[0.001,0.001,0.001,0.002,0.003,0.003,0.003,0.003,0.003,0.002,0.002,0.003,0.003,0.003,0.003,0.003,0.004,0.004,0.005,0.006,0.006,0.007,0.007,0.006,0.006,0.005,0.004,0.003,0.003,0.003,0.005,0.009,0.014,0.018,0.019,0.018,0.015,0.012,0.009,0.006,0.005,0.004,0.003,0.003,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.002,0.004,0.005,0.006,0.007,0.006,0.005,0.004,0.003,0.002,0.002,0.003,0.011,0.035,0.086,0.164,0.255,0.337,0.39,0.41,0.405,0.386,0.362,0.337,0.313,0.294,0.282,0.277,0.278,0.285,0.295,0.308,0.323,0.342,0.362,0.379,0.385,0.378,0.36,0.338,0.318,0.305,0.299,0.297,0.293,0.285,0.275,0.267,0.267,0.273,0.284,0.298,0.319,0.347,0.38,0.406,0.416,0.409,0.392,0.375,0.362,0.355,0.351,0.351,0.357,0.372,0.397,0.427,0.455,0.469,0.466,0.448,0.426,0.405,0.388,0.373,0.359,0.345,0.329,0.309,0.293,0.289,0.302,0.335,0.384,0.443,0.499,0.539,0.554,0.546,0.522,0.492,0.461,0.432,0.407,0.387,0.373,0.366,0.366,0.372,0.381,0.388,0.391,0.392,0.39,0.385,0.375,0.364,0.358,0.358,0.359,0.356,0.342,0.323,0.306,0.299,0.304,0.317,0.336,0.364,0.4,0.441,0.474,0.49,0.486,0.469,0.45,0.434,0.421,0.407,0.39,0.375,0.365,0.365,0.374,0.389,0.409,0.431,0.45,0.458,0.454,0.443,0.433,0.428,0.423,0.414,0.399,0.378,0.357,0.336,0.316,0.297,0.281,0.271,0.267,0.27,0.28,0.297,0.319,0.342,0.361,0.375,0.384,0.389,0.392,0.391,0.39,0.389,0.393,0.409,0.436,0.472,0.508,0.532,0.538,0.528,0.51,0.491,0.475,0.459,0.444,0.436,0.442,0.464,0.499,0.533,0.555,0.556,0.538,0.508,0.47,0.428,0.383,0.342,0.312,0.294,0.289,0.292,0.298,0.305,0.314,0.33,0.358,0.393,0.426,0.452,0.472,0.489,0.509,0.525,0.536,0.542,0.555,0.582,0.623,0.668,0.703,0.723,0.727,0.721,0.711,0.702,0.693,0.685,0.672,0.651,0.617,0.574,0.53,0.494,0.467,0.446,0.424,0.4,0.38,0.367,0.361,0.364,0.381,0.416,0.468,0.52,0.555,0.561,0.548,0.532,0.524,0.523,0.519,0.506,0.488,0.477,0.478,0.49,0.506,0.522,0.53,0.526,0.503,0.459,0.402,0.346,0.306,0.287,0.283,0.285,0.283,0.275,0.264,0.254,0.248,0.247,0.253,0.268,0.293,0.324,0.352,0.373,0.392,0.42,0.466,0.527,0.583,0.614,0.607,0.567,0.517,0.484,0.482,0.511,0.556,0.607,0.656,0.699,0.727,0.731,0.712,0.682,0.657,0.644,0.642,0.645,0.642,0.627,0.597,0.556,0.515,0.482,0.455,0.431,0.406,0.388,0.384,0.399,0.432,0.476,0.522,0.558,0.579,0.583,0.572,0.55,0.526,0.508,0.503,0.506,0.511,0.508,0.493,0.462,0.419,0.374,0.338,0.317,0.309,0.309,0.311,0.318,0.334,0.36,0.391,0.418,0.433,0.436,0.429,0.419,0.413,0.419,0.439,0.47,0.504,0.529,0.537,0.522,0.493,0.46,0.438,0.434,0.449,0.48,0.518,0.547,0.555,0.539,0.507,0.472,0.447,0.431,0.422,0.417,0.418,0.427,0.444,0.463,0.478,0.485,0.487,0.485,0.479,0.467,0.449,0.424,0.397,0.374,0.358,0.353,0.356,0.368,0.388,0.413,0.44,0.468,0.495,0.52,0.539,0.551,0.555,0.555,0.554,0.55,0.539,0.515,0.478,0.441,0.419,0.419,0.439,0.471,0.505,0.538,0.564,0.575,0.563,0.531,0.493,0.465,0.451,0.446,0.438,0.429,0.426,0.441,0.474,0.518,0.563,0.601,0.626,0.636,0.641,0.651,0.672,0.692,0.701,0.69,0.667,0.636,0.598,0.55,0.493,0.436,0.39,0.362,0.35,0.349,0.353,0.362,0.374,0.389,0.404,0.415,0.416,0.404,0.384,0.36,0.34,0.324,0.312,0.302,0.294,0.289,0.288,0.289,0.295,0.312,0.347,0.399,0.457,0.507,0.544,0.573,0.606,0.643,0.675,0.688,0.672,0.629,0.569,0.508,0.461,0.434,0.426,0.429,0.435,0.438,0.437,0.436,0.439,0.454,0.484,0.526,0.57,0.604,0.621,0.628,0.639,0.655,0.668,0.669,0.663,0.66,0.665,0.674,0.674,0.666,0.657,0.66,0.674,0.685,0.677,0.642,0.588,0.529,0.481,0.453,0.447,0.459,0.482,0.503,0.509,0.497,0.475,0.454,0.443,0.437,0.431,0.42,0.405,0.39,0.376,0.364,0.356,0.354,0.358,0.365,0.37,0.373,0.374,0.377,0.385,0.404,0.437,0.48,0.523,0.552,0.557,0.541,0.511,0.481,0.456,0.436,0.42,0.408,0.399,0.395,0.393,0.389,0.384,0.379,0.38,0.387,0.397,0.401,0.394,0.376,0.357,0.347,0.357,0.39,0.442,0.497,0.532,0.535,0.513,0.49,0.485,0.502,0.523,0.534,0.53,0.517,0.505,0.499,0.495,0.491,0.484,0.475,0.458,0.43,0.391,0.351,0.321,0.307,0.306,0.31,0.31,0.305,0.297,0.287,0.281,0.281,0.294,0.321,0.356,0.386,0.402,0.404,0.408,0.434,0.489,0.559,0.619,0.648,0.645,0.623,0.602,0.591,0.592,0.6,0.612,0.623,0.634,0.636,0.627,0.604,0.567,0.518,0.459,0.396,0.339,0.293,0.26,0.241,0.235,0.243,0.269,0.316,0.38,0.45,0.509,0.542,0.545,0.53,0.511,0.502,0.502,0.507,0.51,0.506,0.491,0.469,0.448,0.436,0.434,0.438,0.445,0.451,0.456,0.458,0.454,0.446,0.441,0.446,0.46,0.477,0.487,0.482,0.458,0.418,0.373,0.339,0.326,0.339,0.373,0.415,0.453,0.477,0.482,0.473,0.455,0.441,0.437,0.449,0.468,0.489,0.502,0.507,0.507,0.509,0.522,0.552,0.596,0.635,0.649,0.626,0.582,0.54,0.52,0.523,0.535,0.544,0.546,0.549,0.554,0.559,0.556,0.537,0.5,0.454,0.414,0.392,0.395,0.419,0.45,0.475,0.489,0.493,0.492,0.488,0.482,0.476,0.477,0.49,0.511,0.523,0.515,0.482,0.438,0.398,0.374,0.363,0.356,0.346,0.336,0.333,0.343,0.364,0.385,0.403,0.412,0.415,0.415,0.413,0.413,0.421,0.437,0.461,0.487,0.509,0.521,0.516,0.494,0.468,0.455,0.467,0.504,0.553,0.597,0.617,0.606,0.568,0.519,0.479,0.456,0.448,0.443,0.436,0.424,0.412,0.408,0.415,0.434,0.458,0.479,0.489,0.484,0.465,0.436,0.406,0.384,0.372,0.371,0.377,0.387,0.399,0.414,0.433,0.454,0.472,0.484,0.491,0.499,0.515,0.538,0.558,0.562,0.541,0.501,0.455,0.42,0.405,0.411,0.433,0.463,0.497,0.527,0.547,0.555,0.557,0.559,0.568,0.575,0.573,0.562,0.558,0.581,0.634,0.698,0.744,0.753,0.722,0.668,0.61,0.57,0.562,0.589,0.64,0.689,0.717,0.715,0.694,0.666,0.635,0.596,0.548,0.498,0.459,0.436,0.423,0.408,0.39,0.374,0.37,0.379,0.392,0.398,0.387,0.364,0.337,0.317,0.308,0.31,0.321,0.337,0.352,0.363,0.365,0.36,0.354,0.351,0.354,0.356,0.355,0.349,0.34,0.332,0.328,0.332,0.343,0.354,0.362,0.367,0.373,0.387,0.406,0.422,0.423,0.407,0.377,0.345,0.322,0.315,0.323,0.346,0.378,0.416,0.45,0.467,0.464,0.443,0.419,0.407,0.417,0.453,0.512,0.587,0.66,0.714,0.731,0.709,0.66,0.606,0.568,0.553,0.551,0.55,0.541,0.527,0.519,0.52,0.534,0.557,0.584,0.608,0.622,0.626,0.627,0.63,0.635,0.635,0.617,0.577,0.518,0.454,0.398,0.364,0.353,0.362,0.386,0.42,0.459,0.498,0.527,0.544,0.55,0.555,0.565,0.575,0.573,0.549,0.509,0.466,0.433,0.416,0.408,0.404,0.399,0.398,0.406,0.423,0.448,0.475,0.499,0.514,0.516,0.504,0.48,0.449,0.417,0.387,0.358,0.331,0.311,0.311,0.337,0.387,0.442,0.485,0.504,0.505,0.5,0.492,0.484,0.476,0.471,0.467,0.464,0.461,0.463,0.473,0.491,0.509,0.52,0.522,0.514,0.496,0.472,0.442,0.412,0.386,0.367,0.357,0.354,0.353,0.35,0.346,0.347,0.36,0.387,0.42,0.453,0.478,0.495,0.507,0.519,0.533,0.55,0.566,0.578,0.582,0.579,0.57,0.561,0.555,0.553,0.559,0.577,0.61,0.657,0.707,0.745,0.761,0.755,0.736,0.712,0.692,0.675,0.661,0.648,0.631,0.607,0.575,0.542,0.513,0.492,0.478,0.473,0.478,0.491,0.503,0.506,0.498,0.482,0.461,0.434,0.397,0.353,0.313,0.288,0.287,0.311,0.358,0.419,0.477,0.518,0.54,0.552,0.563,0.576,0.585,0.584,0.572,0.551,0.523,0.49,0.462,0.449,0.454,0.472,0.488,0.494,0.486,0.464,0.429,0.388,0.349,0.32,0.304,0.296,0.291,0.29,0.294,0.305,0.322,0.34,0.361,0.383,0.406,0.425,0.434,0.434,0.439,0.466,0.518,0.583,0.638,0.668,0.674,0.666,0.655,0.644,0.632,0.622,0.619,0.629,0.647,0.666,0.677,0.675,0.664,0.653,0.645,0.64,0.635,0.626,0.61,0.586,0.554,0.518,0.483,0.456,0.435,0.424,0.422,0.431,0.449,0.471,0.493,0.511,0.524,0.536,0.548,0.566,0.589,0.609,0.619,0.614,0.598,0.581,0.568,0.556,0.539,0.515,0.491,0.478,0.482,0.501,0.521,0.53,0.528,0.518,0.509,0.507,0.511,0.52,0.535,0.557,0.584,0.608,0.623,0.626,0.621,0.614,0.606,0.595,0.576,0.55,0.519,0.492,0.472,0.463,0.462,0.466,0.473,0.482,0.499,0.525,0.561,0.601,0.637,0.66,0.664,0.646,0.612,0.568,0.525,0.492,0.475,0.481,0.507,0.539,0.559,0.559,0.544,0.532,0.534,0.545,0.553,0.543,0.51,0.463,0.415,0.38,0.363,0.364,0.381,0.413,0.456,0.503,0.54,0.555,0.546,0.523,0.5,0.483,0.467,0.444,0.408,0.364,0.323,0.299,0.302,0.336,0.396,0.467,0.527,0.559,0.562,0.546,0.527,0.514,0.506,0.494,0.471,0.437,0.398,0.363,0.335,0.316,0.303,0.295,0.294,0.308,0.339,0.382,0.426,0.463,0.493,0.518,0.536,0.539,0.521,0.489,0.462,0.452,0.459,0.476,0.498,0.524,0.55,0.568,0.57,0.559,0.541,0.526,0.512,0.498,0.48,0.461,0.445,0.433,0.425,0.422,0.431,0.453,0.485,0.513,0.53,0.535,0.534,0.533,0.533,0.528,0.515,0.493,0.466,0.441,0.416,0.394,0.375,0.365,0.369,0.39,0.423,0.46,0.49,0.502,0.492,0.461,0.418,0.372,0.333,0.305,0.288,0.278,0.276,0.284,0.302,0.327,0.353,0.376,0.395,0.41,0.418,0.418,0.409,0.397,0.383,0.369,0.354,0.339,0.333,0.337,0.349,0.361,0.37,0.381,0.402,0.433,0.462,0.476,0.469,0.454,0.451,0.465,0.49,0.507,0.507,0.493,0.474,0.455,0.44,0.433,0.437,0.45,0.464,0.468,0.456,0.432,0.404,0.381,0.363,0.346,0.329,0.316,0.31,0.312,0.316,0.316,0.311,0.309,0.322,0.359,0.419,0.49,0.558,0.61,0.646,0.663,0.659,0.636,0.601,0.566,0.541,0.528,0.529,0.538,0.554,0.571,0.584,0.592,0.596,0.595,0.585,0.562,0.528,0.491,0.462,0.45,0.452,0.458,0.463,0.464,0.462,0.458,0.452,0.447,0.447,0.457,0.477,0.5,0.52,0.531,0.532,0.532,0.536,0.543,0.546,0.542,0.531,0.521,0.514,0.508,0.5,0.488,0.477,0.47,0.472,0.479,0.486,0.488,0.486,0.484,0.486,0.488,0.492,0.495,0.495,0.486,0.46,0.416,0.366,0.328,0.31,0.31,0.32,0.332,0.342,0.356,0.374,0.397,0.42,0.437,0.445,0.443,0.435,0.426,0.424,0.439,0.47,0.505,0.529,0.535,0.527,0.513,0.499,0.49,0.489,0.502,0.524,0.546,0.554,0.54,0.51,0.475,0.446,0.433,0.435,0.447,0.46,0.47,0.476,0.483,0.498,0.522,0.55,0.573,0.584,0.585,0.58,0.573,0.568,0.565,0.564,0.564,0.56,0.547,0.524,0.49,0.452,0.42,0.401,0.395,0.4,0.41,0.427,0.453,0.489,0.527,0.56,0.576,0.569,0.544,0.512,0.483,0.461,0.451,0.455,0.478,0.51,0.539,0.551,0.546,0.538,0.541,0.557,0.575,0.588,0.6,0.615,0.629,0.63,0.608,0.566,0.517,0.474,0.444,0.425,0.417,0.421,0.439,0.47,0.504,0.526,0.532,0.529,0.528,0.533,0.535,0.527,0.511,0.498,0.5,0.513,0.523,0.517,0.496,0.471,0.456,0.454,0.458,0.462,0.464,0.466,0.471,0.475,0.471,0.456,0.432,0.409,0.398,0.402,0.419,0.441,0.463,0.477,0.482,0.482,0.487,0.504,0.536,0.58,0.624,0.655,0.661,0.639,0.599,0.558,0.532,0.525,0.535,0.549,0.562,0.571,0.583,0.604,0.634,0.668,0.693,0.702,0.693,0.668,0.632,0.59,0.548,0.514,0.491,0.482,0.482,0.489,0.5,0.519,0.546,0.575,0.593,0.593,0.574,0.547,0.519,0.494,0.468,0.442,0.417,0.395,0.375,0.357,0.34,0.326,0.317,0.315,0.324,0.346,0.381,0.421,0.455,0.477,0.484,0.482,0.471,0.449,0.416,0.375,0.34,0.323,0.329,0.354,0.387,0.418,0.441,0.46,0.477,0.494,0.504,0.505,0.499,0.494,0.495,0.5,0.505,0.509,0.513,0.519,0.535,0.565,0.605,0.645,0.671,0.676,0.665,0.644,0.621,0.602,0.589,0.581,0.571,0.556,0.536,0.519,0.516,0.529,0.554,0.578,0.592,0.592,0.579,0.562,0.548,0.542,0.543,0.544,0.537,0.52,0.497,0.473,0.448,0.419,0.391,0.372,0.367,0.374,0.38,0.376,0.359,0.337,0.321,0.321,0.337,0.362,0.379,0.376,0.355,0.333,0.321,0.325,0.339,0.355,0.371,0.385,0.402,0.42,0.436,0.441,0.429,0.402,0.373,0.354,0.354,0.365,0.378,0.389,0.405,0.438,0.491,0.553,0.604,0.625,0.61,0.576,0.545,0.531,0.529,0.527,0.518,0.504,0.488,0.47,0.452,0.44,0.443,0.465,0.497,0.525,0.537,0.529,0.502,0.462,0.417,0.376,0.346,0.328,0.319,0.313,0.306,0.3,0.301,0.318,0.356,0.417,0.496,0.576,0.639,0.67,0.667,0.645,0.62,0.601,0.589,0.583,0.588,0.604,0.629,0.654,0.67,0.673,0.668,0.661,0.654,0.643,0.623,0.591,0.553,0.52,0.5,0.493,0.49,0.478,0.453,0.42,0.389,0.369,0.363,0.369,0.382,0.393,0.399,0.399,0.404,0.42,0.451,0.486,0.513,0.523,0.516,0.502,0.49,0.485,0.484,0.483,0.484,0.491,0.507,0.529,0.549,0.566,0.578,0.587,0.587,0.574,0.551,0.533,0.522,0.512,0.487,0.448,0.408,0.386,0.388,0.408,0.435,0.46,0.478,0.488,0.494,0.503,0.52,0.542,0.562,0.567,0.555,0.534,0.522,0.533,0.567,0.611,0.649,0.673,0.682,0.683,0.679,0.671,0.659,0.645,0.632,0.616,0.591,0.557,0.524,0.505,0.505,0.517,0.527,0.527,0.513,0.491,0.471,0.46,0.461,0.471,0.48,0.477,0.458,0.424,0.387,0.364,0.368,0.402,0.454,0.5,0.52,0.504,0.46,0.408,0.364,0.336,0.325,0.33,0.351,0.382,0.415,0.438,0.448,0.448,0.444,0.438,0.429,0.423,0.422,0.433,0.451,0.476,0.502,0.53,0.556,0.573,0.578,0.57,0.559,0.554,0.561,0.579,0.603,0.629,0.646,0.645,0.621,0.58,0.536,0.502,0.483,0.478,0.485,0.501,0.523,0.544,0.558,0.565,0.572,0.583,0.599,0.612,0.613,0.593,0.554,0.508,0.469,0.446,0.438,0.441,0.45,0.465,0.479,0.486,0.482,0.47,0.461,0.461,0.474,0.496,0.521,0.538,0.544,0.533,0.51,0.482,0.461,0.459,0.481,0.523,0.571,0.611,0.63,0.627,0.602,0.561,0.513,0.465,0.428,0.406,0.404,0.422,0.456,0.498,0.534,0.557,0.563,0.555,0.54,0.531,0.538,0.567,0.613,0.654,0.675,0.67,0.653,0.638,0.626,0.615,0.601,0.587,0.575,0.561,0.54,0.514,0.49,0.479,0.482,0.495,0.507,0.511,0.503,0.483,0.456,0.431,0.415,0.412,0.418,0.424,0.424,0.416,0.408,0.415,0.446,0.498,0.555,0.598,0.623,0.635,0.644,0.652,0.649,0.627,0.587,0.535,0.484,0.443,0.421,0.419,0.436,0.464,0.495,0.527,0.56,0.596,0.628,0.65,0.659,0.663,0.672,0.688,0.696,0.679,0.629,0.563,0.509,0.488,0.505,0.547,0.595,0.63,0.648,0.652,0.655,0.666,0.689,0.715,0.736,0.742,0.728,0.697,0.658,0.626,0.611,0.619,0.648,0.691,0.736,0.764,0.767,0.743,0.706,0.672,0.65,0.632,0.602,0.556,0.5,0.448,0.41,0.387,0.383,0.404,0.452,0.514,0.566,0.588,0.58,0.555,0.527,0.498,0.465,0.433,0.415,0.417,0.437,0.462,0.477,0.477,0.463,0.439,0.411,0.383,0.362,0.353,0.364,0.397,0.448,0.51,0.569,0.61,0.624,0.613,0.589,0.567,0.558,0.563,0.579,0.595,0.603,0.593,0.561,0.512,0.457,0.409,0.378,0.363,0.365,0.381,0.41,0.446,0.476,0.492,0.497,0.498,0.5,0.499,0.487,0.465,0.446,0.439,0.446,0.466,0.494,0.524,0.548,0.554,0.535,0.496,0.452,0.422,0.417,0.441,0.49,0.549,0.595,0.608,0.582,0.535,0.492,0.471,0.468,0.471,0.471,0.471,0.478,0.494,0.514,0.534,0.558,0.584,0.607,0.618,0.609,0.581,0.545,0.509,0.481,0.46,0.446,0.44,0.445,0.458,0.473,0.486,0.502,0.531,0.577,0.637,0.697,0.748,0.786,0.814,0.831,0.83,0.806,0.764,0.713,0.664,0.621,0.587,0.57,0.573,0.59,0.611,0.622,0.618,0.599,0.572,0.542,0.516,0.494,0.482,0.485,0.502,0.53,0.561,0.588,0.609,0.623,0.637,0.658,0.686,0.708,0.706,0.671,0.611,0.546,0.492,0.457,0.438,0.431,0.432,0.435,0.435,0.432,0.426,0.419,0.413,0.411,0.413,0.422,0.437,0.455,0.467,0.468,0.458,0.44,0.418,0.393,0.366,0.339,0.316,0.298,0.288,0.287,0.299,0.327,0.369,0.418,0.458,0.478,0.475,0.455,0.428,0.402,0.384,0.378,0.392,0.425,0.469,0.509,0.529,0.526,0.514,0.509,0.516,0.528,0.536,0.537,0.535,0.531,0.529,0.535,0.558,0.601,0.654,0.703,0.731,0.732,0.715,0.696,0.692,0.7,0.706,0.692,0.656,0.61,0.569,0.538,0.513,0.489,0.464,0.437,0.41,0.382,0.357,0.34,0.334,0.344,0.366,0.394,0.422,0.44,0.444,0.433,0.413,0.39,0.371,0.359,0.351,0.346,0.34,0.334,0.327,0.318,0.308,0.302,0.304,0.321,0.351,0.388,0.422,0.443,0.451,0.45,0.448,0.449,0.453,0.454,0.451,0.443,0.433,0.421,0.405,0.385,0.361,0.338,0.32,0.31,0.305,0.301,0.294,0.282,0.267,0.251,0.239,0.23,0.225,0.222,0.217,0.212,0.205,0.198,0.191,0.184,0.178,0.175,0.175,0.178,0.182,0.187,0.191,0.194,0.195,0.193,0.187,0.181,0.175,0.17,0.166,0.162,0.157,0.15,0.143,0.137,0.131,0.126,0.122,0.119,0.118,0.116,0.112,0.107,0.1,0.094,0.092,0.094,0.098,0.099,0.097,0.092,0.086,0.081,0.078,0.076,0.076,0.078,0.079,0.078,0.075,0.07,0.065,0.061,0.058,0.058,0.058,0.059,0.059,0.058,0.055,0.052,0.048,0.044,0.04,0.035,0.029,0.024,0.018,0.014,0.011,0.009,0.007,0.006,0.004,0.003,0.003,0.003,0.003,0.004,0.006,0.007,0.009,0.01,0.01]