Hard,2,606,477,597,476,30,1265,282,1243,158,986,202,850,219,848,220,924,476,1206,477,1269,282,856,220,744,218,856,220,984,203,1244,153,858,220,858,220,864,220,744,218,744,218,1242,158,792,222,918,475,856,218,923,473,1241,167,849,217,981,473,852,220,1241,288,1266,282,856,218,7,1497,86,1498,83,1976,343,1816,475,1799,297,1592,477,1496,3,17,2520,3,2513,475,2104,472,2520,3,2568,474,2095,482,2409,477,2479,477,2346,480,2099,482,2087,482,2182,473,2545,3,2105,473,2524,476,2162,473,2069,481,37,3091,478,3130,183,3046,473,3288,473,2694,81,3129,177,2694,82,3321,344,3322,344,2696,60,3288,474,3045,477,3037,478,2696,110,3320,344,3131,175,3130,184,3320,344,2998,480,3188,476,3130,173,3320,343,3320,344,3129,173,3320,339,3130,181,3323,344,3172,474,3321,344,2721,109,3166,474,2998,477,3129,184,3130,183,3131,165,3321,344,3056,475,53,3992,253,3992,355,3992,196,3544,474,3926,474,3544,479,3714,155,3958,475,3581,477,3463,199,3992,261,3914,475,3946,472,3918,475,3992,463,3483,185,3799,477,3942,472,3993,261,3544,472,3931,475,3617,479,3594,475,3817,479,3822,479,3992,253,3575,474,3489,185,3992,213,3942,481,3791,477,3556,474,3463,214,3503,474,3483,185,3992,246,3993,239,3652,473,3792,477,3818,479,3587,475,3630,474,3835,479,3463,207,3437,98,3588,472,3528,185,3444,89,3365,375,3634,479,3919,478,3580,475,3957,473,28,4664,334,4665,421,4666,342,4664,265,4186,204,4665,169,4666,421,4665,396,4513,472,4664,246,4206,204,4578,122,4428,201,4603,479,4593,479,4040,139,4431,201,4256,201,4527,472,4494,472,4592,479,4665,199,4608,472,4332,204,4040,151,4384,479,4587,479,4664,282,76,4983,121,5318,367,4922,124,4972,121,5288,36,4923,121,5169,479,5272,367,5127,474,4921,124,5170,479,4923,124,4934,150,5256,367,4962,121,5278,36,4980,121,5293,276,4982,121,4969,121,5252,52,4996,165,4872,478,5271,367,4922,123,5299,276,4982,121,5296,276,5173,479,5320,367,4977,121,4967,121,4999,163,4962,121,4922,124,5251,367,4921,121,4926,124,4936,121,5180,479,4922,124,4922,123,4921,123,5304,476,4976,121,4922,121,4862,478,4906,478,4922,121,5127,472,5123,473,4983,121,4899,199,4925,121,4983,121,4938,150,4971,121,5272,155,5123,473,5118,472,4925,121,5127,472,4902,198,4925,121,4958,121,5115,475,4926,126,5282,476,4922,121,4925,123,5281,476,5049,472,4924,124,4975,121,4908,140,4966,121,97,5726,213,5604,105,5606,105,5643,107,5641,109,5641,119,5562,105,5563,105,5607,105,5562,105,5528,479,5562,107,5767,249,5736,249,5641,125,5641,119,5725,213,5721,213,5600,105,5723,213,5739,249,5602,105,5562,105,5546,479,5528,479,5528,479,5528,479,5562,110,5528,479,5528,479,5528,479,5528,479,5528,479,5560,475,5722,211,5560,475,5562,112,5754,249,5642,115,5854,213,5563,105,5641,113,5869,375,5603,105,5758,249,5641,115,5851,209,5641,119,5462,479,5606,105,5746,249,5605,105,5514,479,5641,122,5766,249,5641,115,5641,119,5762,249,5722,213,5721,215,5602,105,5641,119,5642,109,5591,105,5561,105,5561,105,5606,105,5561,105,5603,105,5645,115,5643,117,5598,105,5561,107,5528,479,5605,105,5605,105,5601,105,5560,475,5561,107,5642,117,5561,105,5528,479,5598,105,5561,107,5725,209,5561,107,5642,117,5594,105,5605,105,5561,107,5528,479,5528,479,5561,107,5604,105,5641,128,5560,475,5600,105,25,6203,475,6255,267,6368,472,6430,472,6134,151,6133,265,6463,472,6552,475,6456,476,6285,236,6672,473,6216,267,6168,266,6350,475,6176,265,6238,266,6168,268,6303,473,6275,266,6168,265,6478,476,6407,472,6464,472,6517,472,6168,265,39,6887,274,6885,250,6885,252,6889,372,6881,122,6881,276,7056,89,7021,89,7080,473,7021,473,6977,476,7042,473,6907,211,7027,473,6936,473,6934,321,7091,477,6931,343,6822,249,6969,473,6980,473,6935,341,6809,256,6908,213,7057,89,6887,272,6887,262,6874,345,7059,89,6933,336,6959,473,6905,200,6976,476,6922,341,7054,89,6935,216,7016,473,6930,216,7051,473,62,7527,237,7724,237,7911,137,8011,199,7685,364,7912,480,7551,237,7518,472,7687,164,7660,361,7851,480,7908,151,7611,472,7532,237,7726,234,7795,233,7636,472,8026,182,7912,479,7909,151,7724,233,7912,476,7724,235,7908,158,7833,473,7718,236,7714,236,7908,150,7880,473,7488,237,7518,477,7908,159,7728,233,7835,474,7527,237,7544,237,7908,156,7544,233,7716,236,8028,187,7623,474,7881,137,7718,233,7542,472,7726,234,7497,237,7544,237,7526,237,7833,473,7593,477,7909,137,7902,137,7725,237,7736,235,7900,137,7534,237,7536,237,7464,237,7521,237,7726,237,7762,234,7558,237,21,8487,430,8653,217,8487,430,8535,340,8505,412,8444,285,8270,473,8487,430,8487,436,8487,436,8511,412,8535,343,8635,219,8535,337,8478,140,8633,217,8513,412,8487,440,8408,478,8523,342,8633,222,79,9145,176,9095,344,8937,479,8894,479,8904,479,9227,450,8744,22,8953,479,9147,171,9124,2,8901,476,8744,25,8792,361,9225,439,9094,176,8900,472,8776,361,8936,479,9048,478,8904,481,8902,476,8903,479,8806,361,9226,453,8845,361,8867,476,8792,361,9048,476,8840,361,9094,169,8996,482,8942,479,8798,361,9058,7,9128,7,8897,472,9024,7,9371,287,8818,361,9145,167,8872,361,8902,480,9145,55,8743,28,9145,181,8936,479,8903,472,8743,28,8904,479,8904,476,8954,479,8936,479,8775,476,9145,353,8936,479,8947,479,8904,472,8951,479,8895,476,8901,472,9000,476,8808,361,8904,472,8904,472,8957,479,8744,54,9094,250,8886,478,8902,472,8936,479,8813,476,8808,361,9000,476,9145,62,8951,479,8899,476,8974,479,8744,21,8742,27,129,9640,206,9954,275,9994,275,10001,275,9848,203,9672,479,9876,462,9784,6,9718,462,9769,220,9880,462,9769,228,9615,479,9753,464,9755,461,9752,6,9752,6,9715,462,9736,6,9672,478,9754,459,9786,275,9800,275,9720,460,9865,462,9956,275,9937,275,9772,202,9879,462,9687,215,9772,220,9474,275,9538,466,9786,275,9852,203,9752,465,9887,206,9797,275,9760,459,9753,463,9702,479,9687,214,9672,479,9752,465,9746,6,9560,476,9677,202,9745,6,9769,214,9672,202,9994,275,9806,275,9686,204,9735,6,9876,462,9672,275,10008,275,9788,275,9880,462,9672,478,9789,275,9692,479,9960,275,9686,479,9992,275,9640,207,9640,201,9640,203,9959,275,9640,208,9637,476,10008,275,9997,275,9672,479,9955,275,9787,275,9724,6,9626,6,9640,208,9878,462,9480,458,9945,462,9787,275,9753,6,9958,275,9455,275,9672,275,9788,275,9640,203,9799,275,9994,275,9640,206,9769,213,9757,6,9723,6,9737,6,9746,6,9672,202,9941,275,9789,275,9640,208,9878,462,9995,275,9640,203,9672,275,9877,275,9954,275,9997,275,10000,275,9738,6,9672,275,9472,275,9729,6,9622,479,9672,275,9791,275,9750,6,9672,275,9720,465,9672,6,9944,275,9996,275,9787,275,9786,275,9674,202,10004,275,9727,6,9730,6,9536,457,702