[0,0.002,0.011,0.032,0.069,0.118,0.167,0.202,0.217,0.218,0.213,0.21,0.209,0.212,0.216,0.222,0.23,0.237,0.243,0.249,0.256,0.265,0.279,0.295,0.31,0.321,0.328,0.329,0.326,0.319,0.309,0.298,0.284,0.27,0.257,0.253,0.263,0.289,0.322,0.349,0.362,0.36,0.351,0.341,0.334,0.329,0.325,0.321,0.32,0.321,0.325,0.328,0.325,0.315,0.299,0.283,0.271,0.263,0.258,0.252,0.243,0.232,0.22,0.209,0.2,0.193,0.185,0.179,0.177,0.183,0.199,0.223,0.247,0.263,0.271,0.274,0.276,0.279,0.28,0.278,0.271,0.259,0.246,0.235,0.228,0.224,0.223,0.221,0.218,0.214,0.209,0.204,0.2,0.197,0.195,0.193,0.192,0.19,0.185,0.179,0.172,0.169,0.171,0.18,0.196,0.214,0.23,0.244,0.257,0.271,0.288,0.309,0.331,0.353,0.379,0.412,0.455,0.504,0.552,0.592,0.626,0.658,0.692,0.726,0.755,0.773,0.775,0.764,0.745,0.72,0.696,0.678,0.667,0.661,0.657,0.648,0.634,0.622,0.622,0.634,0.653,0.666,0.67,0.666,0.66,0.651,0.642,0.631,0.619,0.605,0.586,0.568,0.555,0.556,0.566,0.579,0.588,0.592,0.596,0.606,0.62,0.635,0.643,0.641,0.63,0.614,0.595,0.573,0.545,0.512,0.478,0.445,0.414,0.383,0.355,0.334,0.323,0.322,0.326,0.332,0.342,0.362,0.398,0.448,0.5,0.545,0.575,0.595,0.609,0.621,0.626,0.623,0.611,0.597,0.586,0.582,0.589,0.605,0.627,0.645,0.655,0.654,0.647,0.637,0.624,0.606,0.586,0.57,0.562,0.56,0.558,0.55,0.532,0.507,0.477,0.452,0.441,0.449,0.469,0.491,0.502,0.499,0.49,0.485,0.491,0.504,0.515,0.517,0.511,0.501,0.492,0.483,0.473,0.464,0.458,0.462,0.472,0.476,0.466,0.44,0.406,0.371,0.339,0.312,0.291,0.287,0.308,0.353,0.41,0.459,0.488,0.5,0.504,0.508,0.511,0.511,0.507,0.505,0.507,0.504,0.49,0.465,0.443,0.434,0.443,0.462,0.483,0.501,0.51,0.509,0.504,0.5,0.502,0.51,0.519,0.522,0.518,0.507,0.49,0.474,0.463,0.46,0.465,0.473,0.479,0.479,0.476,0.472,0.468,0.456,0.428,0.379,0.317,0.263,0.244,0.271,0.332,0.4,0.453,0.491,0.531,0.587,0.654,0.713,0.749,0.76,0.754,0.738,0.72,0.706,0.699,0.703,0.715,0.73,0.745,0.758,0.77,0.776,0.77,0.743,0.695,0.631,0.561,0.492,0.432,0.383,0.35,0.339,0.351,0.38,0.416,0.453,0.483,0.499,0.497,0.483,0.471,0.48,0.515,0.569,0.624,0.667,0.69,0.698,0.701,0.71,0.728,0.747,0.755,0.746,0.724,0.696,0.671,0.653,0.646,0.652,0.665,0.676,0.677,0.661,0.626,0.579,0.526,0.48,0.444,0.419,0.397,0.373,0.346,0.316,0.288,0.26,0.234,0.208,0.184,0.165,0.156,0.16,0.181,0.215,0.255,0.289,0.309,0.313,0.304,0.29,0.284,0.297,0.336,0.393,0.447,0.478,0.475,0.441,0.396,0.365,0.37,0.409,0.463,0.51,0.537,0.548,0.552,0.556,0.56,0.564,0.569,0.576,0.583,0.591,0.598,0.604,0.608,0.608,0.603,0.596,0.59,0.586,0.585,0.583,0.582,0.581,0.582,0.585,0.589,0.592,0.594,0.596,0.6,0.605,0.611,0.615,0.616,0.613,0.608,0.598,0.581,0.551,0.508,0.458,0.409,0.37,0.347,0.345,0.364,0.4,0.447,0.495,0.531,0.55,0.551,0.536,0.513,0.488,0.466,0.448,0.431,0.413,0.392,0.371,0.362,0.372,0.395,0.416,0.423,0.417,0.412,0.423,0.45,0.484,0.515,0.54,0.562,0.583,0.601,0.611,0.61,0.598,0.581,0.562,0.544,0.53,0.52,0.508,0.49,0.466,0.438,0.415,0.405,0.416,0.446,0.479,0.501,0.503,0.492,0.475,0.457,0.438,0.421,0.406,0.396,0.387,0.377,0.362,0.341,0.318,0.299,0.295,0.309,0.34,0.376,0.404,0.414,0.41,0.399,0.384,0.365,0.339,0.308,0.277,0.252,0.241,0.242,0.248,0.251,0.252,0.256,0.267,0.282,0.291,0.291,0.283,0.275,0.271,0.272,0.274,0.273,0.267,0.264,0.274,0.305,0.354,0.408,0.449,0.467,0.466,0.46,0.462,0.474,0.493,0.514,0.531,0.536,0.521,0.487,0.445,0.413,0.398,0.397,0.399,0.394,0.379,0.359,0.341,0.327,0.32,0.317,0.316,0.318,0.328,0.348,0.378,0.407,0.423,0.42,0.402,0.379,0.357,0.342,0.331,0.32,0.312,0.31,0.32,0.339,0.358,0.37,0.374,0.374,0.381,0.407,0.455,0.509,0.547,0.562,0.567,0.58,0.601,0.618,0.619,0.605,0.586,0.572,0.565,0.56,0.555,0.545,0.529,0.506,0.476,0.438,0.396,0.354,0.316,0.286,0.266,0.255,0.25,0.249,0.249,0.25,0.256,0.272,0.301,0.331,0.349,0.348,0.333,0.314,0.303,0.3,0.304,0.31,0.319,0.335,0.365,0.41,0.465,0.516,0.552,0.57,0.574,0.57,0.563,0.553,0.539,0.523,0.509,0.5,0.5,0.505,0.508,0.503,0.489,0.474,0.475,0.502,0.551,0.605,0.646,0.667,0.671,0.669,0.667,0.663,0.655,0.643,0.63,0.622,0.618,0.618,0.617,0.616,0.617,0.618,0.616,0.61,0.597,0.582,0.564,0.546,0.529,0.517,0.512,0.511,0.509,0.499,0.479,0.454,0.426,0.4,0.376,0.357,0.344,0.336,0.331,0.327,0.323,0.327,0.346,0.383,0.433,0.483,0.526,0.558,0.585,0.602,0.608,0.6,0.588,0.585,0.597,0.62,0.641,0.649,0.641,0.617,0.586,0.553,0.532,0.529,0.546,0.571,0.592,0.599,0.595,0.589,0.587,0.588,0.582,0.559,0.519,0.473,0.435,0.416,0.421,0.447,0.488,0.533,0.573,0.599,0.611,0.611,0.602,0.585,0.565,0.545,0.53,0.521,0.517,0.514,0.512,0.509,0.505,0.498,0.483,0.46,0.433,0.41,0.395,0.391,0.394,0.407,0.434,0.476,0.524,0.561,0.58,0.587,0.602,0.631,0.666,0.688,0.69,0.677,0.661,0.652,0.647,0.638,0.617,0.586,0.549,0.514,0.487,0.475,0.479,0.495,0.513,0.523,0.525,0.522,0.518,0.514,0.51,0.507,0.506,0.509,0.514,0.518,0.518,0.516,0.515,0.517,0.524,0.531,0.532,0.521,0.493,0.448,0.393,0.34,0.304,0.299,0.329,0.383,0.443,0.493,0.533,0.569,0.602,0.623,0.624,0.608,0.592,0.592,0.611,0.64,0.664,0.681,0.699,0.721,0.743,0.754,0.753,0.741,0.72,0.682,0.624,0.554,0.489,0.443,0.424,0.423,0.431,0.436,0.438,0.445,0.465,0.5,0.535,0.553,0.542,0.512,0.483,0.475,0.491,0.521,0.55,0.573,0.591,0.611,0.632,0.652,0.666,0.673,0.674,0.676,0.679,0.685,0.689,0.69,0.685,0.674,0.658,0.641,0.629,0.623,0.622,0.628,0.647,0.678,0.71,0.727,0.718,0.683,0.635,0.589,0.553,0.529,0.513,0.503,0.495,0.489,0.482,0.478,0.476,0.482,0.491,0.493,0.479,0.447,0.404,0.362,0.333,0.325,0.345,0.395,0.464,0.537,0.595,0.629,0.638,0.629,0.612,0.6,0.6,0.61,0.625,0.634,0.634,0.624,0.608,0.588,0.57,0.557,0.555,0.567,0.592,0.623,0.651,0.672,0.687,0.699,0.708,0.715,0.72,0.725,0.729,0.73,0.722,0.702,0.672,0.643,0.624,0.62,0.627,0.639,0.648,0.653,0.655,0.655,0.656,0.658,0.661,0.665,0.666,0.66,0.642,0.611,0.569,0.52,0.474,0.443,0.433,0.445,0.467,0.486,0.492,0.486,0.478,0.48,0.495,0.515,0.527,0.519,0.494,0.464,0.444,0.439,0.447,0.461,0.475,0.485,0.483,0.464,0.431,0.396,0.373,0.368,0.378,0.395,0.407,0.408,0.396,0.38,0.371,0.376,0.393,0.413,0.426,0.43,0.428,0.428,0.433,0.437,0.431,0.411,0.379,0.347,0.326,0.325,0.334,0.341,0.34,0.338,0.343,0.354,0.363,0.361,0.349,0.332,0.317,0.309,0.305,0.303,0.298,0.289,0.281,0.278,0.285,0.302,0.321,0.335,0.341,0.342,0.345,0.347,0.345,0.331,0.304,0.271,0.245,0.234,0.239,0.248,0.257,0.266,0.282,0.307,0.334,0.351,0.356,0.351,0.342,0.331,0.318,0.299,0.278,0.267,0.281,0.329,0.396,0.46,0.501,0.514,0.505,0.489,0.479,0.48,0.494,0.518,0.549,0.583,0.608,0.606,0.57,0.508,0.443,0.396,0.379,0.385,0.401,0.412,0.41,0.396,0.377,0.361,0.351,0.349,0.349,0.348,0.342,0.331,0.319,0.313,0.319,0.335,0.352,0.363,0.362,0.353,0.345,0.347,0.366,0.4,0.437,0.465,0.478,0.478,0.469,0.457,0.454,0.473,0.512,0.555,0.581,0.585,0.581,0.584,0.596,0.609,0.616,0.614,0.608,0.601,0.596,0.594,0.592,0.585,0.573,0.555,0.536,0.52,0.508,0.499,0.489,0.474,0.453,0.427,0.397,0.364,0.331,0.305,0.293,0.301,0.322,0.345,0.358,0.361,0.362,0.368,0.381,0.398,0.414,0.426,0.431,0.427,0.415,0.399,0.388,0.383,0.384,0.389,0.394,0.397,0.398,0.399,0.407,0.425,0.452,0.484,0.512,0.531,0.542,0.549,0.556,0.563,0.569,0.576,0.588,0.607,0.629,0.642,0.636,0.608,0.566,0.526,0.504,0.507,0.526,0.551,0.571,0.579,0.568,0.535,0.485,0.435,0.4,0.387,0.389,0.398,0.407,0.424,0.451,0.489,0.529,0.565,0.591,0.609,0.621,0.627,0.632,0.639,0.652,0.674,0.698,0.715,0.719,0.713,0.707,0.71,0.719,0.726,0.721,0.702,0.672,0.636,0.604,0.581,0.569,0.566,0.564,0.559,0.554,0.551,0.554,0.562,0.574,0.585,0.594,0.598,0.597,0.594,0.59,0.577,0.547,0.498,0.438,0.384,0.354,0.353,0.369,0.384,0.387,0.38,0.369,0.36,0.356,0.356,0.361,0.371,0.385,0.405,0.431,0.462,0.488,0.502,0.503,0.504,0.517,0.542,0.567,0.578,0.573,0.557,0.539,0.525,0.516,0.508,0.502,0.5,0.504,0.518,0.536,0.552,0.563,0.568,0.566,0.556,0.535,0.506,0.48,0.47,0.483,0.514,0.551,0.585,0.612,0.635,0.663,0.699,0.743,0.786,0.817,0.833,0.836,0.833,0.825,0.807,0.776,0.735,0.692,0.658,0.639,0.634,0.64,0.647,0.654,0.656,0.657,0.657,0.66,0.666,0.672,0.677,0.68,0.684,0.689,0.69,0.683,0.663,0.637,0.614,0.605,0.613,0.633,0.655,0.671,0.677,0.673,0.663,0.65,0.635,0.622,0.608,0.594,0.573,0.545,0.508,0.466,0.425,0.391,0.365,0.346,0.332,0.325,0.329,0.347,0.376,0.407,0.43,0.44,0.437,0.425,0.411,0.403,0.41,0.432,0.461,0.485,0.495,0.492,0.483,0.474,0.469,0.469,0.476,0.489,0.508,0.532,0.561,0.592,0.621,0.644,0.659,0.665,0.662,0.654,0.641,0.623,0.601,0.573,0.542,0.512,0.49,0.481,0.48,0.485,0.494,0.507,0.518,0.521,0.514,0.501,0.487,0.475,0.461,0.444,0.429,0.425,0.438,0.467,0.501,0.53,0.549,0.555,0.548,0.532,0.511,0.487,0.462,0.441,0.425,0.416,0.415,0.42,0.431,0.447,0.467,0.495,0.534,0.582,0.63,0.67,0.697,0.712,0.719,0.724,0.726,0.725,0.719,0.708,0.695,0.689,0.694,0.709,0.723,0.729,0.725,0.717,0.71,0.702,0.693,0.683,0.678,0.678,0.681,0.682,0.679,0.673,0.671,0.673,0.671,0.652,0.61,0.545,0.474,0.414,0.374,0.352,0.34,0.328,0.311,0.29,0.269,0.254,0.251,0.268,0.309,0.373,0.446,0.512,0.558,0.579,0.58,0.569,0.552,0.532,0.51,0.486,0.461,0.437,0.415,0.402,0.404,0.422,0.451,0.479,0.496,0.498,0.487,0.469,0.452,0.438,0.429,0.425,0.423,0.427,0.439,0.457,0.478,0.496,0.507,0.511,0.509,0.504,0.498,0.492,0.486,0.482,0.478,0.475,0.471,0.465,0.457,0.449,0.443,0.444,0.448,0.445,0.427,0.388,0.333,0.28,0.244,0.236,0.248,0.267,0.284,0.305,0.338,0.383,0.43,0.465,0.482,0.484,0.479,0.474,0.47,0.463,0.452,0.44,0.435,0.442,0.459,0.478,0.492,0.498,0.501,0.506,0.523,0.559,0.611,0.666,0.707,0.727,0.731,0.733,0.741,0.753,0.765,0.77,0.766,0.757,0.745,0.735,0.728,0.724,0.721,0.718,0.715,0.714,0.713,0.711,0.705,0.695,0.679,0.659,0.638,0.615,0.588,0.552,0.508,0.466,0.436,0.424,0.425,0.429,0.427,0.421,0.413,0.408,0.406,0.407,0.413,0.433,0.472,0.525,0.578,0.619,0.642,0.65,0.642,0.618,0.584,0.556,0.55,0.568,0.599,0.628,0.645,0.651,0.647,0.635,0.617,0.598,0.591,0.602,0.628,0.659,0.687,0.703,0.706,0.698,0.685,0.675,0.67,0.665,0.648,0.619,0.583,0.551,0.53,0.526,0.536,0.554,0.573,0.587,0.596,0.601,0.604,0.602,0.594,0.581,0.567,0.555,0.546,0.54,0.536,0.534,0.53,0.521,0.502,0.475,0.448,0.425,0.409,0.398,0.388,0.376,0.365,0.362,0.374,0.402,0.442,0.489,0.534,0.57,0.593,0.603,0.601,0.594,0.586,0.584,0.589,0.602,0.614,0.623,0.625,0.617,0.599,0.573,0.547,0.532,0.532,0.544,0.566,0.595,0.629,0.665,0.697,0.723,0.742,0.755,0.765,0.774,0.782,0.793,0.806,0.818,0.824,0.819,0.803,0.777,0.741,0.692,0.625,0.545,0.464,0.402,0.376,0.387,0.423,0.469,0.516,0.567,0.63,0.698,0.761,0.805,0.828,0.835,0.832,0.825,0.816,0.807,0.802,0.8,0.799,0.797,0.79,0.774,0.743,0.695,0.636,0.577,0.53,0.5,0.48,0.46,0.434,0.405,0.383,0.37,0.366,0.364,0.366,0.381,0.415,0.459,0.493,0.505,0.501,0.502,0.529,0.587,0.66,0.73,0.783,0.816,0.831,0.835,0.832,0.826,0.82,0.817,0.815,0.812,0.805,0.792,0.769,0.74,0.709,0.68,0.655,0.631,0.602,0.568,0.535,0.508,0.494,0.489,0.485,0.475,0.458,0.437,0.417,0.402,0.392,0.384,0.376,0.367,0.358,0.351,0.351,0.358,0.37,0.375,0.36,0.315,0.254,0.205,0.197,0.245,0.334,0.429,0.502,0.541,0.559,0.571,0.589,0.613,0.636,0.653,0.662,0.667,0.672,0.678,0.684,0.686,0.683,0.676,0.673,0.676,0.682,0.686,0.684,0.682,0.682,0.686,0.688,0.692,0.705,0.736,0.777,0.808,0.813,0.792,0.757,0.723,0.701,0.688,0.681,0.675,0.672,0.672,0.675,0.68,0.689,0.706,0.73,0.756,0.772,0.764,0.724,0.656,0.573,0.49,0.423,0.385,0.384,0.422,0.484,0.548,0.594,0.615,0.616,0.609,0.601,0.597,0.597,0.598,0.6,0.601,0.601,0.6,0.601,0.603,0.602,0.591,0.573,0.556,0.547,0.55,0.561,0.571,0.578,0.581,0.582,0.583,0.586,0.59,0.595,0.598,0.6,0.601,0.604,0.61,0.617,0.624,0.631,0.637,0.644,0.651,0.655,0.655,0.646,0.629,0.604,0.577,0.557,0.553,0.564,0.583,0.598,0.606,0.61,0.617,0.625,0.629,0.626,0.617,0.609,0.605,0.605,0.608,0.613,0.619,0.626,0.63,0.634,0.639,0.644,0.644,0.636,0.62,0.599,0.575,0.544,0.502,0.449,0.392,0.341,0.302,0.279,0.268,0.265,0.266,0.274,0.293,0.321,0.35,0.371,0.381,0.382,0.378,0.374,0.371,0.369,0.366,0.359,0.351,0.349,0.362,0.396,0.445,0.493,0.525,0.534,0.526,0.513,0.503,0.5,0.504,0.516,0.54,0.576,0.619,0.651,0.661,0.645,0.614,0.58,0.551,0.527,0.507,0.488,0.466,0.438,0.398,0.349,0.303,0.276,0.278,0.309,0.357,0.402,0.433,0.448,0.45,0.443,0.43,0.417,0.41,0.415,0.434,0.465,0.495,0.511,0.506,0.483,0.454,0.442,0.462,0.513,0.571,0.61,0.619,0.616,0.62,0.639,0.661,0.671,0.663,0.642,0.617,0.594,0.576,0.562,0.551,0.54,0.528,0.512,0.492,0.47,0.445,0.421,0.395,0.366,0.336,0.308,0.288,0.277,0.271,0.267,0.264,0.262,0.258,0.254,0.254,0.267,0.3,0.348,0.394,0.414,0.407,0.387,0.375,0.372,0.365,0.345,0.316,0.294,0.291,0.311,0.35,0.402,0.456,0.497,0.508,0.481,0.428,0.371,0.331,0.304,0.279,0.251,0.224,0.207,0.205,0.218,0.244,0.277,0.308,0.33,0.35,0.381,0.428,0.471,0.482,0.444,0.372,0.294,0.236,0.203,0.188,0.188,0.21,0.264,0.352,0.452,0.532,0.573,0.579,0.566,0.55,0.527,0.495,0.453,0.408,0.373,0.351,0.342,0.338,0.338,0.343,0.354,0.359,0.345,0.304,0.247,0.194,0.168,0.18,0.224,0.282,0.329,0.355,0.359,0.356,0.347,0.337,0.323,0.314,0.315,0.323,0.325,0.32,0.323,0.365,0.452,0.561,0.642,0.66,0.61,0.523,0.436,0.379,0.353,0.342,0.326,0.305,0.294,0.309,0.344,0.38,0.397,0.395,0.386,0.382,0.381,0.381,0.38,0.382,0.378,0.364,0.34,0.319,0.313,0.325,0.342,0.353,0.348,0.333,0.319,0.322,0.345,0.381,0.408,0.406,0.369,0.313,0.269,0.261,0.287,0.33,0.364,0.379,0.37,0.342,0.306,0.279,0.276,0.299,0.333,0.369,0.406,0.446,0.475,0.476,0.442,0.386,0.328,0.282,0.253,0.24,0.242,0.253,0.267,0.27,0.257,0.226,0.183,0.141,0.107,0.084,0.07,0.065,0.075,0.115,0.196,0.31,0.425,0.502,0.522,0.499,0.457,0.418,0.383,0.353,0.327,0.317,0.334,0.384,0.449,0.498,0.507,0.476,0.427,0.386,0.361,0.342,0.312,0.264,0.205,0.146,0.099,0.069,0.058,0.076,0.135,0.237,0.363,0.473,0.534,0.541,0.516,0.482,0.45,0.419,0.397,0.388,0.395,0.406,0.406,0.381,0.336,0.282,0.233,0.193,0.162,0.134,0.109,0.086,0.067,0.057,0.062,0.092,0.153,0.233,0.299,0.319,0.284,0.224,0.187,0.21,0.289,0.391,0.47,0.506,0.504,0.49,0.473,0.45,0.405,0.341,0.274,0.227,0.209,0.217,0.24,0.267,0.286,0.287,0.263,0.217,0.159,0.104,0.067,0.058,0.085,0.147,0.231,0.311,0.364,0.382,0.376,0.364,0.366,0.388,0.421,0.441,0.431,0.393,0.349,0.32,0.311,0.306,0.297,0.278,0.257,0.234,0.203,0.159,0.112,0.076,0.069,0.098,0.16,0.233,0.291,0.317,0.311,0.292,0.276,0.274,0.282,0.3,0.315,0.314,0.281,0.22,0.148,0.086,0.046,0.031,0.041,0.081,0.15,0.234,0.31,0.361,0.387,0.398,0.405,0.414,0.423,0.42,0.395,0.345,0.284,0.233,0.212,0.23,0.277,0.33,0.364,0.37,0.353,0.325,0.29,0.245,0.188,0.13,0.084,0.067,0.096,0.175,0.291,0.404,0.474,0.485,0.458,0.421,0.392,0.37,0.353,0.348,0.361,0.388,0.408,0.406,0.379,0.344,0.322,0.319,0.328,0.332,0.322,0.3,0.268,0.229,0.185,0.141,0.113,0.116,0.156,0.221,0.285,0.331,0.358,0.384,0.417,0.45,0.463,0.449,0.415,0.373,0.331,0.295,0.271,0.27,0.294,0.334,0.37,0.375,0.341,0.282,0.243,0.256,0.319,0.391,0.434,0.447,0.458,0.485,0.51,0.503,0.453,0.379,0.312,0.269,0.246,0.226,0.194,0.147,0.096,0.058,0.053,0.091,0.168,0.261,0.34,0.392,0.42,0.44,0.452,0.454,0.44,0.42,0.397,0.378,0.353,0.32,0.274,0.217,0.154,0.094,0.047,0.018,0.005,0.001,0,0,0,0,0,0,0,0]