[0.123,0.129,0.139,0.147,0.15,0.147,0.14,0.132,0.122,0.11,0.097,0.083,0.07,0.058,0.049,0.042,0.037,0.034,0.031,0.03,0.029,0.028,0.026,0.024,0.022,0.02,0.019,0.018,0.017,0.015,0.014,0.014,0.013,0.012,0.011,0.01,0.009,0.01,0.01,0.01,0.009,0.007,0.005,0.004,0.004,0.004,0.004,0.003,0.003,0.004,0.005,0.007,0.008,0.007,0.006,0.004,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.003,0.004,0.004,0.004,0.004,0.004,0.003,0.004,0.004,0.005,0.006,0.007,0.007,0.007,0.006,0.006,0.006,0.006,0.006,0.007,0.007,0.007,0.006,0.005,0.004,0.003,0.004,0.006,0.009,0.015,0.02,0.024,0.025,0.023,0.021,0.019,0.018,0.018,0.018,0.017,0.017,0.018,0.019,0.021,0.022,0.024,0.025,0.026,0.028,0.03,0.033,0.037,0.041,0.045,0.05,0.055,0.06,0.066,0.074,0.085,0.105,0.136,0.173,0.207,0.228,0.229,0.214,0.19,0.163,0.138,0.118,0.103,0.093,0.087,0.084,0.08,0.077,0.074,0.071,0.068,0.064,0.06,0.056,0.052,0.048,0.046,0.043,0.04,0.037,0.034,0.031,0.03,0.03,0.03,0.031,0.031,0.031,0.03,0.028,0.027,0.027,0.028,0.03,0.031,0.03,0.028,0.026,0.024,0.023,0.024,0.026,0.028,0.03,0.031,0.032,0.032,0.032,0.031,0.03,0.03,0.031,0.034,0.043,0.06,0.087,0.12,0.147,0.162,0.161,0.146,0.124,0.103,0.085,0.072,0.064,0.06,0.057,0.054,0.051,0.048,0.045,0.043,0.041,0.039,0.036,0.033,0.031,0.031,0.031,0.031,0.032,0.032,0.032,0.031,0.03,0.029,0.028,0.027,0.026,0.026,0.025,0.026,0.026,0.026,0.026,0.026,0.026,0.028,0.03,0.03,0.031,0.03,0.031,0.032,0.035,0.04,0.046,0.054,0.061,0.067,0.072,0.077,0.081,0.087,0.096,0.111,0.134,0.161,0.186,0.2,0.2,0.19,0.175,0.159,0.145,0.133,0.123,0.116,0.109,0.102,0.095,0.088,0.083,0.08,0.079,0.078,0.077,0.075,0.073,0.071,0.069,0.067,0.066,0.064,0.064,0.064,0.064,0.061,0.057,0.052,0.048,0.044,0.042,0.04,0.04,0.042,0.043,0.043,0.042,0.039,0.036,0.035,0.034,0.035,0.036,0.036,0.036,0.034,0.033,0.032,0.032,0.033,0.035,0.035,0.036,0.038,0.041,0.044,0.046,0.046,0.043,0.04,0.038,0.036,0.036,0.036,0.037,0.038,0.038,0.039,0.038,0.038,0.037,0.036,0.034,0.033,0.03,0.028,0.027,0.026,0.026,0.026,0.026,0.025,0.024,0.023,0.023,0.024,0.032,0.049,0.075,0.107,0.136,0.154,0.158,0.152,0.14,0.127,0.116,0.109,0.106,0.106,0.108,0.11,0.112,0.116,0.119,0.12,0.118,0.113,0.106,0.099,0.093,0.089,0.086,0.082,0.079,0.075,0.074,0.077,0.092,0.123,0.167,0.214,0.248,0.263,0.258,0.239,0.217,0.2,0.19,0.189,0.191,0.193,0.19,0.183,0.173,0.164,0.157,0.152,0.146,0.14,0.134,0.129,0.128,0.13,0.132,0.132,0.13,0.128,0.126,0.124,0.122,0.119,0.114,0.108,0.103,0.1,0.097,0.095,0.09,0.085,0.079,0.076,0.074,0.074,0.073,0.073,0.071,0.068,0.065,0.062,0.059,0.056,0.054,0.051,0.05,0.05,0.051,0.053,0.055,0.057,0.06,0.064,0.07,0.078,0.086,0.091,0.092,0.089,0.086,0.082,0.079,0.078,0.076,0.075,0.072,0.069,0.067,0.064,0.061,0.058,0.054,0.052,0.051,0.051,0.051,0.052,0.053,0.054,0.055,0.056,0.059,0.068,0.091,0.125,0.165,0.196,0.211,0.209,0.196,0.179,0.164,0.153,0.146,0.144,0.143,0.145,0.146,0.149,0.153,0.157,0.16,0.161,0.159,0.155,0.149,0.14,0.13,0.121,0.116,0.115,0.118,0.122,0.127,0.133,0.14,0.15,0.163,0.178,0.197,0.218,0.234,0.238,0.225,0.202,0.179,0.165,0.163,0.168,0.175,0.179,0.176,0.166,0.153,0.14,0.129,0.12,0.115,0.113,0.115,0.119,0.124,0.128,0.131,0.133,0.134,0.132,0.126,0.115,0.103,0.093,0.093,0.102,0.112,0.117,0.112,0.1,0.088,0.084,0.089,0.096,0.101,0.099,0.094,0.09,0.091,0.096,0.102,0.108,0.11,0.11,0.109,0.108,0.109,0.112,0.114,0.115,0.118,0.124,0.134,0.144,0.152,0.155,0.151,0.142,0.131,0.122,0.116,0.113,0.111,0.109,0.104,0.098,0.093,0.089,0.088,0.088,0.09,0.091,0.09,0.084,0.077,0.069,0.064,0.061,0.059,0.057,0.056,0.057,0.059,0.061,0.063,0.064,0.065,0.065,0.064,0.061,0.057,0.053,0.052,0.052,0.055,0.057,0.059,0.059,0.059,0.06,0.061,0.063,0.066,0.069,0.073,0.076,0.077,0.078,0.078,0.078,0.079,0.083,0.094,0.113,0.137,0.157,0.167,0.164,0.151,0.135,0.12,0.108,0.098,0.092,0.089,0.089,0.091,0.093,0.094,0.093,0.088,0.083,0.078,0.075,0.074,0.073,0.071,0.067,0.062,0.058,0.055,0.055,0.054,0.054,0.054,0.055,0.058,0.059,0.059,0.057,0.054,0.053,0.052,0.053,0.054,0.054,0.054,0.053,0.052,0.05,0.049,0.047,0.047,0.048,0.05,0.053,0.058,0.064,0.071,0.077,0.08,0.082,0.082,0.084,0.092,0.11,0.138,0.171,0.198,0.211,0.211,0.202,0.189,0.176,0.167,0.16,0.155,0.152,0.149,0.145,0.14,0.134,0.128,0.122,0.116,0.112,0.11,0.108,0.107,0.105,0.102,0.101,0.1,0.101,0.103,0.105,0.107,0.107,0.105,0.101,0.095,0.091,0.086,0.082,0.077,0.071,0.067,0.065,0.066,0.069,0.071,0.069,0.065,0.061,0.06,0.062,0.068,0.074,0.078,0.081,0.083,0.084,0.084,0.083,0.082,0.082,0.084,0.089,0.099,0.113,0.129,0.143,0.153,0.161,0.171,0.181,0.188,0.187,0.176,0.159,0.142,0.128,0.119,0.115,0.113,0.113,0.112,0.111,0.108,0.104,0.099,0.095,0.09,0.087,0.084,0.083,0.083,0.083,0.083,0.083,0.083,0.082,0.08,0.077,0.074,0.073,0.073,0.074,0.074,0.073,0.07,0.068,0.065,0.063,0.061,0.058,0.056,0.054,0.053,0.052,0.053,0.054,0.054,0.054,0.053,0.053,0.055,0.057,0.06,0.063,0.065,0.066,0.065,0.065,0.064,0.063,0.063,0.064,0.064,0.064,0.063,0.062,0.06,0.059,0.059,0.058,0.058,0.056,0.054,0.052,0.049,0.048,0.047,0.046,0.046,0.046,0.045,0.044,0.044,0.048,0.059,0.083,0.12,0.164,0.204,0.226,0.23,0.22,0.207,0.197,0.191,0.187,0.183,0.177,0.17,0.164,0.16,0.156,0.151,0.143,0.132,0.12,0.111,0.105,0.102,0.101,0.102,0.103,0.103,0.103,0.103,0.103,0.106,0.116,0.133,0.155,0.174,0.188,0.195,0.197,0.195,0.192,0.194,0.202,0.215,0.228,0.236,0.235,0.227,0.216,0.204,0.193,0.183,0.176,0.172,0.169,0.166,0.164,0.161,0.158,0.154,0.148,0.141,0.131,0.122,0.115,0.111,0.111,0.111,0.112,0.112,0.111,0.109,0.107,0.105,0.104,0.103,0.102,0.101,0.1,0.098,0.094,0.089,0.084,0.079,0.075,0.073,0.072,0.071,0.072,0.074,0.077,0.08,0.082,0.084,0.087,0.09,0.093,0.095,0.096,0.098,0.101,0.104,0.105,0.103,0.097,0.09,0.085,0.081,0.08,0.081,0.086,0.093,0.101,0.107,0.109,0.108,0.103,0.098,0.093,0.088,0.085,0.084,0.084,0.089,0.106,0.139,0.186,0.234,0.267,0.274,0.261,0.238,0.217,0.202,0.194,0.19,0.187,0.181,0.173,0.164,0.157,0.157,0.161,0.166,0.168,0.167,0.163,0.158,0.154,0.15,0.146,0.14,0.133,0.126,0.122,0.123,0.129,0.14,0.155,0.169,0.182,0.194,0.202,0.206,0.204,0.195,0.18,0.164,0.149,0.138,0.13,0.128,0.134,0.145,0.159,0.168,0.168,0.16,0.147,0.131,0.115,0.1,0.088,0.08,0.078,0.079,0.084,0.089,0.092,0.094,0.092,0.087,0.08,0.072,0.065,0.059,0.055,0.052,0.052,0.053,0.056,0.06,0.064,0.067,0.066,0.064,0.062,0.06,0.059,0.058,0.059,0.062,0.067,0.072,0.076,0.078,0.078,0.079,0.081,0.085,0.09,0.095,0.099,0.101,0.101,0.101,0.102,0.104,0.105,0.104,0.1,0.094,0.086,0.079,0.074,0.072,0.072,0.074,0.075,0.076,0.076,0.077,0.078,0.079,0.079,0.078,0.075,0.074,0.074,0.08,0.09,0.106,0.123,0.135,0.138,0.131,0.118,0.104,0.092,0.084,0.08,0.079,0.08,0.081,0.083,0.085,0.086,0.086,0.084,0.082,0.079,0.078,0.077,0.077,0.077,0.077,0.079,0.08,0.082,0.083,0.089,0.105,0.133,0.166,0.195,0.211,0.212,0.203,0.189,0.175,0.161,0.149,0.139,0.131,0.126,0.123,0.121,0.118,0.113,0.105,0.095,0.085,0.078,0.073,0.07,0.069,0.069,0.069,0.068,0.068,0.068,0.069,0.07,0.07,0.069,0.067,0.063,0.059,0.056,0.054,0.055,0.058,0.063,0.067,0.068,0.067,0.065,0.062,0.059,0.058,0.058,0.059,0.061,0.065,0.071,0.077,0.083,0.089,0.094,0.097,0.099,0.1,0.103,0.113,0.135,0.168,0.203,0.226,0.231,0.218,0.198,0.179,0.166,0.158,0.152,0.147,0.142,0.139,0.137,0.134,0.131,0.126,0.121,0.115,0.11,0.105,0.102,0.101,0.102,0.102,0.102,0.1,0.098,0.096,0.095,0.097,0.101,0.104,0.107,0.107,0.106,0.103,0.1,0.097,0.094,0.093,0.093,0.094,0.095,0.098,0.104,0.113,0.124,0.132,0.134,0.131,0.126,0.12,0.117,0.115,0.112,0.109,0.105,0.1,0.096,0.096,0.105,0.122,0.145,0.164,0.174,0.175,0.174,0.179,0.19,0.202,0.208,0.204,0.192,0.176,0.16,0.146,0.134,0.123,0.114,0.107,0.103,0.1,0.097,0.095,0.092,0.088,0.085,0.082,0.079,0.076,0.071,0.066,0.063,0.061,0.059,0.058,0.057,0.057,0.056,0.057,0.058,0.06,0.061,0.061,0.059,0.056,0.052,0.048,0.045,0.043,0.043,0.045,0.048,0.051,0.053,0.055,0.056,0.057,0.058,0.06,0.061,0.064,0.07,0.077,0.086,0.093,0.093,0.087,0.08,0.075,0.075,0.079,0.084,0.086,0.084,0.08,0.075,0.071,0.069,0.069,0.068,0.067,0.065,0.061,0.058,0.056,0.057,0.059,0.062,0.063,0.063,0.062,0.062,0.069,0.088,0.118,0.152,0.181,0.196,0.2,0.196,0.191,0.186,0.182,0.175,0.167,0.159,0.152,0.148,0.149,0.157,0.167,0.174,0.173,0.164,0.152,0.141,0.135,0.131,0.127,0.12,0.113,0.105,0.101,0.101,0.11,0.127,0.15,0.173,0.191,0.199,0.2,0.197,0.195,0.197,0.203,0.212,0.223,0.234,0.24,0.24,0.231,0.217,0.199,0.183,0.17,0.162,0.157,0.155,0.155,0.153,0.149,0.143,0.137,0.13,0.125,0.121,0.119,0.118,0.117,0.116,0.114,0.113,0.113,0.112,0.111,0.11,0.107,0.104,0.101,0.098,0.094,0.091,0.088,0.085,0.083,0.08,0.075,0.069,0.063,0.058,0.054,0.052,0.051,0.05,0.05,0.052,0.054,0.055,0.056,0.056,0.055,0.053,0.051,0.048,0.045,0.043,0.042,0.041,0.04,0.038,0.037,0.035,0.034,0.034,0.034,0.034,0.035,0.035,0.035,0.034,0.033,0.032,0.032,0.031,0.031,0.03,0.03,0.029,0.029,0.028,0.029,0.029,0.03,0.031,0.032,0.033,0.033,0.034,0.034,0.034,0.034,0.035,0.037,0.04,0.044,0.048,0.053,0.058,0.063,0.068,0.074,0.08,0.086,0.092,0.099,0.107,0.117,0.131,0.153,0.182,0.216,0.253,0.301,0.374,0.479,0.602,0.713,0.788,0.824,0.832,0.822,0.791,0.734,0.651,0.567,0.518,0.528,0.589,0.67,0.738,0.777,0.78,0.748,0.681,0.595,0.52,0.492,0.527,0.602,0.669,0.688,0.646,0.569,0.503,0.488,0.534,0.622,0.711,0.772,0.799,0.804,0.799,0.795,0.791,0.791,0.793,0.8,0.808,0.816,0.821,0.821,0.814,0.795,0.756,0.686,0.594,0.505,0.458,0.474,0.541,0.613,0.646,0.618,0.545,0.471,0.439,0.469,0.547,0.636,0.706,0.744,0.754,0.748,0.726,0.686,0.624,0.555,0.503,0.499,0.547,0.629,0.71,0.766,0.792,0.798,0.796,0.793,0.792,0.793,0.795,0.794,0.782,0.751,0.694,0.614,0.536,0.494,0.509,0.57,0.642,0.678,0.657,0.591,0.521,0.493,0.529,0.614,0.713,0.791,0.836,0.852,0.849,0.823,0.768,0.683,0.581,0.499,0.473,0.515,0.597,0.669,0.685,0.633,0.537,0.436,0.366,0.34,0.361,0.419,0.502,0.59,0.662,0.704,0.72,0.718,0.706,0.68,0.634,0.571,0.509,0.475,0.488,0.542,0.614,0.675,0.709,0.709,0.678,0.616,0.539,0.472,0.447,0.474,0.536,0.591,0.604,0.564,0.494,0.435,0.421,0.462,0.538,0.615,0.668,0.695,0.706,0.71,0.713,0.714,0.714,0.714,0.713,0.713,0.71,0.704,0.695,0.682,0.661,0.626,0.572,0.505,0.444,0.416,0.434,0.487,0.542,0.567,0.549,0.503,0.457,0.445,0.479,0.545,0.615,0.668,0.697,0.709,0.711,0.699,0.665,0.605,0.534,0.483,0.478,0.525,0.6,0.673,0.722,0.746,0.755,0.76,0.764,0.768,0.77,0.769,0.764,0.748,0.714,0.655,0.578,0.504,0.466,0.482,0.539,0.602,0.629,0.602,0.536,0.468,0.442,0.476,0.557,0.649,0.719,0.757,0.767,0.76,0.736,0.691,0.62,0.537,0.467,0.441,0.47,0.535,0.594,0.61,0.573,0.499,0.422,0.37,0.357,0.39,0.464,0.566,0.671,0.753,0.802,0.82,0.819,0.805,0.77,0.706,0.618,0.535,0.493,0.514,0.587,0.677,0.749,0.786,0.784,0.743,0.666,0.571,0.493,0.471,0.514,0.596,0.666,0.682,0.634,0.55,0.479,0.465,0.517,0.61,0.703,0.767,0.796,0.802,0.798,0.794,0.792,0.794,0.797,0.802,0.807,0.811,0.813,0.81,0.803,0.784,0.745,0.68,0.596,0.518,0.481,0.501,0.562,0.624,0.646,0.614,0.546,0.482,0.461,0.497,0.574,0.657,0.718,0.75,0.757,0.749,0.723,0.675,0.604,0.527,0.476,0.479,0.538,0.629,0.714,0.77,0.795,0.798,0.793,0.787,0.786,0.789,0.793,0.794,0.781,0.745,0.677,0.587,0.503,0.465,0.494,0.572,0.654,0.69,0.663,0.594,0.525,0.501,0.539,0.626,0.723,0.798,0.838,0.85,0.841,0.812,0.757,0.674,0.581,0.51,0.493,0.539,0.621,0.687,0.699,0.647,0.556,0.462,0.395,0.37,0.396,0.468,0.566,0.657,0.718,0.743,0.748,0.745,0.737,0.712,0.662,0.593,0.53,0.506,0.536,0.602,0.669,0.71,0.72,0.704,0.666,0.606,0.536,0.481,0.469,0.502,0.557,0.596,0.592,0.545,0.484,0.448,0.467,0.54,0.635,0.711,0.751,0.76,0.759,0.757,0.758,0.759,0.757,0.754,0.75,0.745,0.737,0.727,0.716,0.705,0.688,0.657,0.606,0.542,0.49,0.476,0.51,0.569,0.615,0.617,0.572,0.505,0.454,0.452,0.506,0.588,0.661,0.702,0.712,0.708,0.7,0.682,0.646,0.588,0.526,0.489,0.502,0.559,0.628,0.677,0.695,0.693,0.688,0.687,0.687,0.687,0.685,0.681,0.676,0.662,0.633,0.582,0.516,0.459,0.44,0.474,0.543,0.606,0.625,0.587,0.51,0.428,0.379,0.383,0.442,0.528,0.609,0.666,0.694,0.699,0.681,0.64,0.575,0.499,0.44,0.429,0.475,0.552,0.614,0.625,0.578,0.499,0.419,0.365,0.349,0.38,0.456,0.565,0.676,0.763,0.81,0.825,0.821,0.803,0.767,0.705,0.622,0.545,0.507,0.528,0.597,0.681,0.746,0.779,0.775,0.735,0.664,0.577,0.509,0.492,0.536,0.615,0.679,0.689,0.637,0.556,0.492,0.484,0.54,0.631,0.72,0.778,0.803,0.807,0.802,0.797,0.794,0.792,0.793,0.798,0.806,0.814,0.82,0.821,0.815,0.794,0.749,0.673,0.577,0.493,0.456,0.482,0.553,0.621,0.646,0.609,0.535,0.466,0.445,0.484,0.564,0.649,0.712,0.745,0.754,0.748,0.727,0.684,0.62,0.548,0.5,0.502,0.556,0.639,0.716,0.768,0.79,0.796,0.795,0.794,0.795,0.797,0.796,0.791,0.775,0.74,0.679,0.598,0.524,0.491,0.517,0.587,0.656,0.681,0.647,0.574,0.507,0.49,0.537,0.63,0.729,0.804,0.846,0.86,0.853,0.822,0.759,0.665,0.561,0.485,0.472,0.526,0.613,0.68,0.685,0.622,0.52,0.419,0.356,0.34,0.369,0.434,0.52,0.607,0.673,0.71,0.721,0.717,0.703,0.674,0.623,0.557,0.497,0.471,0.494,0.556,0.629,0.686,0.713,0.706,0.669,0.603,0.527,0.465,0.449,0.483,0.547,0.598,0.603,0.556,0.484,0.43,0.427,0.477,0.556,0.628,0.676,0.7,0.711,0.717,0.72,0.72,0.718,0.717,0.716,0.714,0.711,0.705,0.696,0.683,0.662,0.626,0.569,0.501,0.442,0.419,0.442,0.496,0.549,0.568,0.545,0.496,0.452,0.446,0.487,0.558,0.63,0.682,0.709,0.718,0.716,0.699,0.659,0.595,0.525,0.48,0.484,0.539,0.617,0.687,0.73,0.75,0.757,0.759,0.763,0.766,0.769,0.769,0.763,0.745,0.706,0.642,0.562,0.491,0.461,0.486,0.549,0.61,0.63,0.597,0.528,0.465,0.447,0.489,0.572,0.661,0.726,0.76,0.768,0.759,0.733,0.684,0.61,0.525,0.458,0.439,0.477,0.547,0.604,0.613,0.566,0.488,0.411,0.364,0.36,0.402,0.483,0.587,0.687,0.762,0.802,0.814,0.809,0.792,0.754,0.688,0.602,0.527,0.498,0.53,0.609,0.696,0.76,0.789,0.78,0.732,0.649,0.554,0.483,0.472,0.527,0.615,0.68,0.684,0.623,0.533,0.466,0.464,0.527,0.625,0.716,0.776,0.803,0.808,0.804,0.797,0.793,0.792,0.794,0.8,0.806,0.812,0.815,0.814,0.807,0.785,0.74,0.668,0.579,0.504,0.476,0.506,0.573,0.634,0.65,0.609,0.537,0.475,0.462,0.507,0.588,0.67,0.727,0.755,0.761,0.753,0.726,0.675,0.598,0.517,0.468,0.479,0.546,0.64,0.723,0.774,0.796,0.799,0.796,0.792,0.79,0.791,0.793,0.79,0.774,0.734,0.662,0.571,0.492,0.464,0.505,0.589,0.666,0.691,0.655,0.583,0.521,0.508,0.556,0.645,0.738,0.805,0.84,0.849,0.839,0.809,0.75,0.663,0.568,0.501,0.494,0.549,0.634,0.696,0.697,0.637,0.542,0.449,0.387,0.37,0.404,0.482,0.581,0.668,0.723,0.743,0.745,0.741,0.732,0.704,0.65,0.58,0.521,0.506,0.543,0.611,0.675,0.711,0.718,0.699,0.657,0.594,0.525,0.476,0.472,0.511,0.566,0.6,0.589,0.538,0.478,0.449,0.478,0.556,0.649,0.72,0.753,0.76,0.759,0.758,0.759,0.758,0.756,0.753,0.749,0.743,0.735,0.726,0.716,0.703,0.683,0.649,0.594,0.532,0.485,0.481,0.521,0.581,0.621,0.615,0.563,0.494,0.448,0.456,0.518,0.604,0.674,0.708,0.714,0.708,0.7,0.681,0.641,0.579,0.517,0.485,0.505,0.567,0.636,0.681,0.697,0.695,0.691,0.691,0.692,0.69,0.688,0.684,0.677,0.662,0.628,0.572,0.504,0.448,0.437,0.479,0.551,0.61,0.621,0.575,0.494,0.416,0.375,0.389,0.454,0.54,0.617,0.668,0.691,0.693,0.674,0.63,0.563,0.487,0.433,0.431,0.485,0.564,0.62,0.619,0.559,0.469,0.389,0.351]