文章目录
- 209.长度最小的子数组
- 题目描述
- 暴力
209.长度最小的子数组
题目描述
给定一个含有 n 个正整数的数组和一个正整数 target 。
找出该数组中满足其总和大于等于 target 的长度最小的 连续子数组 [numsl, numsl+1, …, numsr-1, numsr] ，并返回其长度。如果不存在符合条件的子数组，返回 0 。
示例 1：
输入：target = 7, nums = [2,3,1,2,4,3]
输出：2
解释：子数组 [4,3] 是该条件下的长度最小的子数组。
示例 2：
输入：target = 4, nums = [1,4,4]
输出：1
示例 3：
输入：target = 11, nums = [1,1,1,1,1,1,1,1]
输出：0
示例 4：
输入：target = 15, nums = [5,1,3,5,10,7,4,9,2,8]
输出：2
提示：
- 1 <= target <= 109
- 1 <= nums.length <= 105
- 1 <= nums[i] <= 105
进阶：
如果你已经实现 O(n) 时间复杂度的解法, 请尝试设计一个 O(n log(n)) 时间复杂度的解法。
暴力
后面力扣更新了数据，暴力解法已经超时了。
超时输入样例：
target =396893380
nums =
[3571,9780,8138,1030,2959,6988,2983,9220,6800,7669,2528,3994,6090,311,5683,9232,9698,1784,6543,4018,1340,3170,5097,9876,8881,6303,7964,2469,1119,9259,9429,9355,9904,2971,6240,3973,4972,1874,7037,4631,4666,7809,6878,5656,7227,1833,4772,8200,9594,9250,1881,4811,2669,7077,7531,8497,3821,5741,7488,2521,469,6108,431,3985,1641,8732,398,9934,4785,5061,4882,4819,9986,3317,2683,7800,9887,7277,5145,9537,7089,1467,5458,1598,3083,2867,9046,6089,2657,1107,2110,9020,7771,4928,848,896,558,6416,5128,9534,5410,2349,3430,4081,5996,9447,420,3514,6814,9873,1486,4576,6161,9400,2381,969,7588,2920,513,4612,4689,2870,8775,5787,2606,9221,5002,6515,5810,8611,3326,1580,3606,9445,4729,7623,4335,395,4868,8000,4069,8557,9207,1542,7,8620,3058,6822,1606,3857,141,503,9810,2869,9464,3702,4779,5942,4678,3416,2621,4710,6116,2819,5592,9227,8783,6164,3563,4957,1465,3269,2764,3359,2829,586,4145,5330,1549,3296,7842,7311,7981,3901,8132,856,2152,7367,5174,5689,5033,1459,321,2497,5488,7991,1801,9769,6373,3969,6081,4558,8560,3760,9423,2132,9460,1811,2788,5617,3934,9564,3661,4875,558,801,4735,2660,7026,6178,479,1833,9904,3168,2350,2497,2748,9356,2025,5476,6660,9296,6743,667,626,322,1659,3481,6037,9228,7865,3483,8790,763,619,4117,6217,8178,9505,2026,2712,3551,239,7257,7496,9015,9199,6660,3322,8111,7895,3347,7881,7496,9265,1865,7057,5644,2550,7551,8687,9669,5470,8994,2770,4556,5644,5162,5788,7151,8139,9451,811,7694,973,1814,183,533,9425,756,7591,6678,6373,1774,1541,2027,7581,3312,6492,9830,7013,2563,4983,8464,3708,8193,244,194,1770,3155,3657,6384,2723,1581,4958,6507,5811,1975,2287,6764,1210,4138,3536,6646,7880,8106,1833,8035,8625,8979,213,8296,7911,9162,2632,9986,3351,2852,6485,3414,2108,702,9291,1946,7344,5971,5466,4390,9497,4790,9102,149,2458,751,9333,2938,678,2140,8179,9921,2277,9615,3335,3265,1293,8197,3108,820,8750,9473,1490,7536,1241,1478,3616,7319,2230,8591,6698,6457,2224,2649,6490,8021,9701,5423,8149,6417,709,4536,5813,65,9769,1320,977,9724,8558,6737,7087,5861,2569,9979,6583,6102,1173,9641,7428,2304,5674,4397,6569,6609,1966,3206,5471,2961,9762,7825,1416,3647,5964,1521,6746,3255,9808,3780,4822,9778,5152,533,4121,1257,13,410,6220,4646,3309,5369,5790,4758,9374,2905,4485,821,140,3278,1824,7591,9323,4921,4363,1219,6108,9454,5782,4103,2757,6351,1029,6493,3737,7214,403,9586,3106,6,1924,6254,1503,6527,2346,506,2242,2206,9378,9295,2147,2259,5520,3711,1360,5287,2446,548,863,6649,1898,5877,7114,5764,9091,3343,6698,2456,9560,853,7534,5450,2888,7835,1746,7363,932,5292,9225,6905,2650,1847,4767,595,3766,9709,5735,993,9929,6982,6186,6124,3933,2816,1361,1086,3295,328,1478,9747,4400,5852,3544,2775,1234,7571,821,1290,8210,3593,8467,4629,7532,9608,1958,8430,5426,455,7313,9802,6950,9450,1870,1940,2114,4685,823,5147,8512,8909,9100,1170,9513,5287,787,8045,7700,5900,7025,2447,2337,3523,7160,2734,2008,1657,2007,9097,2423,3434,3617,4590,9412,1733,8891,6485,6135,4116,9184,8527,6233,1597,687,9551,4479,1935,8141,2245,8045,3820,8863,8156,9551,7926,786,9523,4874,1823,2771,2863,9601,4737,1085,3153,8559,6079,5833,9487,8183,4344,8786,6321,939,3483,9447,9993,2436,3712,5364,9520,6887,1677,3009,5402,4270,141,5139,5683,6778,2522,8106,6684,76,647,9590,4186,1651,1604,9498,1164,1378,3814,30,8490,220,9638,7768,1754,1519,7520,814,5242,5641,1463,4759,6539,3316,5278,9467,5342,5033,686,6661,7507,29,2693,3730,5021,9051,572,6775,4005,6047,9089,2115,8202,184,3727,5996,4502,4552,5242,3329,4797,6834,9030,4294,7891,493,842,2101,4126,4920,4426,3768,4770,521,4253,877,6026,1510,1394,4914,5542,1696,6313,5966,7931,8574,9203,6222,8887,7304,5617,9003,7702,4371,6583,652,3068,3115,6808,4611,5385,7791,5416,8733,3785,28,2806,5731,2889,4529,7553,1265,942,5721,4521,4874,3505,8382,1879,321,4740,8582,591,1972,9896,3740,4807,256,2717,4872,4650,2537,8088,3272,858,6088,9938,8581,418,6914,4488,8417,5200,8271,8055,7715,5060,6651,1639,448,3108,6893,5616,2886,8528,3376,7654,7474,5190,4144,4787,8235,8188,2633,8004,5978,6733,6573,3752,3861,9721,4429,1652,2678,6555,6765,6653,8605,5726,218,929,4818,4411,1058,448,2679,823,5466,6709,2761,1353,292,6437,3533,3199,1156,1868,1434,7219,2733,9467,6349,4266,1410,2836,245,645,5952,5415,4992,8136,9092,2431,3985,7427,6323,7011,4858,9517,7897,3630,2441,6565,2303,2180,4654,1815,4992,8835,7647,1011,7020,585,942,8639,7955,646,4531,8248,6779,9557,3570,237,4692,2765,1660,4833,7419,2244,4522,6476,1395,7876,8532,1264,5959,5884,1601,260,5264,23,8330,6329,4526,4188,2368,566,1957,7258,9777,5099,7896,6578,4123,6456,9754,8610,8879,7975,8648,6360,7114,8542,6889,9930,3560,7809,6856,2456,5967,6189,8154,2285,5130,7299,559,2201,874,511,5185,2107,6283,1295,4747,2197,3023,8097,1448,3969,2937,3689,9846,347,5288,137,5838,5955,337,5888,2272,6465,1973,5694,4223,1174,569,9502,1431,1699,752,6167,9223,1936,3567,197,661,8464,3102,4847,6971,9945,7765,7960,1153,407,5600,7978,6821,8496,312,2798,8862,494,6748,6896,3244,5096,3158,6930,310,5550,5911,8528,5854,8477,1085,1719,8380,6299,7471,9334,6208,7741,3159,8766,8430,7009,2957,6364,5739,5484,9329,8895,6749,9302,3078,7914,7171,7576,7198,367,3752,7628,4987,3657,1647,4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5362,2297,4259,4863,7629,3107,4278,1384,6451,9336,2121,1198,5678,9476,5775,3567,8335,9618,4947,2892,4116,6365,6987,9641,4310,5063,3289,2640,3691,1518,2892,974,2794,3807,8793,7518,3776,284,6985,7803,2366,2981,104,5859,562,5531,2597,1882,617,5866,5064,30,7715,7204,3630,1625,7938,8759,5022,2006,6573,5252,3957,7377,946,2236,2338,532,9601,4210,5026,2188,6028,8189,7709,7005,7832,8017,2732,3441,8437,6707,6636,9144,9694,2056,3122,8091,4779,2706,4267,7461,5010,7827,902,8488,7183,9578,6641,1457,7832,4370,7271,653,9596,8173,9689,174,7050,9312,831,9361,7665,9142,4909,8398,4001,4473,3976,8177,1032,7519,5736,9654,3932,9531,7791,9877,3580,9634,197,3913,9106,7576,9156,3890,8220,2193,2761,2310,4674,9990,1426,3187,6454,8807,2298,8483,9741,6326,3499,1241,2275,7370,5392,1053,9986,6857,2060,9359,5078,6752,8315,9494,1033,1655,2446,26,4836,8585,7995,9858,4813,5874,4985,605,3451,3449,8704,324,8317,4675,163,9217,6271,5422,8677,5175,1650,9909,9687,6075,4902,490,6218,7740,12,4527,4272,9276,6273,1365,5081,7555,5621,3669,3457,5089,2721,4157,7569,3518,3940,4060,365,8311,4205,6941,1121,7122,1561,4924,6073,9978,18,5458,6848,8609,5328,5929,5200,348,3886,4899,4726,3393,3466,1363,6247,5388,5724,741,8700,927,3460,2754,4989,9460,4989,6070,8958,155,6664,520,5378,2833,1160,5941,2073,4336,8650,2171,4510,7086,9298,1742,1256,2279,8102,8066,3986,2272,594,2836,1038,8763,708,4381,5826,801,4545,8437,4950,6846,592,4108,8496,949,638,53,7650,2336,1481,2995,4442,1419,7609,5751,3906,9238,5240,4865,822,4664,7409,3892,1648,219,5104,8872,2493,2850,7082,649,8532,9850,6209,8994,7730,1018,2136,1308,6061,1,6202,9626,6549,4111,377,3876,7356,7559,9622,6641,798,2768,3755,2652,2792,2839,6414,9181,8020,4989,4031,2211,3234,9568,2012,9613,9735,4570,2482,7746,2000,9336,2147,8133,2169,7121,5464,2121,6356,9705,2147,503,159,9062,7457,1996,949,285,8519,9963,9239,7082,6854,8503,4242,1985,35,2848,5234,1634,1828,3595,3037,447,7234,592,2841,5236,4551,7887,6207,5173,9048,324,4712,8695,3584,6266,7164,1374,1288,2361,9434,3292,4398,9637,2170,1590,3706,7173,9386,3463,7276,3933,7644,9077,6941,3932,50,9535,1670,6270,429,9825,8660,8876,7737,3982,5621,9670,7335,3789,66,5948,6307,391,6820,1358,8475,8285,9965,8100,2929,4087,3580,3116,6439,3558,6337,4827,9470,3935,458,1445,8688,6243,4576,4873,6141,8522,9095,9015,6737,8105,8094,4141,6475,3925,1329,3954,6270,3348,2613,1820,4052,6082,9192,537,3669,9874,2189,7337,4792,6387,4124,2791,6582,9017,5647,8128,8695,9867,7736,9076,7230,8145,1625,6147,4600,7063,7696,8321,5,9156,4876,1471,1790,4345,3751,6239,5780,1688,7400,4252,4899,9999,3189,6980,3667,7086,4471,2000,7583,1456,8121,9362,4036,3316,2112,1326,2431,6803,7327,4515,719,6622,124,9267,9565,7268,6973,1781,832,5949,9928,2911,3435,7535,7857,5776,2420,6913,7373,4752,9931,8669,2469,9699,7788,792,6425,4827,5795,8964,2815,2165,3787,4352,6450,9904,916,6413,3346,7798,753,4328,2978,1187,8578,2289,7404,8916,5872,4834,4859,5229,7455,7290,8607,3347,2235,868,3656,1660,5392,1377,3846,1679,7815,162,4347,3245,3411,9460,4035,6353,1199,2011,9956,4135,2525,3628,9387,8513,9613,1537,504,1500,6369,9120,3807,8761,3850,3140,2817,9836,8466,4226,6619,9848,8846,695,424,7840,3828,6615,7738,3126,7428,4047,4341,3433,43,5605,628,4440,3691,3109,701,6071,6072,2916,9420,1840,2262,8803,7905,7048,6864,8252,4697,8884,3097,2487,7577,5766,3038,8590,679,1981,5162,620,1266,6050,4712,1519,7231,4041,3986,5691,9129,1806,7842,2700,7840,5746,9052,9568,9403,6242,8272,6180,3374,2679,7687,3639,7197,6313,7174,8478,687,9289,5897,9506,8660,1292,2261,7104,8829,6450,5805,2739,5522,3013,7866,4227,2707,1749,1957,9920,4229,8507,4685,3415,3362,6824,2293,4464,6927,7948,6823,6533,6414,6774,7418,3190,5318,2672,4119,8724,9498,6736,1291,8992,5391,2565,5073,5558,1137,240,4046,5553,8549,9778,9746,5940,2088,3197,5440,2009,3611,6483,8110,4744,1177,3265,9413,2780,5446,4448,6802,8244,5394,5434,3917,3116,1193,8158,2291,8391,9841,291,4424,7248,6388,2083,3583,5039,7174,2545,5352,8880,8333,212,6805,3139,9148,1628,7683,3423,5460,2968,4810,2726,7222,3644,7841,9757,3004,3945,3269,3870,8644,6710,1727,9152,792,2912,789,7307,1824,3690,1753,4652,8817,179,5532,4230,6697,1982,9426,4403,7109,5785,2145,8041,2493,8940,2263,4013,1397,3676,9053,1096,7929,262,1450,6439,6647,5288,6566,8308,4110,5408,5862,8746,6379,2122,2214,5993,4796,2090,3586,6037,3332,5083,2810,2259,1983,2279,7187,6555,7061,9180,35,5290,1649,1721,9011,64,5961,7331,1080,3224,7416,6320,6375,7700,7531,7542,2491,1811,5972,8922,676,7039,1153,5644,7537,8948,3493,7861,1040,9879,5516,4223,4356,1134,4535,4509,6974,3283,8772,5200,4488,2970,2269,9584,8748,3417,7935,3843,1133,3286,4054,7943,3195,2581,5273,9141,7694,3636,8143,2020,2924,8119,1271,3276,1680,492,3567,8365,6929,3845,6855,223,5240,144,2061,7423,4191,5804,1437,9919,9100,8730,2324,653,8396,8541,9678,3295,5687,3384,9170,4800,2738,8886,8118,7275,1677,7794,1290,9903,1888,3282,7942,269,9522,7191,9991,5599,8644,2944,9350,7303,2717,4903,1832,4038,1077,4209,241,1299,7322,3637,3601,4535,461,257,1529,831,4230,2272,2913,9632,5649,2779,1474,8657,1423,8814,7326,6781,6027,255,9807,2220,40,8347,4247,2415,2786,7082,7371,8631,2651,7650,1000,2510,3414,540,3624,5314,7989,9141,7413,1375,9982,3460,8663,7106,6948,5423,2536,2965,9690,8895,5680,232,7629,717,899,7636,9155,290,6674,2983,8614,5849,4723,6153,3743,898,8450,189,907,419,3393,780,8800,3855,8169,5484,6616,7667,7500,3475,60,8342,3706,8595,8024,1082,1091,1260,3418,5706,54,7252,7826,2342,708,6811,9238,8188,2489,5802,2050,1331,5063,1718,2851,3065,4492,2480,62,4296,5347,2673,5327,5504,2395,1146,3642,7054,8924,1338,8071,1888,3631,3436,3516,2435,7085,5370,8303,4110,2049,7345,2118,5050,4944,4937,8058,1008,9167,7868,9763,9689,6436,3774,3863,5950,7490,5918,3622,1787,2667,1564,347,8749,9530,308,8591,4205,3724,4910,2162,352,1245,2127,4594,3877,9199,3720,2568,5653,983,6648,5805,3590,7107,5,7200,2715,1356,2993,7268,9913,5068,4185,5036,5979,91,4059,367,6906,2367,6122,6373,7304,1001,4355,9811,4580,2236,3737,5942,7011,2938,9377,1641,9849,6308,4355,1407,7135,7032,2528,9076,2784,7437,8140,7127,8844,5302,3353,9183,6910,7490,6467,4924,4170,9861,3408,7151,936,5124,9713,2770,1170,6842,1648,5699,2695,9552,2554,6303,4776,8686,4548,6636,7264,7834,6235,5049,161,3807,3112,2884,483,2559,5170,3151,6361,7584,9174,5907,5773,780,9564,4561,498,4622,9016,9205,7594,8719,5961,66,9593,5798,3571,8453,6503,8143,8987,3133,497,4715,4320,3669,1583,9320,4895,8080,4842,275,143,5662,5899,590,5387,7578,4213,917,9927,3008,5623,9108,8892,7074,5964,7285,2818,341,8632,5994,2993,9274,4147,3569,5912,3405,2708,2480,1016,2873,6194,2685,9313,6034,5660,7058,1512,7936,8023,4418,3194,5204,434,3544,6819,3912,24,2017,2390,8698,7801,41,3850,9798,9009,853,9966,787,3755,2642,7425,2960,9113,6453,6386,3270,9051,9843,4878,3264,8991,3270,5945,4186,343,189,9877,9872,968,4213,3278,7530,6966,3503,1119,3842,2149,4144,213,8733,1789,1155,1228,284,9063,3668,4806,5600,8897,849,5395,9562,3338,4266,5310,2432,8803,264,6698,7888,1248,3293,9564,7324,8744,8129,6608,6508,7717,4692,6103,4149,73,4249,5995,7021,8618,2294,1223,5852,6891,6460,1426,6049,1764,4356,7290,8066,3649,8994,2982,7089,8862,4533,1217,227,7260,6662,1282,5321,3322,4297,9333,4985,6828,6787,8077,9534,1182,2492,2318,1769,4698,2757,2605,6961,2052,3988,117,5109,7017,1221,3843,2608,7785,1161,6835,4013,3251,9341,7818,6033,8332,9809,4449,8894,8298,9698,3538,8777,4475,5378,8746,2995,4922,2423,2269,5231,6851,2520,1225,8930,5659,1509,772,6851,2249,2477,2063,3215,8313,5,3626,5574,9772,4500,9575,8915,8352,1053,1515,1491,8723,4504,6957,6443,9225,465,7500,8868,6178,7008,3723,2701,8881,2226,3615,8949,3862,6385,3864,372,3713,6636,9073,1198,8694,4209,5481,1490,1577,7906,9218,3669,618,9675,1254,1984,7360,8256,9454,9774,2454,8961,2840,2666,4368,8332,3169,8176,3373,6332,7113,5525,9824,4084,8208,6400,9446,8789,4120,3697,1399,9081,1785,2358,7707,4084,1288,1443,9724,3357,6954,7236,3756,2759,5035,7427,1377,6505,2192,7330,3706,8112,3208,8085,3171,8569,9672,5851,9340,1686,1120,6904,7111,8718,8079,9642,7771,2435,6959,6446,3025,6624,6418,2181,7467,2303,3669,3350,3386,6017,8882,1830,4101,5684,3013,65,4757,81,4980,3786,1654,7913,3671,3703,4247,2584,7894,4051,8834,775,9903,3493,4863,3897,5746,2823,381,7712,8020,4578,9418,1908,4669,8612,4067,6080,9710,3014,9020,1661,2674,4081,5735,8480,1103,1022,8941,2297,7882,6247,8169,9355,1905,495,5918,4991,9242,8408,231,9473,7453,5705,5756,2970,3833,2543,3062,5417,5251,5697,3707,9522,1760,2294,7150,4539,2007,8367,1047,6545,4410,9929,7868,3124,8217,6947,3720,2399,7738,169,4749,8918,6521,7727,9384,2279,7284,3047,4978,7822,3723,165,273,2704,5750,6165,2058,9803,4480,9057,6726,1098,6670,2742,7306,6035,4401,4080,656,9004,5297,9618,4555,9086,5788,962,8463,7588,9956,1190,1532,2199,2932,9454,2879,8063,4602,8027,7312,7203,5297,1542,2667,7791,2214,4396,182,7705,9337,2517,5949,7473,1535,9915,7871,7734,3280,9158,9596,4892,9439,8023,1289,5148,181,8763,380,3059,5248,3567,6232,7603,6153,9596,4821,8675,1319,5935,5339,6669,6448,3469,7394,2376,1163,1736,2943,9770,6159,7548,2252,3385,2741,9990,8540,9729,7637,2221,5557,6885,9306,9126,5466,5347,2661,6162,1325,399,9199,9548,7219,6051,8063,4688,9980,4841,5115,6336,9950,7281,7931,1335,6814,3132,2923,4746,4075,9557,6345,947,7403,4454,5305,9069,5988,4564,6499,5253,6831,3038,6776,3505,6527,8243,8896,6831,230,7719,2001,543,458,8101,311,7981,6101,89,306,8038,2219,2528,9552,8992,6351,3365,267,9237,7927,55,2859,1100,6950,2079,5628,8280,5712,9843,5479,1431,6321,3310,7405,6746,6017,4435,1494,5444,1688,1224,1593,6552,7751,6526,905,1950,942,2222,4469,7948,552,8076,3364,7577,514,9850,9154,2977,6183,9222,5701,4143,547,58,5058,829,7385,2774,6442,6403,9312,3528,9300,4573,6267,3743,9131,9152,3709,9250,4138,243,508,3848,7158,7304,4830,252,6752,9270,6940,5919,2561,4489,559,8176,2375,4292,220,4972,2251,8597,3952,7554,3849,5697,868,2293,783,7891,6047,1843,3557,1806,7618,7838,8025,1295,8552,2187,4803,5404,5915,3619,1348,5993,1072,189,6059,9227,23,8454,2023,3596,76,8077,2384,8387,5606,6722,1631,5746,3985,5477,1926,1982,9919,5786,6686,4011,208,6967,6332,5482,5456,7666,722,2773,5757,1761,1704,7111,4181,8975,2773,882,2172,4742,2975,2074,7914,2369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198,4094,3384,7443,2017,2401,9832,45,3239,9950,539,1579,7654,6764,4813,3422,8593,9391,2230,5743,1127,4522,314,3408,907,5348,7676,1934,9300,9783,5438,5830,2171,9243,4775,6074,2381,7289,8185,1082,7094,8512,3913,136,5784,7565,4911,14,3487,4399,6569,9395,6385,9395,2209,1664,5917,8114,579,9259,2020,6079,6530,2893,57,9487,6616,9472,6706,234,7593,7213,5006,7938,7217,4331,7490,291,7310,8321,4116,8939,6850,4534,2765,5408,1146,4765,396,1052,2096,1515,9829,6001,4805,2254,6827,9953,6619,4086,946,4374,4112,2617,6569,481,1157,4860,2468,3462,5521,1641,8998,4450,764,6242,2092,8722,5102,1212,9744,393,2153,1193,1858,4027,9758,5859,2562,8124,2703,6937,5062,7980,247,5930,5776,4114,838,5281,7413,3779,7678,8820,1079,4078,6691,3838,2359,6285,3566,5402,2353,725,4669,5945,3414,1969,1859,9650,4992,5725,7563,285,4350,3032,8478,8234,5617,8722,2964,7732,1682,1663,3327,5433,4209,2730,9110,8694,1526,3677,2647,9083,1620,6609,908,8771,1500,5828,8009,3007,723,611,7966,7766,572,4748,5527,4035,1474,6416,4515,6777,5921,3487,9351,2001,8360,6006,2813,1237,7974,9270,976,575,1612,36,2323,7142,7450,4448,8677,7059,8114,7181,9444,4367,3777,9730,2568,6507,5025,9152,9826,299,2360,6103,9620,6084,4292,1427,4843,9994,17,1828,8962,8952,87,7459,8316,779,4917,1487,9851,9457,1427,8182,3387,2085,1428,2729,6206,9238,8351,4281,9709,5071,8143,9251,702,2830,180,5421,155,3515,1256,1586,6080,261,7283,6872,9937,9521,6968,2110,7302,998,6373,5494,2306,9136,1008,8899,6680,78,9463,9863,6886,893,8385,7763,7198,5430,8893,4623,281,2402,1507,5529,3716,786,2830,2906,9388,7885,586,1752,6360,4995,1764,7997,9889,5418,7195,1872,5543,8648,9592,5635,1788,4356,788,4774,9116,4301,872,8437,7949,259,6044,7814,1200,2481,5917,1100,3807,4174,2489,507,852,4442,8026,7154,1980,3639,6646,8437,3522,4666,9771,2432,686,5491,4359,1588,6716,183,7516,352,7242,1611,3394,5022,8757,6108,3900,6715,3539,3787,331,4653,8757,1082,8347,2138,1580,8757,3870,9569,1129,8142,9775,9424,6263,7213,8219,9829,9208,5258,9787,8873,9883,9157,6106,8874,4064,9859,289,5968,8953,2596,6957,9916,9806,2479,400,7360,8194,8210,518,3036,7163,8633,4052,8131,6799,6768,6476,390,1172,3328,3463,3297,8992,3753,8451,8217,8118,8285,2775,1970,7289,4321,8168,7349,6325,8146,6813,5500,2142,7498,3714,7970,9343,2279,5462,9960,234,1762,5326,7827,5957,7999,6119,9949,4064,7841,1667,8323,5808,547,2965,5140,1109,1637,8975,8892,3895,2977,6576,8169,4815,5291,1413,4945,8170,371,9839,8262,7805,9340,8839,3015,3943,7596,402,8641,5026,1248,3515,6192,7226,9663,3168,1520,1679,9632,5935,6025,2008,3701,2617,7838,6980,9503,6674,1124,8005,8052,827,3027,1251,5540,4204,3398,9069,4017,2548,296,5076,1059,5573,9281,555,7553,4124,1609,7559,6233,5004,7762,7484,8966,6077,2998,5343,9729,8555,5967,6728,1054,2189,1267,8961,6909,3843,3626,8500,616,9899,7574,1903,5488,7728,9821,157,6714,1752,6483,2750,902,5399,540,5110,8447,9368,8243,3428,8027,3891,177,909,299,298,6564,6107,3812,6939,4656,6040,4953,9720,4870,1380,8716,892,6045,1526,1261,6280,6718,7506,1417,3355,2807,6550,2409,5410,8941,563,9902,3737,7732,8111,8316,5681,8503,8386,2739,288,4032,8251,4428,2312,1615,928,4231,2644,2509,8681,8454,2143,7471,329,5765,8234,4599,153,9051,5652,7325,2060,9035,1404,5177,506,7008,2802,565,6114,110,6870,6221,7476,3060,1357,1685,6278,9176,3983,8021,7397,1837,3781,785,3689,6888,1718,4132,2243,3871,4718,5502,1034,2341,2429,8402,3810,7351,9919,4976,6533,2071,5363,9003,2518,1668,2074,8130,3064,304,9856,5165,7047,2376,2949,1004,9512,7498,8605,8598,3081,8063,3118,6832,8129,8208,8993,1094,3192,8235,5212,1385,8275,6368,3422,6379,2770,6532,9629,8237,5579,449,1973,4147,7008,2338,9489,9460,9603,9491,4267,7201,8851,5325,2076,9189,3134,5657,6950,8702,8458,5453,3524,2134,8789,2317,7111,4905,9722,3668,6966,5584,4971,8534,335,7815,8684,6177,5644,6765,9519,6782,3741,2533,9870,1925,3044,9925,8262,3340,3679,5207,5856,8219,4028,8050,5588,3764,8881,2449,6024,8466,590,5368,6344,7834,1483,6801,4920,1290,2099,3468,2476,4638,1404,6494,7140,4966,7964,1168,7927,9678,3627,7321,536,4172,1467,51,2006,1384,4765,9981,4122,5839,2525,7152,8949,6635,1616,5508,1678,8596,9741,9533,2928,6721,5035,5692,9403,2527,2919,9004,1089,5999,3927,6472,3281,6129,566,3743,1470,9096,3005,753,7436,2555,548,5659,6153,2927,3864,2189,8091,9274,8102,7043,3937,7764,8794,5326,2806,4989,4915,8685,6256,1169,8629,4735,3879,351,2623,76,2880,3725,5132,8309,858,3433,2171,6056,8320,2261,4962,8430,6642,1628,6127,9240,7833,8650,9853,5819,9188,6678,3539,6720,861,7658,6369,1267,2342,7224,9907,6860,8186,20,265,5261,3560,2113,422,8075,2896,9443,6725,2831,3667,5639,5611,2399,4890,7407,5136,907,6284,7235,1478,809,6861,5967,6955,7780,6069,6984,6481,1953,6254,7822,9791,6819,8657,4898,2361,7811,328,7667,3870,6804,371,9546,8686,2547,3034,6243,4657,4601,2365,405,7757,8183,1084,6307,7934,6121,6042,9287,5058,3966,7111,5048,1457,1770,7399,3048,5757,2128,3396,5215,1748,3261,6989,9562,4035,1548,6402,164,74,1369,60,3199,986,7378,9916,8101,1896,6835,1783,3654,8815,9002,9850,3057,2863,4707,5351,4106,7620,9772,3284,2572,4007,2295,1780,2304,2432,4324,3581,6031,9530,5579,7266,6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848,8281,5715,3442,567,6114,5550,5758,381,2528,7017,5249,9232,9627,3151,4570,4366,7474,3101,1188,2194,7162,7847,4838,876,4886,6738,1472,1560,223,1283,6140,9882,1343,864,7720,5363,308,6492,1677,870,8292,6969,2185,4457,2171,5493,1862,8162,1499,7378,5763,8898,7080,7560,6361,9539,4440,2306,9965,4610,207,5022,9416,3586,834,2815,6687,5003,7194,5240,4196,6814,1338,3812,7568,8136,1987,8391,4334,1425,8422,8708,5492,2901,3995,9053,1899,727,1127,1284,8591,172,7835,4235,5464,5117,6494,264,9300,1781,5202,7059,5336,7248,1819,5861,8139,1769,6962,1983,2451,6753,3331,2651,4969,1289,5150,9792,8731,4999,2474,3453,7683,462,7249,9816,7881,8973,674,6486,9368,1489,6697,3318,8250,141,5248,509,1768,9210,104,154,3249,7648,6473,9024,3371,7761,7641,4193,8205,6615,9082,5129,1204,7642,3816,7356,1642,7527,2296,6815,6203,390,5132,1494,4349,9983,356,1969,123,8016,1101,4513,124,5877,9541,9933,1122,2207,8755,8889,6833,3713,1370,5511,1002,5843,8257,5508,8532,2509,1277,2679,8133,6792,1014,97,6516,7498,263,3196,6365,8924,3322,9208,5270,5539,3058,9844,5240,6642,101,6300,4137,177,5578,9909,2632,3284,8187,4823,522,357,5289,5926,6317,6421,6439,8543,5965,9442,3452,418,1244,987,1049,9483,1817,5259,4532,5500,5997,9720,4042,6376,6907,5423,6895,2217,7416,9975,8735,9816,6381,2347,348,2794,2425,2004,712,4933,2407,8425,796,6670,5911,2771,1269,6006,7895,9110,5443,3846,4698,5905,8577,9312,307,5042,1606,437,1999,3814,8393,4399,2358,7442,7665,8255,6786,2240,1878,702,8843,4044,8201,1913,4649,4011,249,2582,3308,9335,8130,4156,2367,9867,920,5270,6408,1688,218,6477,8339,9862,7823,4854,795,2432,8800,4006,5616,8785,6537,5820,3243,2050,1517,6155,6767,2802,8624,525,7891,3409,934,1416,5867,1535,2603,8876,3058,5177,7679,6454,8994,8987,4799,1324,2121,1794,601,7294,5871,8182,9058,1047,5306,3998,5207,7846,3077,723,9205,3576,2900,6188,4048,4086,27,6123,1044,6236,1890,5158,5860,1147,6133,1844,2273,9482,6679,6409,6528,6747,7715,4737,4181,3958,8348,2639,2313,1603,6756,5612,5244,9897,7298,4838,3681,9307,5253,5304,6231,5088,8329,2026,5553,8892,2374,5990,8270,106,2538,4838,9877,3468,967,6803,2281,2504,3611,4094,6758,8585,7369,2603,3551,6037,9892,683,6371,7381,4122,1203,955,2933,5086,3227,5611,29,4715,1979,8426,8665,4775,2485,4625,61,4269,5349,5632,5101,7510,5880,781,2517,6599,3295,6176,8202,5242,734,9281,8505,6933,8969,4973,3343,367,9052,4418,2175,1330,8900,2262,9569,6755,2597,540,2321,4407,9201,88,826,6471,8381,7737,2264,8799,9516,4306,680,581,9877,9416,4754,7492,2459,3833,5582,1114,7894,2323,4779,6653,7857,3470,7236,4394,6431,5515,7848,5767,6731,3506,19,2123,4702,4364,2541,5623,9530,6001,8596,1995,6401,4916,4320,3152,1919,1001,6300,211,6817,9670,7733,6136,5455,5911,6074,6803,58,4951,2415,6852,9138,8214,3391,2611,7372,9055,1116,7322,1974,8174,228,3148,5036,2107,8026,4370,2580,9774,7934,9449,4884,5730,968,4857,5882,2532,7133,3471,8927,1657,6575,8443,8499,2874,745,5611,5556,1092,270,9133,8311,4432,2886,1396,7059,7624,2635,2768,3830,3901,4368,8362,9002,2677,4675,6699,3319,1515,6837,5735,3428,9814,1791,6195,6065,8765,8417,9668,9017,1616,5340,1159,2127,513,371,1831,8380,2975,2800,3585,5496,1712,988,5899,9751,9574,3150,6184,788,5618,5997,4151,7944,6552,8888,3486,7515,4189,4414,7818,3094,11,2865,839,3746,1366,1314,2872,4329,7560,5314,3835,9773,3103,6790,6458,1750,5491,2151,1980,4680,7687,7852,6589,5629,7158,8782,5010,1203,3482,2935,2330,4948,4277,8495,8968,1572,7596,9709,7469,3265,3856,4704,7012,8995,1760,1822,9572,9779,5973,4830,7699,6694,2492,7063,9151,8344,2384,5828,518,2524,2296,8531,9876,5869,1877,6928,6928,6245,2871,6365,8338,3792,6604,3385,6348,1049,8828,2577,1155,1869,4462,1738,3715,544,9215,1390,8921,3317,9195,9002,9513,7120,5557,3049,6837,4385,929,5789,6521,329,866,8846,3262,4569,8937,48,480,2436,6858,2348,745,1381,2956,6975,4627,9333,81,3241,6856,2377,8741,7767,6055,3875,3824,4607,3360,7727,7050,1980,1311,1593,4043,2938,6093,2663,7794,3171,3664,5638,8714,8829,8493,6385,1925,926,2491,3329,3655,2311,1709,1652,9962,3806,4538,5191,1797,5266,7135,3899,1961,2383,9753,2984,5068,393,4865,6157,2574,7081,1420,9090,3825,6077,7557,5763,3148,9086,7016,3149,2350,7215,4595,6873,8317,5462,6165,9416,3161,8662,575,8747,6375,2201,7840,6435,7281,8183,5882,6556,8100,3786,3524,7219,3157,1302,7421,2410,2617,753,630,2974,90,943,4270,3587,5194,6637,5969,7587,2334,8986,513,3054,528,6397,1021,5758,9761,2,1583,6855,1476,9167,8129,8751,6424,9984,56,5424,4170,3397,3625,5900,463,6080,7024,5762,8123,1532,9034,6824,2859,811,543,4054,1185,2321,6008,8424,8775,8024,1126,6490,4416,5501,948,9953,555,8422,2458,8529,4865,9500,2886,3825,4992,9708,2987,6508,9932,1222,6662,3893,7288,8117,8446,3870,7184,8609,4934,2718,5281,2470,8524,2495,2654,3348,2192,3784,6253,5523,6022,3075,4069,3919,8854,8244,8044,9980,884,5866,5773,7720,6437,5401,4855,1651,2655,832,6233,9553,562,4063,6201,6026,5479,1545,4034,912,6583,617,326,8558,9848,9027,2088,4517,7453,7249,7517,4223,738,7790,5709,6515,3270,3218,5764,3522,9746,6762,8976,5726,9329,726,6764,6126,1967,5413,9774,8848,8676,4879,7436,7974,813,9894,7795,4233,6000,2385,670,520,5203,401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