.316,0.327,0.324,0.315,0.317,0.337,0.372,0.406,0.422,0.425,0.423,0.426,0.429,0.423,0.405,0.384,0.365,0.353,0.344,0.339,0.338,0.346,0.36,0.376,0.382,0.376,0.36,0.343,0.325,0.306,0.283,0.259,0.245,0.247,0.268,0.297,0.323,0.339,0.345,0.345,0.344,0.343,0.344,0.344,0.338,0.322,0.299,0.278,0.267,0.268,0.273,0.272,0.261,0.244,0.227,0.21,0.194,0.185,0.192,0.223,0.274,0.331,0.375,0.394,0.387,0.359,0.318,0.272,0.233,0.214,0.224,0.258,0.3,0.334,0.348,0.343,0.321,0.293,0.264,0.242,0.233,0.238,0.254,0.273,0.283,0.279,0.26,0.231,0.198,0.168,0.141,0.12,0.106,0.102,0.108,0.117,0.122,0.118,0.108,0.101,0.102,0.11,0.117,0.121,0.123,0.125,0.129,0.13,0.127,0.121,0.117,0.116,0.116,0.114,0.109,0.102,0.099,0.103,0.115,0.13,0.14,0.139,0.132,0.124,0.119,0.115,0.108,0.1,0.094,0.094,0.101,0.109,0.114,0.115,0.114,0.115,0.117,0.122,0.139,0.179,0.248,0.337,0.417,0.466,0.477,0.468,0.457,0.452,0.452,0.455,0.458,0.463,0.474,0.491,0.515,0.537,0.549,0.547,0.535,0.52,0.505,0.49,0.475,0.462,0.451,0.439,0.425,0.413,0.411,0.424,0.448,0.47,0.477,0.467,0.447,0.433,0.431,0.437,0.444,0.442,0.433,0.426,0.433,0.458,0.493,0.522,0.537,0.538,0.535,0.533,0.529,0.518,0.499,0.476,0.453,0.432,0.416,0.414,0.429,0.456,0.484,0.497,0.488,0.462,0.434,0.415,0.411,0.413,0.413,0.408,0.402,0.404,0.42,0.449,0.481,0.503,0.505,0.497,0.488,0.486,0.485,0.478,0.463,0.447,0.435,0.43,0.427,0.427,0.433,0.444,0.453,0.448,0.428,0.398,0.373,0.36,0.364,0.375,0.385,0.39,0.394,0.407,0.432,0.469,0.504,0.529,0.537,0.537,0.534,0.534,0.531,0.523,0.51,0.499,0.493,0.489,0.487,0.488,0.498,0.512,0.525,0.526,0.514,0.492,0.469,0.452,0.442,0.438,0.438,0.441,0.452,0.472,0.501,0.53,0.55,0.555,0.547,0.532,0.514,0.493,0.47,0.446,0.43,0.421,0.417,0.412,0.408,0.41,0.423,0.445,0.462,0.464,0.449,0.427,0.413,0.414,0.425,0.437,0.44,0.438,0.437,0.449,0.474,0.505,0.527,0.533,0.528,0.519,0.512,0.502,0.488,0.47,0.453,0.44,0.431,0.428,0.433,0.448,0.467,0.479,0.473,0.449,0.42,0.399,0.395,0.403,0.413,0.415,0.41,0.405,0.411,0.432,0.467,0.5,0.52,0.52,0.509,0.499,0.495,0.491,0.482,0.466,0.451,0.44,0.435,0.435,0.44,0.449,0.457,0.458,0.446,0.423,0.398,0.384,0.382,0.388,0.393,0.39,0.383,0.381,0.394,0.424,0.465,0.5,0.522,0.528,0.527,0.526,0.525,0.518,0.505,0.49,0.479,0.474,0.472,0.467,0.452,0.421,0.371,0.306,0.237,0.177,0.136,0.114,0.103,0.096,0.087,0.078,0.072,0.071,0.075,0.08,0.084,0.088,0.092,0.097,0.1,0.098,0.092,0.086,0.083,0.087,0.093,0.1,0.103,0.105,0.107,0.11,0.114,0.117,0.116,0.112,0.106,0.102,0.099,0.097,0.095,0.092,0.09,0.091,0.092,0.093,0.092,0.092,0.093,0.098,0.104,0.107,0.109,0.113,0.122,0.133,0.145,0.153,0.16,0.176,0.217,0.287,0.376,0.452,0.497,0.507,0.501,0.493,0.486,0.475,0.454,0.428,0.41,0.413,0.441,0.488,0.536,0.57,0.582,0.573,0.546,0.505,0.452,0.396,0.349,0.314,0.291,0.277,0.278,0.301,0.347,0.407,0.46,0.49,0.494,0.484,0.473,0.468,0.465,0.456,0.439,0.422,0.42,0.446,0.496,0.553,0.594,0.605,0.59,0.559,0.515,0.459,0.4,0.35,0.324,0.317,0.316,0.312,0.31,0.322,0.353,0.397,0.438,0.464,0.474,0.481,0.49,0.5,0.498,0.479,0.446,0.417,0.41,0.434,0.485,0.539,0.575,0.578,0.555,0.521,0.491,0.462,0.433,0.4,0.367,0.334,0.3,0.266,0.241,0.243,0.277,0.335,0.386,0.411,0.408,0.399,0.399,0.409,0.417,0.406,0.379,0.351,0.347,0.381,0.445,0.51,0.554,0.567,0.563,0.558,0.558,0.557,0.543,0.514,0.474,0.436,0.412,0.41,0.431,0.468,0.506,0.531,0.538,0.529,0.516,0.506,0.501,0.492,0.473,0.441,0.408,0.393,0.411,0.46,0.519,0.562,0.575,0.563,0.539,0.512,0.48,0.442,0.398,0.356,0.316,0.281,0.258,0.26,0.293,0.352,0.418,0.468,0.492,0.491,0.479,0.468,0.463,0.457,0.44,0.408,0.375,0.362,0.386,0.445,0.513,0.566,0.587,0.583,0.561,0.525,0.469,0.403,0.342,0.304,0.288,0.284,0.283,0.288,0.309,0.352,0.409,0.461,0.494,0.503,0.504,0.503,0.503,0.49,0.46,0.421,0.393,0.398,0.44,0.506,0.569,0.611,0.621,0.608,0.575,0.531,0.476,0.42,0.375,0.347,0.335,0.335,0.342,0.357,0.383,0.417,0.453,0.477,0.48,0.467,0.451,0.442,0.441,0.442,0.432,0.412,0.393,0.396,0.432,0.495,0.554,0.589,0.593,0.584,0.576,0.573,0.565,0.542,0.504,0.457,0.416,0.395,0.403,0.439,0.488,0.533,0.559,0.561,0.545,0.526,0.516,0.512,0.504,0.484,0.454,0.43,0.426,0.448,0.489,0.532,0.562,0.57,0.565,0.552,0.538,0.516,0.487,0.451,0.42,0.393,0.367,0.342,0.325,0.329,0.358,0.404,0.449,0.478,0.491,0.498,0.507,0.517,0.515,0.491,0.451,0.418,0.416,0.454,0.515,0.571,0.603,0.607,0.597,0.578,0.549,0.508,0.459,0.412,0.378,0.359,0.354,0.363,0.387,0.426,0.469,0.5,0.507,0.491,0.466,0.45,0.447,0.449,0.438,0.41,0.376,0.359,0.384,0.447,0.526,0.587,0.612,0.604,0.577,0.538,0.485,0.418,0.348,0.292,0.257,0.245,0.25,0.277,0.323,0.385,0.449,0.503,0.534,0.542,0.537,0.533,0.536,0.544,0.547,0.538,0.522,0.51,0.518,0.553,0.602,0.645,0.664,0.66,0.643,0.623,0.602,0.577,0.541,0.493,0.439,0.398,0.383,0.404,0.449,0.501,0.539,0.55,0.537,0.51,0.485,0.472,0.472,0.477,0.475,0.462,0.444,0.44,0.462,0.508,0.557,0.589,0.591,0.572,0.538,0.499,0.453,0.406,0.369,0.351,0.35,0.356,0.361,0.362,0.373,0.403,0.456,0.513,0.555,0.569,0.569,0.565,0.562,0.548,0.516,0.474,0.445,0.452,0.496,0.56,0.613,0.64,0.638,0.617,0.585,0.544,0.498,0.452,0.412,0.38,0.353,0.33,0.318,0.323,0.353,0.404,0.463,0.511,0.541,0.555,0.564,0.57,0.565,0.536,0.486,0.433,0.404,0.415,0.462,0.522,0.573,0.6,0.606,0.59,0.555,0.496,0.423,0.35,0.295,0.256,0.228,0.207,0.2,0.218,0.262,0.323,0.38,0.418,0.433,0.438,0.441,0.444,0.443,0.431,0.408,0.384,0.381,0.409,0.467,0.534,0.586,0.608,0.605,0.589,0.575,0.561,0.539,0.496,0.433,0.365,0.316,0.307,0.34,0.395,0.445,0.474,0.477,0.462,0.44,0.419,0.403,0.39,0.379,0.367,0.354,0.338,0.321,0.307,0.3,0.301,0.31,0.323,0.333,0.334,0.321,0.293,0.257,0.222,0.197,0.182,0.176,0.178,0.191,0.214,0.244,0.27,0.285,0.286,0.276,0.264,0.258,0.26,0.265,0.263,0.249,0.228,0.211,0.207,0.214,0.225,0.237,0.249,0.26,0.269,0.274,0.278,0.285,0.298,0.315,0.329,0.327,0.307,0.277,0.254,0.257,0.288,0.333,0.373,0.389,0.382,0.358,0.328,0.297,0.268,0.241,0.221,0.212,0.211,0.216,0.222,0.225,0.224,0.218,0.205,0.185,0.161,0.136,0.113,0.094,0.081,0.072,0.067,0.065,0.067,0.071,0.075,0.076,0.074,0.071,0.067,0.064,0.061,0.058,0.057,0.057,0.062,0.069,0.076,0.079,0.076,0.072,0.071,0.074,0.078,0.081,0.081,0.082,0.085,0.09,0.096,0.102,0.112,0.139,0.188,0.255,0.321,0.367,0.384,0.374,0.349,0.319,0.289,0.26,0.237,0.229,0.24,0.268,0.3,0.322,0.328,0.322,0.313,0.312,0.321,0.336,0.347,0.347,0.336,0.323,0.32,0.332,0.349,0.357,0.346,0.318,0.283,0.251,0.232,0.226,0.23,0.237,0.244,0.251,0.257,0.263,0.269,0.274,0.28,0.283,0.277,0.26,0.235,0.213,0.202,0.204,0.214,0.223,0.226,0.221,0.208,0.192,0.177,0.17,0.172,0.183,0.194,0.2,0.197,0.186,0.171,0.153,0.133,0.116,0.112,0.128,0.164,0.204,0.23,0.23,0.208,0.175,0.142,0.116,0.097,0.085,0.078,0.074,0.072,0.071,0.071,0.073,0.078,0.083,0.085,0.083,0.077,0.07,0.065,0.062,0.062,0.064,0.066,0.066,0.065,0.066,0.07,0.075,0.078,0.078,0.077,0.078,0.082,0.088,0.093,0.096,0.101,0.107,0.116,0.127,0.143,0.173,0.225,0.299,0.378,0.441,0.473,0.477,0.47,0.462,0.459,0.458,0.455,0.449,0.445,0.448,0.462,0.48,0.495,0.501,0.5,0.499,0.503,0.505,0.499,0.483,0.467,0.455,0.449,0.447,0.452,0.465,0.486,0.505,0.511,0.505,0.492,0.485,0.489,0.498,0.504,0.503,0.496,0.494,0.504,0.527,0.556,0.578,0.587,0.582,0.573,0.564,0.557,0.548,0.534,0.516,0.497,0.48,0.468,0.467,0.48,0.505,0.53,0.545,0.537,0.513,0.484,0.465,0.459,0.461,0.459,0.449,0.434,0.423,0.426,0.449,0.484,0.519,0.538,0.54,0.532,0.525,0.52,0.513,0.501,0.489,0.481,0.478,0.477,0.478,0.48,0.487,0.496,0.499,0.486,0.459,0.426,0.399,0.386,0.385,0.391,0.397,0.404,0.418,0.444,0.481,0.52,0.551,0.566,0.569,0.565,0.56,0.552,0.539,0.522,0.506,0.494,0.488,0.486,0.49,0.502,0.519,0.532,0.532,0.516,0.492,0.471,0.462,0.462,0.465,0.466,0.463,0.457,0.452,0.454,0.464,0.48,0.496,0.504,0.508,0.507,0.507,0.5,0.485,0.463,0.445,0.433,0.43,0.434,0.444,0.462,0.481,0.493,0.488,0.468,0.443,0.428,0.427,0.437,0.45,0.458,0.462,0.468,0.487,0.52,0.557,0.586,0.599,0.595,0.583,0.57,0.558,0.546,0.533,0.518,0.501,0.483,0.47,0.468,0.479,0.499,0.52,0.529,0.521,0.501,0.48,0.468,0.467,0.469,0.466,0.454,0.436,0.422,0.423,0.442,0.472,0.499,0.514,0.515,0.51,0.508,0.507,0.504,0.497,0.49,0.487,0.487,0.487,0.485,0.486,0.49,0.495,0.491,0.472,0.44,0.407,0.386,0.38,0.384,0.392,0.4,0.41,0.428,0.457,0.494,0.528,0.553,0.565,0.569,0.567,0.563,0.553,0.538,0.517,0.499,0.485,0.476,0.469,0.461,0.445,0.419,0.385,0.346,0.309,0.275,0.243,0.217,0.201,0.201,0.213,0.229,0.24,0.242,0.236,0.229,0.226,0.228,0.233,0.237,0.236,0.228,0.216,0.207,0.21,0.224,0.238,0.238,0.223,0.201,0.184,0.18,0.189,0.204,0.218,0.228,0.232,0.232,0.228,0.22,0.208,0.198,0.193,0.194,0.2,0.205,0.207,0.205,0.203,0.2,0.196,0.189,0.179,0.172,0.171,0.179,0.195,0.219,0.247,0.269,0.274,0.259,0.234,0.212,0.201,0.196,0.191,0.184,0.178,0.176,0.179,0.182,0.185,0.189,0.194,0.2,0.205,0.212,0.223,0.238,0.254,0.262,0.26,0.249,0.235,0.223,0.217,0.215,0.214,0.213,0.213,0.216,0.218,0.214,0.204,0.192,0.185,0.19,0.198,0.202,0.192,0.173,0.153,0.14,0.135,0.132,0.128,0.125,0.126,0.132,0.142,0.151,0.159,0.167,0.174,0.175,0.17,0.162,0.165,0.195,0.256,0.335,0.402,0.439,0.447,0.446,0.452,0.472,0.497,0.509,0.502,0.478,0.454,0.445,0.454,0.473,0.485,0.479,0.456,0.429,0.415,0.424,0.452,0.485,0.5,0.487,0.451,0.416,0.403,0.42,0.455,0.486,0.496,0.483,0.462,0.45,0.455,0.47,0.484,0.483,0.47,0.454,0.452,0.47,0.499,0.524,0.527,0.508,0.478,0.454,0.448,0.462,0.488,0.509,0.513,0.5,0.482,0.476,0.49,0.514,0.531,0.526,0.501,0.472,0.459,0.468,0.495,0.523,0.536,0.527,0.502,0.475,0.462,0.472,0.499,0.53,0.547,0.544,0.528,0.515,0.517,0.533,0.552,0.559,0.547,0.521,0.493,0.476,0.476,0.487,0.496,0.488,0.462,0.429,0.41,0.414,0.438,0.465,0.473,0.459,0.43,0.406,0.401,0.417,0.44,0.454,0.448,0.426,0.403,0.394,0.408,0.438,0.469,0.483,0.475,0.452,0.432,0.431,0.455,0.494,0.534,0.562,0.57,0.563,0.55,0.537,0.525,0.514,0.502,0.492,0.488,0.493,0.508,0.531,0.555,0.572,0.58,0.579,0.572,0.558,0.536,0.513,0.499,0.5,0.512,0.528,0.543,0.556,0.564,0.561,0.54,0.504,0.466,0.439,0.429,0.433,0.44,0.443,0.441,0.437,0.438,0.45,0.471,0.492,0.506,0.504,0.494,0.483,0.478,0.472,0.462,0.449,0.442,0.441,0.447,0.459,0.479,0.508,0.541,0.564,0.567,0.548,0.519,0.496,0.486,0.486,0.49,0.491,0.489,0.489,0.498,0.517,0.542,0.564,0.574,0.567,0.553,0.538,0.529,0.523,0.517,0.51,0.504,0.503,0.506,0.515,0.529,0.544,0.553,0.547,0.522,0.489,0.46,0.447,0.45,0.458,0.465,0.465,0.465,0.47,0.484,0.509,0.538,0.564,0.584,0.595,0.599,0.596,0.588,0.575,0.557,0.539,0.523,0.512,0.503,0.498,0.499,0.506,0.52,0.534,0.545,0.55,0.552,0.552,0.551,0.547,0.541,0.535,0.532,0.536,0.547,0.565,0.583,0.597,0.601,0.599,0.592,0.585,0.572,0.554,0.532,0.515,0.508,0.511,0.521,0.533,0.544,0.549,0.543,0.522,0.492,0.464,0.45,0.45,0.46,0.468,0.469,0.464,0.461,0.465,0.48,0.503,0.523,0.534,0.531,0.521,0.507,0.493,0.477,0.46,0.447,0.442,0.445,0.451,0.463,0.481,0.509,0.54,0.561,0.563,0.547,0.525,0.509,0.503,0.506,0.508,0.504,0.495,0.488,0.491,0.508,0.534,0.555,0.562,0.554,0.543,0.535,0.529,0.521,0.506,0.49,0.481,0.482,0.494,0.514,0.539,0.563,0.576,0.569,0.54,0.498,0.455,0.42,0.394,0.374,0.361,0.356,0.363,0.381,0.409,0.445,0.482,0.518,0.545,0.563,0.571,0.574,0.57,0.562,0.55,0.538,0.526,0.516,0.505,0.491,0.467,0.43,0.379,0.319,0.261,0.213,0.187,0.18,0.186,0.191,0.187,0.179,0.177,0.187,0.203,0.214,0.217,0.218,0.224,0.235,0.243,0.241,0.231,0.225,0.23,0.244,0.257,0.26,0.253,0.242,0.237,0.243,0.257,0.268,0.271,0.264,0.255,0.246,0.238,0.229,0.219,0.215,0.221,0.236,0.249,0.251,0.24,0.224,0.213,0.209,0.206,0.196,0.185,0.182,0.195,0.219,0.242,0.254,0.252,0.236,0.208,0.168,0.12,0.072,0.035,0.013,0.005]