[0.05,0.067,0.105,0.154,0.204,0.24,0.255,0.252,0.242,0.239,0.248,0.262,0.268,0.263,0.248,0.231,0.218,0.213,0.217,0.232,0.256,0.284,0.307,0.315,0.307,0.288,0.271,0.265,0.273,0.292,0.312,0.329,0.34,0.347,0.349,0.344,0.333,0.323,0.319,0.321,0.32,0.313,0.301,0.293,0.294,0.299,0.301,0.293,0.278,0.266,0.269,0.3,0.36,0.438,0.51,0.555,0.565,0.549,0.527,0.517,0.525,0.55,0.575,0.584,0.567,0.527,0.481,0.454,0.459,0.494,0.537,0.564,0.56,0.528,0.484,0.45,0.441,0.459,0.491,0.517,0.522,0.501,0.459,0.411,0.371,0.352,0.353,0.366,0.377,0.382,0.379,0.372,0.364,0.363,0.376,0.409,0.455,0.495,0.513,0.506,0.486,0.468,0.459,0.458,0.465,0.483,0.511,0.545,0.575,0.591,0.592,0.578,0.555,0.53,0.516,0.523,0.554,0.594,0.622,0.624,0.602,0.57,0.545,0.535,0.534,0.536,0.539,0.545,0.558,0.58,0.606,0.632,0.651,0.654,0.641,0.621,0.606,0.612,0.64,0.68,0.716,0.734,0.732,0.713,0.685,0.651,0.616,0.581,0.552,0.534,0.528,0.534,0.545,0.553,0.556,0.555,0.551,0.545,0.542,0.545,0.562,0.591,0.624,0.65,0.663,0.659,0.64,0.611,0.578,0.547,0.521,0.507,0.506,0.521,0.545,0.567,0.577,0.574,0.562,0.547,0.535,0.53,0.536,0.553,0.573,0.588,0.59,0.584,0.577,0.578,0.588,0.605,0.62,0.627,0.623,0.609,0.588,0.564,0.542,0.528,0.526,0.536,0.551,0.56,0.557,0.542,0.522,0.501,0.48,0.457,0.436,0.424,0.425,0.434,0.442,0.444,0.447,0.457,0.474,0.489,0.491,0.48,0.466,0.457,0.453,0.45,0.445,0.444,0.456,0.484,0.52,0.55,0.564,0.56,0.546,0.531,0.515,0.501,0.491,0.488,0.495,0.507,0.515,0.512,0.502,0.494,0.494,0.496,0.495,0.486,0.478,0.481,0.498,0.523,0.543,0.553,0.559,0.568,0.579,0.585,0.582,0.574,0.572,0.58,0.592,0.598,0.599,0.603,0.619,0.644,0.669,0.684,0.689,0.69,0.696,0.709,0.722,0.724,0.714,0.695,0.676,0.662,0.657,0.662,0.678,0.7,0.718,0.721,0.703,0.675,0.649,0.636,0.63,0.618,0.593,0.568,0.562,0.584,0.627,0.672,0.705,0.722,0.725,0.722,0.716,0.709,0.701,0.693,0.683,0.665,0.635,0.594,0.549,0.517,0.506,0.514,0.534,0.559,0.585,0.613,0.642,0.669,0.688,0.7,0.707,0.711,0.71,0.701,0.684,0.668,0.658,0.656,0.653,0.642,0.623,0.607,0.601,0.606,0.611,0.607,0.599,0.6,0.616,0.645,0.673,0.69,0.697,0.698,0.696,0.686,0.663,0.626,0.584,0.546,0.52,0.502,0.479,0.449,0.417,0.399,0.404,0.43,0.464,0.499,0.535,0.572,0.602,0.617,0.611,0.593,0.574,0.567,0.566,0.563,0.547,0.526,0.514,0.526,0.561,0.603,0.632,0.644,0.646,0.647,0.647,0.641,0.625,0.605,0.596,0.609,0.64,0.674,0.698,0.705,0.694,0.672,0.646,0.627,0.628,0.651,0.683,0.706,0.704,0.681,0.649,0.623,0.61,0.607,0.613,0.625,0.645,0.67,0.694,0.71,0.716,0.711,0.701,0.691,0.687,0.686,0.684,0.675,0.661,0.649,0.642,0.639,0.634,0.624,0.613,0.608,0.611,0.613,0.604,0.585,0.57,0.57,0.588,0.61,0.622,0.62,0.613,0.61,0.613,0.619,0.623,0.628,0.634,0.634,0.621,0.59,0.548,0.508,0.479,0.467,0.471,0.494,0.533,0.583,0.631,0.666,0.683,0.688,0.69,0.692,0.687,0.666,0.63,0.595,0.578,0.586,0.612,0.64,0.66,0.67,0.676,0.684,0.69,0.687,0.67,0.646,0.63,0.63,0.643,0.658,0.67,0.681,0.696,0.713,0.725,0.729,0.731,0.736,0.743,0.742,0.723,0.686,0.641,0.605,0.588,0.586,0.585,0.577,0.564,0.558,0.57,0.6,0.635,0.66,0.668,0.664,0.657,0.655,0.662,0.681,0.71,0.741,0.76,0.756,0.726,0.687,0.656,0.646,0.651,0.658,0.657,0.653,0.654,0.664,0.674,0.675,0.664,0.647,0.635,0.634,0.642,0.655,0.666,0.673,0.675,0.671,0.666,0.667,0.682,0.708,0.733,0.745,0.744,0.741,0.749,0.764,0.771,0.754,0.713,0.659,0.608,0.572,0.55,0.536,0.523,0.509,0.498,0.491,0.485,0.473,0.454,0.437,0.434,0.451,0.486,0.532,0.588,0.649,0.711,0.764,0.799,0.812,0.805,0.782,0.752,0.722,0.693,0.664,0.639,0.627,0.635,0.655,0.678,0.697,0.716,0.731,0.736,0.731,0.725,0.728,0.739,0.743,0.727,0.693,0.653,0.619,0.596,0.578,0.559,0.535,0.51,0.493,0.489,0.493,0.499,0.497,0.488,0.479,0.481,0.499,0.531,0.573,0.624,0.678,0.73,0.773,0.8,0.807,0.797,0.772,0.738,0.701,0.664,0.635,0.622,0.627,0.645,0.662,0.667,0.663,0.658,0.659,0.66,0.657,0.652,0.647,0.642,0.63,0.608,0.576,0.544,0.522,0.515,0.517,0.519,0.512,0.498,0.486,0.483,0.49,0.504,0.517,0.525,0.53,0.537,0.552,0.576,0.609,0.646,0.685,0.72,0.749,0.764,0.763,0.745,0.72,0.699,0.688,0.684,0.681,0.682,0.693,0.715,0.742,0.765,0.778,0.776,0.758,0.729,0.701,0.689,0.694,0.7,0.687,0.653,0.605,0.562,0.535,0.525,0.523,0.516,0.5,0.479,0.464,0.462,0.469,0.474,0.47,0.463,0.462,0.476,0.503,0.537,0.577,0.623,0.676,0.728,0.771,0.795,0.798,0.782,0.756,0.732,0.71,0.686,0.657,0.632,0.625,0.639,0.665,0.694,0.721,0.746,0.762,0.761,0.745,0.728,0.721,0.724,0.721,0.698,0.652,0.595,0.544,0.513,0.505,0.515,0.532,0.547,0.56,0.571,0.58,0.582,0.57,0.548,0.528,0.525,0.543,0.577,0.618,0.661,0.701,0.736,0.76,0.772,0.775,0.775,0.774,0.775,0.773,0.762,0.738,0.705,0.672,0.649,0.635,0.621,0.596,0.564,0.537,0.527,0.536,0.559,0.591,0.63,0.671,0.705,0.72,0.71,0.677,0.631,0.586,0.549,0.52,0.495,0.478,0.473,0.48,0.487,0.482,0.459,0.43,0.412,0.419,0.446,0.477,0.498,0.508,0.513,0.518,0.522,0.521,0.52,0.524,0.538,0.557,0.571,0.573,0.566,0.562,0.572,0.594,0.621,0.641,0.649,0.649,0.643,0.637,0.632,0.632,0.637,0.653,0.677,0.704,0.723,0.727,0.718,0.708,0.702,0.701,0.702,0.701,0.7,0.704,0.717,0.736,0.754,0.761,0.755,0.74,0.719,0.694,0.67,0.653,0.648,0.656,0.67,0.68,0.682,0.678,0.674,0.674,0.68,0.693,0.712,0.728,0.728,0.7,0.644,0.572,0.508,0.474,0.475,0.502,0.537,0.57,0.602,0.633,0.659,0.672,0.67,0.662,0.656,0.658,0.663,0.664,0.654,0.637,0.621,0.613,0.611,0.607,0.594,0.576,0.567,0.582,0.618,0.657,0.684,0.696,0.701,0.703,0.701,0.692,0.675,0.657,0.644,0.633,0.622,0.608,0.596,0.586,0.578,0.566,0.554,0.555,0.579,0.625,0.673,0.701,0.703,0.692,0.681,0.676,0.667,0.644,0.61,0.574,0.555,0.56,0.585,0.611,0.617,0.598,0.564,0.538,0.536,0.559,0.589,0.612,0.62,0.614,0.593,0.561,0.523,0.493,0.484,0.5,0.53,0.558,0.576,0.587,0.595,0.6,0.602,0.604,0.609,0.62,0.635,0.647,0.651,0.641,0.618,0.586,0.554,0.53,0.523,0.538,0.577,0.626,0.667,0.684,0.676,0.653,0.63,0.616,0.613,0.62,0.633,0.649,0.661,0.667,0.664,0.649,0.623,0.592,0.568,0.56,0.566,0.576,0.578,0.574,0.574,0.588,0.613,0.639,0.657,0.664,0.668,0.67,0.669,0.659,0.644,0.63,0.621,0.613,0.596,0.562,0.515,0.472,0.448,0.45,0.471,0.499,0.529,0.565,0.606,0.65,0.687,0.707,0.708,0.699,0.689,0.686,0.685,0.683,0.678,0.675,0.679,0.688,0.691,0.681,0.658,0.63,0.603,0.581,0.566,0.562,0.572,0.598,0.631,0.654,0.656,0.639,0.616,0.6,0.595,0.597,0.603,0.615,0.634,0.655,0.668,0.663,0.636,0.591,0.542,0.506,0.49,0.494,0.517,0.556,0.608,0.661,0.698,0.712,0.705,0.692,0.684,0.687,0.695,0.7,0.694,0.683,0.669,0.652,0.625,0.585,0.543,0.517,0.515,0.534,0.562,0.588,0.612,0.635,0.654,0.661,0.655,0.64,0.629,0.628,0.64,0.657,0.671,0.679,0.679,0.672,0.656,0.633,0.609,0.592,0.586,0.591,0.603,0.622,0.654,0.695,0.734,0.754,0.744,0.71,0.668,0.632,0.607,0.588,0.566,0.541,0.518,0.502,0.494,0.49,0.483,0.471,0.461,0.462,0.479,0.507,0.541,0.578,0.618,0.661,0.698,0.723,0.728,0.715,0.687,0.656,0.63,0.609,0.589,0.573,0.568,0.581,0.605,0.632,0.655,0.675,0.689,0.692,0.683,0.678,0.693,0.727,0.758,0.76,0.725,0.668,0.616,0.585,0.575,0.572,0.562,0.543,0.524,0.512,0.507,0.5,0.486,0.467,0.457,0.46,0.476,0.497,0.524,0.563,0.616,0.677,0.732,0.77,0.782,0.77,0.742,0.709,0.677,0.646,0.617,0.597,0.597,0.616,0.637,0.646,0.639,0.629,0.623,0.617,0.603,0.583,0.568,0.566,0.569,0.561,0.533,0.495,0.467,0.463,0.478,0.492,0.491,0.477,0.466,0.469,0.486,0.505,0.515,0.512,0.502,0.496,0.495,0.501,0.517,0.552,0.608,0.675,0.735,0.771,0.776,0.756,0.726,0.699,0.68,0.663,0.644,0.628,0.628,0.645,0.669,0.692,0.709,0.726,0.74,0.746,0.743,0.73,0.713,0.692,0.67,0.649,0.633,0.622,0.613,0.603,0.585,0.559,0.525,0.491,0.466,0.453,0.448,0.443,0.435,0.431,0.438,0.46,0.489,0.521,0.554,0.595,0.645,0.697,0.736,0.749,0.734,0.7,0.664,0.636,0.618,0.602,0.589,0.585,0.598,0.624,0.649,0.665,0.676,0.683,0.683,0.673,0.658,0.651,0.656,0.664,0.658,0.634,0.597,0.564,0.546,0.546,0.559,0.572,0.575,0.567,0.553,0.538,0.523,0.505,0.488,0.478,0.485,0.508,0.539,0.567,0.59,0.611,0.631,0.649,0.663,0.675,0.689,0.704,0.714,0.712,0.694,0.663,0.627,0.6,0.587,0.584,0.578,0.562,0.541,0.526,0.521,0.519,0.517,0.517,0.529,0.554,0.582,0.6,0.604,0.593,0.576,0.556,0.533,0.502,0.464,0.428,0.405,0.401,0.405,0.404,0.395,0.388,0.394,0.417,0.447,0.477,0.505,0.537,0.569,0.589,0.587,0.569,0.549,0.538,0.538,0.538,0.531,0.519,0.512,0.516,0.528,0.536,0.533,0.521,0.511,0.511,0.52,0.526,0.524,0.515,0.509,0.512,0.527,0.55,0.573,0.587,0.59,0.584,0.573,0.559,0.54,0.518,0.498,0.484,0.477,0.477,0.483,0.49,0.495,0.491,0.477,0.453,0.43,0.418,0.423,0.441,0.462,0.477,0.479,0.469,0.452,0.434,0.42,0.413,0.413,0.419,0.425,0.424,0.41,0.387,0.367,0.362,0.372,0.391,0.411,0.431,0.457,0.486,0.513,0.529,0.534,0.532,0.531,0.535,0.545,0.556,0.562,0.563,0.562,0.559,0.557,0.553,0.545,0.534,0.526,0.525,0.534,0.552,0.569,0.577,0.571,0.555,0.538,0.524,0.513,0.506,0.507,0.52,0.541,0.554,0.547,0.521,0.492,0.479,0.486,0.507,0.529,0.546,0.559,0.569,0.577,0.579,0.573,0.562,0.55,0.536,0.521,0.501,0.482,0.468,0.468,0.478,0.492,0.501,0.502,0.501,0.5,0.501,0.505,0.515,0.529,0.539,0.538,0.521,0.497,0.476,0.467,0.469,0.473,0.472,0.464,0.458,0.459,0.471,0.484,0.486,0.472,0.448,0.426,0.413,0.408,0.408,0.411,0.423,0.448,0.488,0.534,0.574,0.594,0.592,0.572,0.545,0.52,0.501,0.489,0.483,0.483,0.484,0.479,0.463,0.441,0.424,0.42,0.424,0.429,0.428,0.428,0.439,0.465,0.498,0.524,0.534,0.528,0.515,0.5,0.486,0.479,0.481,0.491,0.502,0.505,0.498,0.488,0.487,0.5,0.516,0.522,0.514,0.503,0.5,0.509,0.521,0.525,0.519,0.514,0.523,0.546,0.573,0.588,0.588,0.581,0.573,0.569,0.561,0.547,0.528,0.514,0.506,0.499,0.485,0.465,0.449,0.449,0.464,0.486,0.502,0.508,0.513,0.522,0.532,0.533,0.519,0.498,0.485,0.483,0.485,0.48,0.466,0.454,0.457,0.478,0.508,0.533,0.547,0.556,0.57,0.589,0.608,0.62,0.623,0.617,0.607,0.589,0.563,0.529,0.499,0.482,0.48,0.483,0.478,0.464,0.454,0.462,0.487,0.513,0.527,0.528,0.529,0.539,0.555,0.56,0.545,0.521,0.506,0.517,0.546,0.574,0.582,0.571,0.555,0.544,0.534,0.521,0.506,0.498,0.503,0.517,0.529,0.531,0.529,0.534,0.551,0.574,0.594,0.606,0.609,0.608,0.606,0.605,0.604,0.601,0.592,0.58,0.566,0.552,0.54,0.529,0.52,0.511,0.498,0.476,0.448,0.428,0.431,0.461,0.502,0.534,0.547,0.543,0.532,0.517,0.498,0.477,0.458,0.445,0.438,0.433,0.425,0.412,0.398,0.39,0.385,0.378,0.364,0.355,0.365,0.405,0.461,0.512,0.541,0.551,0.55,0.546,0.541,0.533,0.525,0.519,0.515,0.514,0.511,0.504,0.497,0.493,0.496,0.507,0.525,0.546,0.565,0.574,0.568,0.547,0.521,0.502,0.493,0.492,0.492,0.49,0.488,0.492,0.504,0.523,0.545,0.564,0.574,0.571,0.559,0.545,0.537,0.536,0.535,0.529,0.52,0.517,0.528,0.546,0.558,0.555,0.539,0.527,0.534,0.562,0.604,0.641,0.662,0.662,0.645,0.62,0.599,0.589,0.592,0.602,0.605,0.59,0.558,0.521,0.493,0.484,0.489,0.495,0.494,0.486,0.482,0.492,0.512,0.531,0.534,0.524,0.511,0.508,0.513,0.519,0.517,0.508,0.502,0.505,0.52,0.541,0.559,0.572,0.576,0.57,0.551,0.522,0.486,0.455,0.438,0.437,0.447,0.457,0.468,0.483,0.502,0.518,0.522,0.513,0.502,0.502,0.519,0.544,0.567,0.582,0.592,0.599,0.6,0.586,0.555,0.517,0.489,0.481,0.487,0.492,0.486,0.472,0.466,0.478,0.504,0.533,0.558,0.579,0.596,0.605,0.599,0.581,0.558,0.542,0.542,0.556,0.578,0.594,0.597,0.589,0.575,0.556,0.535,0.515,0.506,0.516,0.543,0.574,0.599,0.611,0.616,0.614,0.603,0.578,0.544,0.509,0.488,0.483,0.485,0.48,0.46,0.436,0.424,0.433,0.457,0.486,0.507,0.521,0.533,0.544,0.553,0.559,0.563,0.571,0.58,0.586,0.576,0.55,0.518,0.495,0.492,0.504,0.515,0.515,0.505,0.497,0.496,0.499,0.499,0.495,0.495,0.507,0.533,0.565,0.595,0.622,0.649,0.675,0.695,0.705,0.704,0.697,0.693,0.696,0.699,0.697,0.69,0.683,0.682,0.688,0.698,0.711,0.725,0.74,0.747,0.741,0.719,0.689,0.66,0.643,0.641,0.647,0.656,0.661,0.662,0.663,0.67,0.679,0.684,0.681,0.675,0.671,0.672,0.674,0.675,0.674,0.674,0.671,0.666,0.663,0.663,0.67,0.678,0.687,0.695,0.701,0.704,0.703,0.699,0.698,0.7,0.704,0.71,0.717,0.721,0.716,0.695,0.655,0.606,0.564,0.544,0.55,0.57,0.593,0.614,0.635,0.659,0.684,0.707,0.721,0.728,0.727,0.726,0.727,0.732,0.739,0.745,0.747,0.742,0.731,0.725,0.73,0.748,0.77,0.782,0.775,0.752,0.723,0.701,0.693,0.698,0.707,0.713,0.715,0.716,0.718,0.719,0.712,0.697,0.679,0.662,0.645,0.621,0.587,0.547,0.513,0.5,0.513,0.543,0.579,0.613,0.644,0.672,0.693,0.701,0.696,0.684,0.673,0.671,0.674,0.676,0.668,0.651,0.634,0.629,0.64,0.657,0.665,0.661,0.654,0.655,0.662,0.664,0.651,0.631,0.623,0.642,0.683,0.724,0.746,0.742,0.721,0.699,0.684,0.682,0.693,0.712,0.73,0.738,0.726,0.696,0.658,0.623,0.602,0.597,0.603,0.619,0.641,0.666,0.688,0.702,0.707,0.708,0.706,0.704,0.7,0.695,0.685,0.67,0.655,0.644,0.637,0.631,0.62,0.605,0.595,0.598,0.613,0.629,0.633,0.624,0.614,0.618,0.638,0.669,0.698,0.721,0.736,0.741,0.734,0.718,0.7,0.686,0.674,0.656,0.626,0.583,0.54,0.51,0.505,0.521,0.547,0.571,0.593,0.611,0.627,0.638,0.649,0.67,0.702,0.733,0.746,0.736,0.716,0.706,0.717,0.742,0.767,0.783,0.786,0.781,0.774,0.767,0.761,0.75,0.725,0.688,0.651,0.633,0.642,0.672,0.708,0.734,0.744,0.741,0.733,0.732,0.745,0.767,0.786,0.785,0.759,0.718,0.679,0.659,0.66,0.674,0.68,0.668,0.646,0.632,0.642,0.671,0.702,0.718,0.716,0.707,0.704,0.71,0.725,0.743,0.759,0.763,0.749,0.713,0.664,0.619,0.592,0.587,0.598,0.617,0.637,0.657,0.677,0.694,0.704,0.708,0.704,0.694,0.682,0.667,0.653,0.641,0.631,0.623,0.617,0.615,0.622,0.643,0.676,0.709,0.728,0.728,0.721,0.726,0.754,0.794,0.826,0.831,0.804,0.758,0.713,0.681,0.665,0.656,0.648,0.64,0.634,0.628,0.617,0.601,0.582,0.57,0.569,0.578,0.597,0.626,0.667,0.718,0.769,0.812,0.839,0.849,0.843,0.826,0.807,0.789,0.77,0.747,0.726,0.718,0.726,0.742,0.758,0.773,0.787,0.797,0.795,0.781,0.772,0.779,0.793,0.793,0.76,0.699,0.63,0.576,0.547,0.542,0.546,0.544,0.53,0.508,0.487,0.474,0.471,0.473,0.477,0.482,0.493,0.51,0.536,0.574,0.627,0.691,0.758,0.813,0.847,0.856,0.84,0.807,0.77,0.738,0.714,0.691,0.666,0.647,0.642,0.652,0.669,0.685,0.696,0.697,0.687,0.673,0.668,0.681,0.705,0.721,0.71,0.668,0.603,0.537,0.492,0.477,0.484,0.494,0.491,0.475,0.462,0.464,0.483,0.509,0.527,0.533,0.535,0.542,0.563,0.598,0.642,0.688,0.734,0.777,0.813,0.837,0.838,0.817,0.784,0.755,0.737,0.726,0.714,0.702,0.697,0.705,0.724,0.748,0.767,0.775,0.763,0.733,0.699,0.687,0.708,0.749,0.779,0.773,0.732,0.675,0.627,0.601,0.592,0.588,0.574,0.549,0.523,0.505,0.5,0.5,0.497,0.492,0.493,0.506,0.533,0.569,0.614,0.67,0.736,0.8,0.85,0.876,0.878,0.861,0.836,0.813,0.796,0.779,0.758,0.735,0.723,0.725,0.738,0.754,0.771,0.789,0.799,0.79,0.766,0.744,0.742,0.756,0.766,0.748,0.702,0.642,0.595,0.575,0.583,0.604,0.62,0.623,0.618,0.618,0.629,0.645,0.653,0.646,0.631,0.619,0.62,0.634,0.658,0.689,0.727,0.766,0.799,0.82,0.831,0.834,0.833,0.832,0.826,0.807,0.771,0.723,0.682,0.662,0.66,0.661,0.651,0.634,0.624,0.63,0.648,0.669,0.69,0.713,0.735,0.747,0.741,0.715,0.679,0.642,0.612,0.586,0.561,0.537,0.522,0.522,0.537,0.553,0.554,0.539,0.52,0.511,0.518,0.53,0.536,0.532,0.527,0.535,0.555,0.575,0.581,0.566,0.541,0.52,0.512,0.52,0.544,0.583,0.626,0.651,0.636,0.58,0.51,0.46,0.456,0.495,0.554,0.608,0.643,0.661,0.668,0.672,0.672,0.669,0.66,0.646,0.628,0.609,0.591,0.575,0.557,0.536,0.509,0.478,0.445,0.415,0.387,0.36,0.334,0.306,0.274,0.24,0.205,0.171,0.14,0.11,0.082,0.058,0.04,0.032]