最近,对数据结构比较迷,利用业余的时间看了些文档,发现中文文档比较难理解,参考了些外文文档,总结一下,希望大家能看的明白,堆排序的简单实现.
解析:
1. 最大堆:根结点的键值是所有堆结点键值中最大者的堆.
2. 最小堆:根结点的键值是所有堆结点键值中最小者的堆.
3. 上述两种堆插入操作: 只需要将节点插在二叉树的最后一个叶子结点位置，然后比较它对它父亲节点的大小，如果大则停止；如果小则交换位置，然后对父亲节点递归该过程直至根节点。复杂度为O(log(n))
4. 存储二叉堆:一般用数组来表示。如果根节点在数组中的位置是1，第n个位置的子节点分别在2n和 2n+1。因此，第1个位置的子节点在2和3，第2个位置的子节点在4和5。以此类推。这种基于1的数组存储方式便于寻找父节点和子节点。
概述:
1. 将原始需排序的数据定义为origins[]
2. 定义两个下标ori、tri,ori为origins[]数组中元素下标,tri为将要构建的完全二叉树trs(本例子按最大堆建树)的下标.(ps:下文中的堆和树是同一样东西)
3. 从ori=0开始,向trs输入元素
建立节点Node时,检查该输入元素origins[ori]是否存在父亲节点,如果存在,则进行判断是否满足最大堆条件,不满足进行递归判断,满足就接着输入origins[ori+1]
4. 生成最大堆trs后,进行排序.
4-i)将生成的trs存储(见:本文解析中的二叉堆存储)ns[]中
4-ii)将数组ns[]的第一个元素即(当前树的根元素)与数组ns[]最后的一个元素交换,并且输出根元素(当前最大元素),且从树中删除该节点,ns[]也删除改元素.
4-iii)处理(4-ii)置换后的当前根元素,按最大堆原则,将该元素放到适当位置
4-iv)重复执行(4-ii)直到树和数组ns[]只剩下一个元素.
例子:
注:此图出于https://en.wikipedia.org/wiki/Heapsort
说实话,没有这幅gif,感觉我应该对堆排序还是迷迷糊糊,在这感谢维基百科,希望对大家有帮助.
代码实现:
def get_parent_id(id):
'获取父亲节点'
if id <
1:
return -
1
return (id -
1) //
2
def swap(nums, pid,cid):
'交换'
temp = nums[pid]
nums[pid] = nums[cid]
nums[cid] = temp
def shift_up(nums, pid, cid):
'从下至上判断是否符合最大堆'
if nums[pid] < nums[cid]:
print 'pid:%d, pdata:%d, 与 cid:%d, cdata:%d 交换' % (pid,nums[pid],cid,nums[cid])
swap(nums, pid, cid)
gpid = get_parent_id(pid)
if gpid == -
1:
return True
else:
return shift_up(nums, gpid, pid)
else:
return True
def shift_down(nums,id):
'从上到下判断是否符合最大堆'
length = len(nums)
if id == (length -
1):
return True
lid = id *
2 +
1
rid = id *
2 +
2
if lid <= (length -
2):
if nums[rid] > nums[lid]:
temp_id = rid
if nums[temp_id] > nums[id]:
swap(nums, id, temp_id)
return shift_down(nums, temp_id)
else:
return True
else:
temp_id = lid
if nums[temp_id] > nums[id]:
swap(nums, id, temp_id)
return shift_down(nums, temp_id)
else:
return True
if lid == (length -
1):
if nums[lid] > nums[id]:
temp_id = lid
swap(nums, id, temp_id)
return shift_down(nums, temp_id)
else:
return True
def build_max_heap(nums):
'构建最大堆'
max_heap = []
index =
0
for n
in nums:
max_heap.append(nums[index])
pid = get_parent_id(index)
print '第%d次,pid: %d,cid %d'%(index, pid, index)
if pid != -
1:
shift_up(max_heap, pid, index)
index +=
1
return max_heap
def heap_sort(nums):
'堆排序'
result = []
max_heap = build_max_heap(nums)
while len(max_heap) >
1:
tail_id = len(max_heap) -
1
swap(max_heap,
0, tail_id)
result.append(max_heap[tail_id])
del max_heap[tail_id]
shift_down(max_heap,
0)
result += max_heap
print max_heap
return result
代码测试:
'''
测试部分
'''
def test(nums):
for i
in range(len(nums)-
1):
if(nums[i] < nums[i +
1]):
print '检验不合格'
print '第%d个:%d < 第%d个:%d' % (i, nums[i], i +
1, nums[i +
1])
return
print '检验通过'
nums = [
9475,
5157,
8919,
94,
770,
8260,
3567,
8002,
2575,
8560,
1341,
5297,
8195,
62,
9833,
413,
7274,
5065,
8523,
4140,
5281,
8582,
8515,
3645,
4742,
5093,
6515,
7518,
7754,
4600,
618,
8879,
7306,
5987,
5741,
3062,
3145,
7824,
8114,
795,
8396,
8317,
9867,
4517,
7612,
4175,
9962,
8635,
790,
6198,
6504,
9619,
4526,
2931,
6365,
4266,
6784,
2304,
9778,
2366,
3739,
9990,
6758,
5844,
7644,
6513,
1948,
7340,
6074,
6639,
7072,
4887,
6253,
6752,
7831,
9959,
2822,
4664,
6324,
1699,
620,
4367,
7018,
9248,
4847,
3055,
6938,
6690,
8298,
1303,
14,
4120,
4741,
5544,
5717,
8730,
7597,
8601,
6535,
5306,
2388,
3133,
1906,
349,
9732,
358,
2746,
1805,
4295,
241,
6620,
9532,
4526,
4632,
3862,
71,
8786,
6082,
3848,
3175,
4214,
5938,
5948,
6738,
8829,
1457,
2081,
4133,
9325,
8416,
4234,
5118,
6193,
823,
8159,
5552,
8809,
9620,
3871,
8475,
4121,
6240,
3560,
8613,
1893,
2171,
1622,
3484,
9736,
5597,
7610,
2861,
3935,
6018,
6202,
3577,
2816,
2941,
6681,
8744,
2919,
4032,
5541,
6002,
2196,
186,
986,
6410,
8476,
4251,
6252,
8795,
4010,
2580,
2808,
5067,
4285,
7787,
6138,
1260,
173,
2107,
5934,
4115,
9417,
7860,
5595,
5512,
3129,
6985,
3312,
6781,
4296,
5347,
1060,
5078,
848,
2037,
9586,
3578,
5498,
8233,
4002,
602,
7684,
7615,
3880,
3164,
3874,
1990,
9803,
2078,
532,
1178,
9107,
1172,
4041,
9018,
8528,
1201,
1391,
3036,
8732,
2383,
3629,
314,
8994,
6720,
2442,
3271,
5007,
83,
2022,
4927,
1236,
663,
9447,
622,
450,
7338,
1993,
3810,
7933,
3925,
5447,
5108,
1538,
4594,
1395,
2882,
6914,
4173,
8092,
2367,
9963,
4757,
1013,
296,
5892,
7317,
6541,
9327,
3869,
5012,
326,
9947,
985,
2972,
2437,
1973,
3140,
6518,
3032,
1785,
5475,
6585,
4963,
2984,
7606,
2309,
7371,
18,
5275,
2400,
5126,
3241,
7617,
1181,
3713,
2887,
7837,
795,
8744,
3253,
698,
7098,
6324,
3309,
7927,
695,
8720,
4451,
7631,
4987,
1230,
4506,
265,
979,
1165,
375,
1104,
574,
6155,
2243,
7328,
8861,
2635,
1624,
6868,
2048,
5570,
8748,
5263,
7335,
5277,
2302,
4370,
1046,
8419,
5443,
1935,
9068,
9282,
9154,
3732,
3213,
1217,
3907,
6391,
722,
1652,
9664,
4178,
9710,
4475,
3654,
2577,
4653,
2825,
2095,
2112,
3393,
4245,
710,
3481,
7648,
3377,
1957,
934,
7441,
7677,
64,
6666,
2731,
5931,
8109,
2598,
6588,
7710,
5529,
2866,
8941,
8590,
8628,
6163,
9672,
212,
1772,
3091,
6319,
1114,
4882,
237,
7678,
1544,
2888,
7029,
7866,
2254,
8668,
1331,
9301,
9013,
3763,
840,
4477,
184,
755,
2165,
1767,
5386,
6657,
1387,
1657,
9566,
4292,
2691,
8262,
2892,
5626,
3033,
5650,
3220,
2075,
7363,
2277,
418,
8982,
4963,
7715,
6528,
4030,
6827,
6851,
3134,
8959,
2085,
5966,
9884,
8906,
7377,
7041,
9106,
8040,
2303,
3167,
266,
9539,
7111,
8401,
4463,
5667,
4777,
6602,
3605,
7938,
920,
7475,
4673,
3751,
5109,
3923,
3683,
5809,
9423,
6775,
565,
6652,
7652,
5458,
6022,
2785,
5446,
8737,
7783,
953,
334,
7911,
1962,
3720,
7384,
6310,
5829,
8847,
8694,
2489,
9075,
3231,
3314,
5893,
2830,
5006,
9625,
8889,
7642,
5726,
3247,
1409,
3276,
3765,
8112,
9596,
9332,
3008,
5389,
7266,
217,
6159,
6076,
8173,
5636,
6778,
9617,
2520,
8625,
2117,
1812,
7321,
231,
3754,
8339,
9945,
4532,
6499,
8666,
9193,
2356,
1350,
3279,
6874,
9924,
1297,
7309,
7407,
9260,
3726,
7142,
8728,
3032,
3469,
9077,
2100,
5023,
2981,
9369,
1673,
9423,
5469,
8851,
4632,
434,
2096,
2956,
2707,
3096,
6262,
3489,
2740,
8055,
2288,
1625,
1664,
1041,
4501,
804,
531,
1015,
5544,
2656,
3833,
5009,
4885,
8799,
8592,
8969,
2798,
7546,
2849,
5014,
7581,
9962,
8709,
3997,
7018,
8274,
2272,
9685,
8678,
458,
3826,
5547,
9737,
5937,
5980,
1009,
8637,
9036,
9928,
2605,
4041,
159,
5750,
598,
3257,
9481,
5178,
4861,
6963,
5575,
8784,
7820,
2473,
9519,
2326,
2267,
9034,
7429,
7002,
6986,
5565,
4904,
885,
531,
2802,
5749,
7853,
3312,
3057,
3340,
9231,
651,
8072,
6096,
4868,
1272,
4886,
3275,
7828,
1165,
8429,
9472,
9521,
3005,
8339,
8833,
8417,
3833,
604,
6406,
689,
2405,
9757,
6736,
5316,
343,
7511,
9906,
4933,
8898,
4876,
7771,
1255,
7195,
3725,
4888,
1511,
9649,
9373,
3075,
786,
1553,
1950,
7591,
7310,
106,
266,
4561,
9429,
4856,
7333,
9082,
9224,
1701,
3742,
7784,
9418,
7484,
52,
4960,
2554,
9774,
8929,
5247,
6591,
6360,
4072,
3694,
9962,
5519,
1291,
2234,
7683,
7966,
1398,
9193,
1643,
6735,
4756,
6089,
9379,
2537,
1894,
4682,
8519,
8607,
2278,
1634,
6404,
7465,
8377,
231,
6707,
5405,
6378,
8125,
648,
630,
8850,
8160,
8662,
4152,
3979,
7436,
5719,
2659,
6346,
809,
6793,
9244,
4757,
9313,
7193,
1540,
7628,
3160,
222,
6766,
3966,
608,
4260,
4900,
3422,
6279,
9977,
6340,
3930,
1428,
7537,
4634,
8629,
6939,
716,
8910,
6935,
7090,
9987,
5143,
1419,
7928,
9207,
6094,
5229,
5796,
4838,
8900,
3349,
5043,
4588,
6410,
282,
4273,
8122,
2999,
78,
1766,
301,
3320,
9267,
1496,
8673,
1827,
8160,
584,
6947,
2872,
8867,
1276,
2158,
230,
7110,
362,
4679,
1069,
9397,
8735,
8157,
2172,
1716,
2007,
9556,
6524,
9302,
4029,
4863,
6107,
1470,
3041,
4150,
9378,
7811,
1490,
8494,
399,
2704,
5617,
2789,
3343,
8457,
4201,
5015,
2437,
4345,
6293,
2719,
2322,
6341,
2041,
2946,
4100,
7849,
2507,
2328,
3663,
6001,
1753,
4097,
4867,
8022,
4978,
9131,
864,
3681,
2019,
1828,
7409,
368,
3286,
5059,
7541,
6883,
4894,
6170,
4267,
2768,
7921,
3225,
3817,
8770,
8819,
5095,
8457,
4044,
3331,
4441,
1898,
1440,
3850,
6108,
6652,
105,
8594,
9518,
9208,
1474,
960,
3681,
707,
5467,
9491,
8185,
9988,
72,
7422,
7292,
6641,
1714,
8420,
7405,
9406,
9289,
6327,
4793,
3903,
9602,
9155,
9279,
263,
8308,
5477,
3923,
4658,
3179,
1280,
3092,
4592,
1634,
8620,
6760,
2280,
9681,
7322,
5633,
67,
1815,
6390,
9175,
8084,
3691,
7648,
3358,
870,
6093,
1146,
6008,
8351,
5779,
7928,
8439,
173,
7132,
9838,
5196,
6068,
8572,
2797,
671,
7121,
687,
4500,
288,
6327,
7126,
5816,
9001,
2442,
8108,
6692,
6201,
4280,
8655,
5143,
1065,
3672,
9207,
4502,
7710,
8184,
9826,
8003,
3232,
7005,
8096,
5671,
4607,
5372,
1240,
5733,
7653,
4331,
5196,
35,
6598,
4780,
7638,
5096,
4142,
3531,
6334,
9792,
8452,
2133,
1397,
2734,
3577,
3822,
2817,
4867,
4378,
2717,
9817,
6376,
1425,
1705,
2955,
6782,
8889,
1484,
7571,
9441,
4565,
1025,
7788,
6126,
9015,
1912,
9935,
8673,
3859,
1199,
8024,
9637,
7317,
4891,
4185,
266,
4603,
5292,
3222,
4254,
2118,
2492,
4837,
6880,
547,
6978,
7181,
1893,
5168,
3026,
5821,
1842,
719,
8311,
7229,
4228,
9702,
1565,
7708,
1356,
5083,
8388,
9098,
8400,
6048,
9965,
5737,
8264,
8398,
292,
5791,
6677,
9051,
9508,
5037,
237,
5541,
4701,
4948,
5688,
9057,
3326,
8361,
61,
3707,
3386,
6878,
260,
9990,
5939,
6526,
5793,
1199,
1405,
7562,
653,
3773,
52,
7944,
8178,
2579,
8291,
7990,
3773,
7050,
6692,
2653,
7075,
4347,
326,
5441,
1232,
7293,
8188,
866,
7823,
6395,
6347,
3589,
1429,
6942,
3920,
3297,
4498,
1740,
2169,
9488,
7132,
625,
833,
7232,
9769,
7508,
830,
3719,
3058,
7986,
8024,
4801,
939,
1959,
461,
2185,
1834,
6758,
3830,
9887,
1952,
540,
2699,
5706,
4080,
5882,
6269,
1542,
5721,
7978,
3835,
9277,
593,
5265,
174,
2217,
1630,
7181,
4529,
873,
7106,
5633,
7598,
237,
6849,
4758,
6936,
7495,
5137,
549,
2227,
2969,
1946,
3973,
4769,
8927,
2736,
2721,
9227,
727,
5801,
9023,
6005,
6228,
9372,
1473,
3867,
5479,
7451,
2908,
7368,
2337,
120,
1691,
4497,
2225,
5509,
7933,
6974,
54,
9338,
4724,
3358,
6823,
5566,
2771,
9027,
6913,
9927,
143,
7418,
1868,
5675,
9746,
8808,
5470,
5098,
882,
6181,
4612,
3163,
4052,
429,
1846,
371,
3993,
9429,
4482,
4723,
8269,
380,
8834,
5662,
5782,
8621,
7111,
9280,
1263,
5492,
1354,
413,
8945,
5596,
9665,
2911,
7229,
2613,
3974,
7037,
4803,
4722,
996,
2821,
9030,
5634,
8348,
5791,
1337,
6472,
5223,
8847,
1362,
154,
1806,
381,
4454,
592,
4246,
6550,
3181,
1426,
2715,
507,
5542,
6692,
1081,
8378,
200,
7710,
2991,
6958,
9290,
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9125,
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295,
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820,
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4322,
8524,
7735,
8968,
3305,
5904,
2890,
1837,
7609,
9319,
7954,
8272,
1967,
9121,
3254,
3114,
3311,
2290,
8643,
7835,
6817,
2140,
5151,
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5265,
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40,
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7189,
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1993,
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597,
482,
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1102,
8783,
5912,
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805,
5450,
1203,
138,
6911,
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1979,
2444,
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8787,
4343,
1120,
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1984,
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1977,
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9927,
790,
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7266,
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1982,
6843,
7426,
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1015,
227,
9065,
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577,
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2057,
9650,
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2013,
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3510,
5189,
2532,
9222,
8888,
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8477,
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4763,
5495,
5123,
7822,
4003,
60,
8130,
9326,
7981,
4191,
6815,
1989,
6286,
5662,
6970,
6958,
829,
7367,
344,
1420,
6929,
4355,
3543,
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4240,
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1988,
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119,
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8626,
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166,
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1995,
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355,
8270,
8271,
7820,
7465,
8566,
6148,
2864,
7224,
4282,
302,
139,
7040,
2522,
4416,
9683,
2811,
1786,
5760,
875,
6895,
4770,
3045,
5851,
9115,
2335,
3793,
6118,
5306,
1004,
8489,
2630,
6837,
8633,
9603,
591,
6947,
3038,
5951,
1878,
270,
6149,
5451,
3977,
3644,
928,
6006,
106,
4494,
7079,
3778,
9321,
172,
1998,
9114,
5295,
2004,
4242,
966,
1303,
4966,
6521,
2133,
1307,
8490,
8190,
8352,
6940,
7976,
8570,
263,
8302,
7416,
5930,
4407,
6130,
5972,
7045,
5583,
124,
7612,
5148,
7043,
4941,
188,
4859,
9055,
1361,
5393,
2095,
5300,
382,
2058,
9152,
405,
1072,
4842,
7697,
5055,
854,
8753,
5771,
3513,
3387,
6092,
3541,
2770,
6471,
7653,
6983,
6709,
5378,
116,
2915,
7866,
3422,
5939,
7399,
5352,
4066,
3003,
4383,
7088,
7975,
4751,
8998,
854,
7621,
465,
6964,
126,
2279,
3860,
6131,
58,
3059,
7247,
1211,
4922,
4429,
9213,
3527,
9413,
5503,
9817,
1714,
6553,
5500,
9431,
8813,
577,
3597,
9722,
9713,
6005,
4175,
8415,
3689,
2601,
1966,
7042,
2551,
5544,
7064,
9758,
2126,
1549,
8250,
9693,
4668,
9133,
6332,
5808,
3631,
573,
8254,
4861,
4569,
5068,
1988,
8549,
5648,
3314,
5458,
8990,
1815,
4809,
4504,
8342,
7067,
5915,
3250,
2963,
7413,
3925,
6775,
9524,
2407,
4199,
2053,
2484,
2196,
3951,
5440,
6299,
317,
8960,
8212,
1539,
7688,
7839,
2770,
3367,
7228,
4113,
1235,
1709,
6432,
2715,
7079,
7400,
3878,
716,
3411,
1956,
5902,
75,
1220,
621,
7455,
9075,
4453,
4464,
7022,
1175,
1685,
6391,
6450,
8265,
8828,
8820,
6181,
8351,
6510,
2496,
9537,
2800,
5705,
1971,
7398,
2185,
6105,
1511,
9323,
4598,
7836,
6916,
6050,
1184,
4575,
6759,
2133,
3846,
5364,
5920,
6351,
6796,
592,
8777,
9556,
8293,
706,
2716,
6667,
5015,
2164,
3142,
4638,
9224,
237,
9075,
3362,
9756,
2447,
8702,
6727,
7521,
4832,
9262,
3486,
1132,
57,
6805,
3622,
1405,
1317,
328,
4691,
1297,
3225,
2117,
7578,
4765,
5270,
175,
143,
1603,
3308,
9569,
2847,
5320,
5213,
9081,
941,
2503,
4257,
6268,
709,
2575,
5115,
8718,
5197,
754,
6275,
2418,
8300,
685,
3019,
6403,
1995,
5007,
5872,
1968,
2418,
8806,
6146,
3200,
2928,
9402,
9895,
4847,
7668,
3750,
9817,
39,
6851,
4350,
6202,
8286,
505,
4890,
3529,
6817,
142,
5383,
5011,
1493,
2763,
3068,
6794,
1524,
9295,
5728,
8391,
4347,
4826,
2908,
4626,
6246,
3736,
8663,
2456,
6520,
6750,
4991,
2228,
4666,
959,
7592,
9860,
9159,
5244,
7068,
635,
9402,
1484,
8170,
6816,
6574,
9240,
8641,
9194,
3840,
3767,
3252,
5940,
2182,
3193,
8690,
1144,
1188,
4437,
7712,
6093,
1922,
8482,
7531,
5774,
6465,
6680,
7606,
2686,
6703,
5138,
7890,
2266,
706,
5518,
5154,
7759,
6105,
5475,
5088,
4039,
3232,
2710,
923,
4656,
7865,
3558,
7162,
2855,
6760,
3324,
3020,
4408,
2553,
590,
5851,
7555,
4058,
2694,
3181,
8369,
2325,
7377,
5585,
3670,
3600,
8580,
9666,
2541,
9221,
2609,
3286,
4887,
4810,
6148,
7674,
9098,
2784,
9088,
2321,
5200,
5156,
5354,
4266,
9975,
6419,
1686,
502,
4213,
4459,
3021,
1319,
9114,
7313,
7095,
2625,
8258,
5411,
6342,
3499,
9278,
5074,
9789,
3394,
9885,
6766,
5928,
2077,
4200,
7497,
7437,
9929,
7797,
632,
5756,
6392,
3672,
2142,
5097,
1866,
9186,
7587,
6277,
4619,
2723,
9772,
25,
8820,
5436,
1548,
9673,
1820,
3040,
7665,
7266,
155,
8067,
7017,
462,
8668,
5539,
700,
3220,
5404,
7107,
2356,
7104,
5028,
7901,
8568,
9843,
6093,
6396,
6244,
4914,
9006,
4291,
3171,
6995,
4023,
6051,
1659,
8320,
3495,
1527,
8382,
5331,
4256,
8535,
5403,
5446,
2977,
1034,
4149,
8912,
5784,
1078,
228,
2425,
3141,
3325,
4629,
9159,
7263,
8511,
5659,
1894,
7482,
9431,
6705,
7531,
4761,
3350,
3444,
5200,
3560,
8304,
9354,
1586,
557,
1530,
3434,
8153,
1929,
490,
9191,
5762,
7627,
8292,
8811,
9786,
2430,
4767,
8869,
6165,
1624,
9280,
9152,
4355,
1987,
4138,
6883,
9626,
7723,
6385,
3751,
424,
3371,
1455,
7564,
5770,
8586,
2458,
1413,
7598,
3630,
4039,
8442,
935,
1365,
2065,
8811,
3984,
8857,
8433,
7331,
6255,
4554,
5650,
231,
5641,
2457,
5352,
1061,
6854,
1996,
6940,
1124,
2430,
1613,
9984,
265,
3722,
3210,
3394,
9611,
5271,
7716,
6761,
4435,
477,
8417,
8537,
8233,
512,
5739,
8826,
9239,
6717,
462,
9215,
4555,
7642,
7538,
1594,
9893,
1574,
585,
6285,
1546,
6147,
5189,
3791,
8465,
4059,
2759,
5604,
4321,
1658,
766,
2691,
4075,
545,
6929,
1756,
504,
5547,
1560,
5921,
6063,
1196,
6780,
4275,
3459,
4868,
9847,
2541,
5058,
3991,
3155,
1352,
7023,
4400,
9274,
4220,
6392,
9712,
1899,
5758,
8073,
6353,
7908,
3110,
4278,
6182,
6099,
1143,
8560,
7957,
32,
1150,
9341,
7987,
451,
4079,
3837,
1215,
3690,
2659,
7880,
773,
7109,
7175,
2874,
5684,
1846,
5063,
9902,
9091,
4003,
789,
2338,
1470,
5721,
9397,
2247,
662,
6996,
9220,
318,
689,
40,
4849,
6091,
9681,
6278,
4816,
4610,
7688,
4777,
1730,
1098,
5810,
463,
4363,
3947,
2940,
6626,
9072,
5517,
2884,
9050,
6240,
8241,
3365,
6886,
9848,
2015,
307,
4308,
8044,
7919,
3377,
2309,
2888,
9357,
6716,
8741,
5789,
9200,
4912,
4049,
5615,
7191,
2448,
6153,
2627,
2365,
4666,
1617,
1827,
8007,
3557,
9657,
5173,
1766,
9711,
247,
6044,
4381,
1427,
9491,
7542,
4317,
5286,
7897,
734,
3789,
2969,
5674,
8205,
7877,
1080,
4901,
5089,
1703,
9915,
8449,
9585,
1403,
7306,
881,
8266,
6152,
6872,
7545,
9603,
5604,
7333,
9166,
3235,
1759,
5553,
7204,
5875,
2548,
7457,
9813,
4037,
7157,
2052,
3097,
2221,
3643,
56,
6370,
7089,
740,
9,
9385,
4571,
7863,
8939,
3033,
7607,
2602,
2615,
486,
3339,
3887,
2975,
1078,
7285,
8242,
7940,
2834,
1518,
2629,
3895,
8277,
5101,
4741,
9831,
6744,
7781,
9685,
3793,
9210,
9584,
267,
110,
5414,
8717,
5045,
9492,
8737,
5311,
5304,
5861,
2772,
2247,
9349,
1379,
5676,
4326,
7310,
4997,
571,
7729,
4115,
894,
3493,
2588,
397,
3145,
4649,
1194,
4131,
3038,
5205,
8951,
9362,
8250,
4076,
3181,
6693,
3772,
1271,
8967,
9409,
5867,
4269,
8806,
2094,
4566,
2636,
5284,
7342,
3684,
9997,
2572,
1220,
6656,
4033,
181,
4255,
7537,
6575,
2274,
2481,
4519,
1560,
9911,
4315,
963,
9347,
2051,
1581,
2371,
8291,
1302,
7841,
3273,
2329,
9052,
5967,
646,
9524,
24,
8845,
9053,
9462,
7042,
6631,
7266,
4407,
9925,
5346,
69,
7022,
8772,
9842,
1478,
3018,
9427,
3651,
936,
21,
6235,
7203,
2027,
6094,
7253,
4624,
8179,
757,
9836,
8480,
1710,
4093,
4926,
3203,
8535,
7027,
5394,
1975,
3034,
2158,
2020,
2173,
7441,
4820,
6599,
3248,
7104,
6396,
7460,
4843,
5157,
3201,
3229,
3630,
6793,
3669,
856,
5834,
9742,
3426,
8716,
6373,
9061,
6172,
4022,
3539,
6297,
2606,
6387,
6057,
6207,
2177,
6114,
3274,
8768,
9337,
6344,
1369,
30,
4745,
3435,
518,
3207,
2793,
809,
8459,
1850,
7186,
8963,
4254,
4781,
438,
6962,
318,
9945,
1355,
1400,
6675,
2504,
5407,
8226,
8294,
5883,
8420,
4394,
5175,
2303,
5871,
7220,
2937,
8352,
6642,
8727,
1767,
8475,
9116,
1802,
6444,
5033,
4860,
7851,
3253,
8133,
8201,
2439,
3982,
332,
3804,
3822,
2663,
4721,
7117,
5693,
5118,
6422,
4405,
1505,
5732,
9719,
2282,
5645,
3437,
6894,
9054,
1633,
5403,
7751,
4849,
9868,
282,
450,
7528,
8381,
7410,
9575,
4071,
1940,
4384,
8113,
4656,
199,
8758,
3466,
1201,
3714,
6250,
650,
7656,
1392,
3254,
5098,
5710,
5495,
244,
5866,
5360,
6203,
4486,
3728,
9704,
6272,
44,
3301,
4056,
5630,
2164,
2656,
675,
7854,
9208,
1008,
747,
5740,
3005,
4425,
5410,
1981,
45,
7580,
4778,
3372,
4612,
8817,
8155,
8099,
3865,
9148,
9734,
617,
142,
793,
7676,
816,
9250,
8594,
7893,
5993,
6381,
2915,
1573,
4985,
5183,
251,
792,
192,
9414,
1565,
4993,
7770,
5698,
2668,
8548,
1958,
4906,
4250,
616,
1266,
1038,
9966,
2442,
5627,
7823,
6182,
8875,
1361,
2997,
2218,
2442,
4562,
9255,
9605,
6796,
2960,
6395,
7690,
4988,
7708,
424,
455,
223,
1026,
3511,
3917,
3032,
5848,
7030,
4058,
5841,
7118,
4137,
6537,
9244,
1117,
1961,
9105,
7586,
2651,
5318,
6200,
3130,
1095,
5899,
6597,
4690,
4756,
2185,
7308,
4713,
3699,
8337,
8483,
1911,
408,
1984,
5555,
4686,
8233,
563,
4274,
6904,
3893,
5112,
8498,
9873,
2682,
442,
9304,
7379,
2387,
9240,
2205,
2565,
1555,
558,
7954,
1088,
2116,
4089,
3858,
4223,
9104,
993,
4942,
1043,
2785,
4118,
9347,
7570,
4398,
5039,
2007,
685,
7322,
4397,
8586,
434,
9328,
4111,
3104,
7023,
3149,
221,
8888,
9106,
6322,
1798,
2215,
8059,
8942,
8523,
5866,
8568,
7496,
8591,
3341,
4295,
6917,
842,
2253,
8603,
1642,
8157,
6897,
4492,
704,
3859,
796,
3070,
8775,
1554,
4039,
7268,
7287,
8757,
7819,
3147,
9749,
1246,
8153,
8593,
2223,
9130,
7922,
7740,
4196,
6193,
3552,
9649,
8634,
7464,
6175,
2448,
7349,
6933,
3273,
7913,
4222,
4393,
9369,
422,
6433,
6067,
7131,
3219,
6807,
821,
779,
4831,
7535,
7285,
8286,
8672,
2079,
3423,
3871,
9292,
5235,
279,
8429,
8853,
6290,
308,
5766,
1634,
3873,
7502,
716,
9322,
3870,
4370,
4235,
9927,
6509,
2759,
2208,
3701,
3093,
5861,
3447,
6944,
5814,
9267,
9527,
9131,
9550,
3074,
1765,
1165,
5526,
7481,
6247,
8281,
6957,
5789,
8148,
4569,
5104,
7029,
6902,
1461,
6621,
1259,
5067,
6874,
5179,
8315,
1072,
7203,
9484,
8019,
9248,
7290,
3657,
9362,
6739,
5069,
9406,
5030,
1547,
3532,
9537,
1805,
3908,
8500,
2487,
453,
4951,
3373,
6568,
6537,
430,
7231,
5597,
1074,
6498,
1511,
8533,
4409,
9231,
7405,
3362,
803,
8434,
2664,
1515,
6982,
690,
6585,
2865,
7251,
3589,
3868,
8754,
4944,
4576,
8549,
9960,
3216,
2003,
3656,
7622,
6858,
6526,
6491,
7910,
1665,
1694,
4297,
2486,
2915,
9651,
7438,
5703,
2848,
8954,
8811,
2380,
7276,
6882,
5682,
9363,
5488,
6705,
4854,
3363,
7419,
9679,
7642,
7822,
478,
9430,
8389,
6133,
4728,
9096,
7254,
799,
3520,
827,
722,
7869,
3406,
5811,
8318,
2400,
5946,
2902,
2939,
6276,
6920,
2968,
4560,
9483,
614,
9818,
7916,
6061,
2673,
1832,
7907,
1345,
3454,
3275,
778,
9081,
9396,
9473,
136,
3074,
989,
3394,
8558,
6574,
1863,
7437,
3288,
8292,
6036,
7737,
3074,
6879,
1690,
5827,
3672,
4400,
2991,
4883,
9382,
6867,
4555,
6277,
9319,
2954,
7231,
2155,
9168,
2565,
954,
8991,
5650,
1307,
4763,
5253,
3881,
2793,
5756,
5884,
5315,
2866,
9382,
3753,
3823,
4183,
4762,
872,
2227,
9526,
7649,
357,
5041,
2521,
3919,
5750,
1116,
2782,
3338,
8311,
7614,
1237,
4023,
4100,
9767,
5595,
5812,
3879,
8505,
3768,
4196,
526,
9301,
7533,
1435,
6129,
7717,
6767,
6543,
2433,
4605,
7043,
8463,
1466,
4171,
4366,
6289,
8879,
6874,
8168,
2766,
6810,
4535,
8254,
4828,
7713,
3794,
2169,
2599,
7816,
236,
9005,
1914,
3735,
8302,
9260,
3296,
4650,
5619,
1943,
6052,
2012,
956,
826,
4456,
213,
8828,
5772,
6491,
4698,
3001,
7386,
6980,
7025,
254,
8017,
2484,
9283,
5044,
6086,
389,
6715,
8408,
723,
141,
7817,
9290,
8230,
2971,
4600,
7745,
5343,
7481,
1748,
7236,
1245,
1795,
8386,
4029,
5423,
6017,
6453,
970,
3157,
5103,
2516,
8641,
6502,
3145,
1421,
6139,
7935,
4732,
2822,
612,
5115,
2534,
660,
3028,
1961,
8586,
5674,
1522,
8979,
3593,
2056,
6575,
8492,
5000,
3253,
4462,
4629,
1452,
6615,
5593,
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6716,
6181,
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1438,
4607,
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245,
9128,
4642,
9388,
4629,
9420,
5592,
4089,
3598,
4058,
7546,
9351,
224,
1548,
2333,
3127,
3627,
7593,
7724,
8515,
3952,
8039,
6800,
1456,
923,
6852,
4807,
5958,
6654,
1045,
1181,
5919,
1927,
1417,
9570,
743,
5715,
3629,
6864,
3649,
8027,
1773,
8987,
865,
1515,
6915,
8166,
1473,
5564,
3349,
5571,
2579,
7794,
8672,
7798,
4898,
2813,
9288,
650,
921,
1791,
6760,
2063,
5086,
4438,
3822,
3923,
3230,
1293,
393,
5238,
4877,
9,
6028,
6854,
1924,
6458,
6003,
9465,
1144,
6899,
8493,
4058,
2520,
5587,
6188,
4694,
2988,
9098,
9813,
8178,
2707,
8655,
2266,
2144,
6947,
4265,
7937,
8170,
4072,
4769,
2205,
398,
8798,
8589,
3406,
5866,
1289,
6806,
3795,
6681,
4346,
4736,
7987,
7980,
346,
9979,
5954,
3222,
6716,
434,
78,
9720,
4661,
9540,
2659,
7139,
4862,
9002,
6416,
6021,
9710,
1252,
3302,
3859,
8253,
568,
1974,
1733,
6508,
1160,
1562,
925,
8194,
6524,
9410,
3353,
5283,
1293,
3301,
1937,
4194,
4508,
5777,
6210,
6667,
9904,
5896,
1820,
3065,
9239,
1189,
5053,
295,
3913,
5644,
9090,
5832,
5748,
7870,
5655,
2041,
6894,
6946,
1034,
7026,
2754,
9785,
8421,
6054,
7683,
9662,
7502,
1106,
6316,
7865,
3266,
4323,
3565,
9563,
4634,
1112,
6261,
7594,
804,
6751,
1232,
475,
6176,
3872,
3779,
5383,
7748,
1220,
1329,
3982,
4621,
2959,
8457,
2494,
7263,
4085,
347,
3318,
205,
4165,
117,
6107,
3315,
2310,
9202,
403,
5552,
9729,
2395,
5916,
699,
2103,
9974,
2508,
5039,
5269,
2035,
720,
2669,
9259,
4011,
4500,
5991,
6128,
7626,
5116,
9916,
5267,
1688,
6804,
439,
8927,
4144,
3165,
4113,
5622,
6369,
1190,
3998,
8471,
6921,
8708,
5799,
3836,
60,
8557,
9948,
14,
1709,
4930,
2648,
3832,
1952,
7818,
8746,
4652,
6823,
3847,
4286,
7641,
5361,
5780,
1890,
2631,
1866,
1877,
6440,
9972,
1805,
7586,
632,
2537,
9390,
5521,
1626,
3800,
2799,
4851,
208,
6228,
9314,
306,
7650,
3264,
5031,
3037,
7810,
4551,
1851,
7318,
143,
3090,
8926,
3810,
1527,
5365,
6657,
8351,
7100,
4061,
9540,
6334,
8150,
9357,
4346,
9882,
784,
6001,
5978,
1808,
2320,
6754,
4880,
4628,
5139,
1378,
9596,
5502,
8750,
3892,
8409,
8723,
9139,
6341,
7575,
5388,
5314,
864,
6236,
8275,
3038,
6739,
8363,
8705,
3155,
638,
3262,
7154,
1719,
4276,
5967,
4507,
452,
667,
9081,
1716,
4753,
2934,
8274,
4729,
4921,
6969,
2963,
3955,
3086,
3554,
783,
2869,
7188,
6754,
1435,
646,
2097,
6753,
56,
4230,
7610,
529,
5199,
9351,
1547,
6651,
6041,
7411,
8135,
8079,
2381,
3821,
9473,
9502,
2892,
2796,
1203,
6393,
7832,
7488,
6269,
7636,
4041,
1626,
6392,
3064,
5804,
9589,
3800,
6964,
4855,
4677,
7556,
7710,
3448,
4274,
8371,
6049,
5747,
4599,
7357,
7898,
346,
9350,
5787,
2048,
1003,
9484,
7593,
2736,
1592,
5122,
2419,
7129,
5097,
8712,
9071,
5986,
1211,
2131,
9408,
9220,
4313,
6304,
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2895,
8474,
8994,
9682,
3613,
2134,
1438,
1889,
9376,
1630,
1769,
7128,
8996,
8978,
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3206,
791,
9420,
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1654,
1245,
7964,
2864,
9068,
2023,
7503,
5253,
1404,
9108,
5503,
5544,
2271,
4617,
2380,
4481,
5140,
22,
329,
7543,
7267,
1635,
8834,
4839,
8874,
7675,
5755,
8260,
8917,
4313,
1779,
3118,
5377,
4566,
7292,
6140,
7815,
153,
3408,
7524,
5388,
2933,
1288,
2999,
797,
7940,
858,
7660,
2129,
917,
6049,
3123,
8740,
5520,
6250,
3069,
63,
7179,
5556,
9992,
9892,
9541,
6851,
4268,
525,
2545,
6399,
7065,
1390,
3506,
1539,
708,
5974,
2685,
4483,
6913,
2751,
6110,
9318,
5021,
6368,
3520,
3165,
6698,
6332,
6058,
9542,
7293,
8972,
7623,
7391,
1334,
2500,
820,
1955,
9313,
1344,
5093,
34,
1480,
84,
1012,
8394,
9299,
8651,
5439,
4421,
2464,
2729,
61,
1493,
3297,
1259,
9187,
6780,
3455,
4828,
3134,
4376,
7056,
7581,
7102,
4920,
2093,
9757,
282,
1237,
2621,
1200,
2047,
7258,
4269,
6433,
2187,
7672,
9799,
6150,
5484,
3873,
154,
5898,
5968,
9035,
5553,
2828,
6718,
7678,
8548,
5691,
9991,
338,
6535,
3230,
847,
224,
2679,
7768,
3725,
1855,
5142,
8517,
9076,
9712,
2687,
2373,
5833,
832,
7735,
1626,
6380,
6279,
1942,
3684,
8482,
9398,
2508,
9577,
3655,
6119,
1788,
8290,
6988,
5517,
809,
7318,
5034,
2250,
6702,
1626,
8206,
5023,
7842,
8751,
3777,
2191,
8253,
7622,
2767,
466,
4958,
2078,
8232,
6597,
7015,
6718,
4063,
7720,
8452,
7379,
6934,
9299,
7575,
6834,
6180,
9203,
3379,
3989,
228,
2455,
637,
6986,
103,
528,
6979,
4759,
5267,
5207,
2735,
8725,
9338,
2937,
7727,
8915,
4227,
6541,
3593,
7796,
8194,
9335,
5664,
823,
7159,
9078,
4217,
542,
6816,
6829,
8977,
626,
2554,
7541,
1162,
4709,
3641,
4693,
6020,
3253,
9896,
4111,
9761,
528,
6790,
1270,
3814,
6038,
4865,
3183,
7920,
2485,
1437,
5296,
1747,
5986,
255,
8432,
3300,
7515,
6385,
9760,
3287,
470,
3142,
4124,
6786,
4092,
7775,
3379,
9415,
5377,
3694,
6772,
4069,
8084,
7640,
396,
9138,
1973,
2550,
4519,
8423,
98,
2217,
3999,
7993,
3706,
2570,
3030,
3062,
7870,
1351,
6939,
5542,
9111,
3271,
4551,
6244,
9140,
5317,
4809,
4871,
6122,
8978,
2083,
7620,
3538,
8149,
4252,
7855,
4560,
4742,
1352,
4969,
9358,
4110,
692,
2924,
605,
7223,
9578,
7240,
5268,
1893,
2702,
4449,
2230,
5595,
5799,
1591,
6396,
6232,
7458,
9083,
6820,
7708,
3649,
768,
9961,
9456,
4397,
7882,
4592,
8412,
976,
6401,
8836,
9759,
7720,
2791,
1668,
8697,
4752,
3319,
7527,
1427,
536,
9795,
6024,
1313,
5398,
1622,
3388,
5328,
5271,
3919,
9793,
290,
4960,
397,
5395,
4944,
2406,
735,
5128,
9821,
8359,
1458,
4698,
2265,
4521,
553,
4406,
9945,
1426,
1834,
2621,
3311,
3152,
995,
670,
6329,
6071,
8086,
6092,
2231,
356,
4367,
1048,
5338,
7167,
1075,
5130,
563,
1482,
550,
2982,
1631,
814,
3013,
3260,
3425,
3729,
833,
3757,
2904,
9657,
884,
437,
6080,
1530,
9278,
7218,
46,
579,
6717,
9879,
5302,
4140,
9110,
1198,
5926,
9007,
8425,
3029,
6382,
6677,
3494,
9289,
1591,
9901,
1975,
6689,
4111,
3127,
9607,
7110,
3605,
591,
6945,
231,
1630,
5138,
7765,
4125,
7257,
4978,
8679,
3747,
4199,
813,
9596,
2744,
7863,
9452,
3299,
347,
6043,
6737,
7336,
7738,
8720,
2006,
5839,
7793,
1743,
4733,
7749,
2481,
5962,
8094,
9642,
2332,
3984,
9896,
264,
9310,
1091,
3312,
9820,
9002,
9119,
8402,
9601,
6377,
4245,
9438,
2837,
6281,
2485,
7405,
5273,
8806,
8132,
4593,
9893,
2379,
3904,
6744,
4178,
8648,
6610,
8284,
9059,
6410,
2083,
9762,
8721,
3056,
7836,
5995,
8920,
5474,
8660,
3861,
6109,
3365,
9729,
2155,
7065,
3431,
1334,
1875,
1725,
7532,
3631,
1575,
1775,
5903,
2156,
5306,
8575,
704,
8902,
1980,
6451,
1301,
2344,
3870,
6827,
4527,
7698,
7636,
4600,
3985,
9127,
8269,
4612,
5305,
8565,
3739,
9697,
9902,
8737,
5606,
4101,
5634,
3220,
3926,
4196,
1587,
4209,
9121,
3461,
7796,
5679,
6592,
8422,
1967,
8900,
3002,
3833,
6889,
8221,
2077,
4392,
3765,
6570,
3611,
8396,
7974,
1746,
604,
134,
6329,
5663,
6840,
7267,
3187,
5947,
3688,
1373,
3444,
9454,
4746,
9001,
6881,
222,
6449,
675,
9485,
5472,
7549,
6570,
2801,
4176,
3926,
998,
6908,
3170,
2135,
1811,
1036,
7798,
4491,
8752,
6776,
7609,
1606,
54,
2083,
9417,
8418,
3452,
8400,
5893,
5707,
927,
5357,
813,
6301,
741,
5447,
6124,
9369,
1890,
9326,
9736,
1758,
377,
3831,
8015,
5661,
7391,
998,
6722,
7816,
424,
3682,
7599,
4782,
2915,
2112,
2894,
2471,
6736,
5280,
5352,
1386,
3280,
1999,
6190,
969,
7590,
241,
3976,
7429,
608,
9547,
4426,
6061,
6441,
8763,
5553,
1014,
1580,
4693,
4451,
4372,
1030,
1573,
5336,
3297,
5370,
5394,
3586,
9130,
2321,
3129,
1217,
1289,
3772,
8068,
2296,
5056,
6497,
5475,
1873,
8273,
9765,
3732,
522,
4175,
7401,
3606,
8674,
3640,
6901,
7858,
7929,
1289,
9485,
6804,
7062,
9705,
4897,
8762,
8830,
594,
4294,
6593,
5272,
2114,
6537,
2094,
2090,
8396,
3244,
6850,
3486,
7262,
9688,
509,
8950,
4322,
3710,
6225,
7930,
1636,
7517,
1832,
5198,
1172,
2214,
3959,
3314,
5926,
6356,
7686,
4890,
8586,
3497,
9537,
1976,
8877,
5837,
1877,
4163,
8934,
760,
8080,
930,
1835,
9609,
6223,
7831,
728,
4527,
9612,
6567,
5956,
1311,
5571,
9510,
4730,
4412,
8316,
2520,
376,
7868,
4196,
4768,
113,
6050,
7001,
7830,
8469,
6491,
8011,
4411,
4663,
1916,
9935,
6463,
1238,
4546,
615,
3904,
8177,
2893,
8995,
2463,
203,
4225,
2828,
8969,
3753,
9744,
5960,
3264,
198,
7162,
4927,
2927,
5896,
8054,
8014,
2929,
6293,
3504,
9423,
6286,
1028,
1155,
7773,
3614,
1408,
5986,
1428,
2321,
4343,
2674,
1187,
8947,
4790,
2896,
7722,
8412,
2969,
6336,
9746,
2445,
5317,
191,
2195,
7830,
1460,
1896,
2758,
9694,
721,
2894,
2641,
9395,
6901,
766,
1664,
5259,
1427,
6470,
7180,
3433,
6590,
9440,
226,
9253,
2982,
1685,
1543,
2075,
6848,
468,
7016,
971,
1032,
9292,
6000,
7600,
2018,
4453,
3433,
7842,
6138,
3900,
4539,
8102,
9954,
6074,
3747,
1924,
1249,
3935,
7696,
7319,
3635,
8582,
1988,
5554,
5851,
4804,
5410,
5225,
3632,
5922,
6412,
4074,
5992,
832,
2909,
9545,
6150,
5591,
2911,
1227,
1738,
5421,
2322,
5902,
1282,
2955,
4069,
7488,
3481,
9124,
6120,
9365,
7733,
7546,
5694,
5317,
7821,
772,
5206,
4406,
997,
1051,
9196,
8864,
7870,
7907,
8446,
1506,
8759,
2618,
7092,
6542,
8072,
7883,
2113,
6577,
9337,
2611,
503,
5669,
4939,
4812,
6798,
7848,
8282,
8528,
7368,
6976,
6495,
8412,
53,
1393,
9210,
3517,
1840,
5139,
63,
7142,
7216,
9811,
8820,
831,
6548,
2704,
9458,
4356,
7514,
5508,
1247,
8365,
2998,
520,
4476,
6150,
8452,
4895,
6357,
3101,
6032,
5342,
270,
7159,
3057,
8058,
7676,
1135,
5271,
5908,
9272,
1335,
4968,
756,
9374,
3066,
1355,
5259,
8460,
4835,
330,
3932,
5249,
565,
5182,
7886,
2010,
1121,
9391,
2928,
3331,
6278,
9175,
615,
7594,
4017,
2760,
8243,
3624,
8614,
8517,
9759,
600,
1556,
8472,
4612,
8976,
2825,
5857,
2175,
5691,
4594,
4597,
1853,
9479,
2163,
6905,
85,
9648,
9165,
3214,
6438,
2368,
9901,
8926,
239,
3864,
7697,
4538,
7678,
2840,
917,
5908,
7768,
9283,
6746,
935,
9963,
6107,
6909,
9599,
7573,
5193,
6071,
4451,
9410,
7770,
8507,
7962,
7861,
5275,
9104,
7598,
5991,
7938,
9335,
3481,
1298,
5613,
2207,
5352,
8135,
1161,
8644,
6572,
3106,
2226,
2336,
7985,
649,
2744,
2481,
2840,
156,
366,
6163,
685,
9887,
7161,
4385,
4837,
3717,
309,
7978,
7673,
8152,
8494,
3866,
6392,
4657,
9689,
8760,
9618,
2676,
8446,
5714,
402,
5082,
9636,
9469,
9759,
756,
3347,
4424,
5582,
7761,
605,
2341,
4242,
9731,
8523,
3810,
5041,
6009,
2396,
7974,
5132,
5432,
6507,
307,
8174,
2863,
8302,
9969,
7362,
2523,
5178,
7409,
8826,
8776,
7308,
3376,
8159,
6014,
8479,
1245,
1047,
7758,
2688,
6341,
1246,
2389,
2790,
3840,
6001,
7462,
8185,
2217,
689,
3682,
4219,
8486,
3297,
416,
9909,
8566,
5033,
1245,
1513,
1928,
3954,
5312,
8946,
9289,
4051,
1909,
4319,
765,
3341,
8952,
3288,
2239,
5545,
8824,
1569,
8420,
6098,
12,
6705,
8692,
6601,
4027,
4971,
1319,
2915,
7578,
5441,
7265,
3285,
3183,
9358,
8680,
4031,
7056,
2909,
7547,
2482,
5132,
7686,
4080,
6856,
3415,
9125,
4127,
9375,
8348,
4586,
2839,
2658,
4326,
7104,
7290,
2209,
3909,
1620,
2540,
1984,
6426,
2753,
4495,
2098,
8116,
3510,
4970,
3771,
9691,
2883,
7478,
9785,
2614,
9932,
4875,
5488,
2002,
1345,
5494,
834,
8773,
1713,
9196,
8656,
765,
5705,
2872,
5373,
3793,
7731,
1145,
2817,
9814,
3945,
7496,
3691,
7190,
4759,
2280,
1960,
439,
2058,
7083,
4750,
9903,
7398,
3292,
4397,
4434,
5519,
4023,
2142,
9202,
2925,
3911,
4706,
6,
7956,
1876,
6316,
3722,
4666,
5870,
5238,
1113,
3953,
8122,
6766,
70,
1367,
6941,
3580,
8364,
9595,
4806,
6173,
6796,
4026,
1911,
2927,
2924,
1712,
1854,
5049,
1343,
3533,
493,
1936,
2375,
8039,
7814,
2948,
360,
8932,
2531,
2296,
2252,
8661,
6852,
5180,
1774,
497,
2036,
2711,
4156,
6764,
7285,
4626,
55,
3320,
8789,
1705,
5240,
9429,
9710,
1996,
5706,
1814,
14,
7523,
3524,
7813,
128,
8096,
9348,
3501,
5257,
5277,
1926,
5877,
2811,
8125,
4123,
7849,
3466,
3585,
2210,
5950,
9995,
45,
7153,
7166,
8682,
4697,
4596,
2342,
9427,
1457,
7159,
5176,
7713,
3422,
4378,
8485,
7519,
2803,
6634,
4529,
5071,
765,
3711,
6813,
866,
4374,
2503,
175,
3403,
6756,
6232,
6496,
607,
549,
4629,
7771,
4391,
2673,
919,
4700,
5985,
2064,
3822,
8736,
4744,
6809,
2763,
1628,
3883,
5135,
263,
4743,
5448,
5313,
5830,
9701,
5980,
8066,
454,
9080,
8840,
6952,
5721,
4415,
796,
6075,
4341,
75,
7644,
6075,
1232,
8036,
8551,
3033,
9691,
9385,
4142,
9350,
5685,
3449,
8068,
5828,
2117,
7468,
4814,
5324,
9626,
5732,
4547,
2496,
477,
3861,
6098,
1607,
3140,
8909,
2282,
787,
1866,
4515,
818,
5405,
5872,
9874,
3877,
5930,
2199,
5468,
8151,
8949,
6269,
9973,
708,
3449,
3663,
5244,
4963,
9441,
5812,
4613,
7607,
2509,
2829,
426,
7337,
9825,
7061,
817,
5847,
5723,
1852,
2221,
8885,
5468,
6026,
878,
2645,
2690,
9106,
6805,
4881,
8467,
7562,
7055,
8209,
2050,
8953,
7912,
5471,
5629,
5941,
569,
8756,
2611,
2265,
2305,
5639,
4598,
255,
8389,
4165,
3580,
3223,
1090,
529,
6097,
5769,
4297,
3068,
351,
2917,
6781,
3161,
7522,
3647,
2257,
3462,
5080,
6130,
5552,
5779,
8201,
9715,
2353,
4105,
6594,
4980,
9128,
3577,
1468,
1213,
3426,
6507,
9485,
5917,
7906,
7451,
8569,
8920,
2879,
5031,
126,
891,
8530,
4841,
3716,
124,
8249,
7715,
4229,
7947,
274,
6500,
1033,
1136,
6682,
8211,
1930,
9553,
3410,
8247,
6695,
2955,
8247,
3181,
4347,
8652,
6119,
6489,
1959,
1836,
7904,
7290,
1097,
3044,
1937,
1569,
900,
6583,
245,
6570,
4366,
6613,
9464,
1531,
1845,
4839,
4851,
785,
3532,
4297,
604,
3340,
2495,
4447,
9340,
2251,
7427,
1487,
3346,
8107,
851,
7656,
6152,
9356,
6704,
9582,
7889,
3584,
427,
7548,
4382,
1538,
3398,
874,
8693,
6916,
1305,
1989,
582,
8302,
8191,
8077,
7458,
3757,
3170,
7360,
3345,
4667,
2204,
9805,
5925,
3858,
9175,
7924,
2466,
4900,
4298,
2607,
3468,
8855,
7235,
7441,
2745,
6523,
6203,
9608,
1664,
3050,
8027,
235,
717,
4992,
3531,
8708,
2740,
582,
6205,
551,
4854,
6856,
1881,
8784,
7510,
7381,
1892,
1113,
3543,
8949,
5420,
8589,
3902,
4837,
2695,
2841,
5790,
823,
7993,
6314,
8584,
376,
5057,
7894,
307,
746,
5741,
8780,
199,
7936,
9986,
3338,
6165,
8333,
2134,
6868,
3220,
5997,
3449,
9537,
2184,
8341,
1012,
5774,
2773,
9828,
9089,
2237,
4937,
9521,
5795,
6460,
7791,
8110,
8278,
9174,
1266,
5970,
2186,
2817,
4713,
498,
5298,
4401,
6777,
1966,
9658,
3787,
4308,
5219,
7874,
9539,
5344,
8508,
2126,
6046,
1672,
4493,
8827,
4135,
2959,
6425,
1102,
9501,
9161,
3222,
2949,
4191,
8252,
2310,
9767,
5479,
9555,
9310,
8031,
5744,
85,
5286,
6729,
8786,
6240,
337,
4676,
5369,
5271,
5887,
2858,
2252,
2656,
162,
9223,
1522,
6956,
6422,
4888,
8171,
5918,
3274,
3787,
7224,
2719,
2026,
9022,
1568,
4909,
825,
7020,
2874,
2749,
5201,
5384,
4870,
9431,
3497,
6879,
4098,
7523,
6185,
9239,
6808,
1621,
2787,
1020,
6245,
3464,
6119,
6836,
7115,
2166,
990,
1080,
1691,
8519,
2773,
7286,
8473,
479,
2808,
791,
1679,
1211,
9270,
5614,
328,
445,
7667,
4514,
2541,
7692,
2955,
8634,
5533,
2695,
6598,
9421,
797,
6093,
9787,
9681,
7139,
9388,
8464,
1419,
1928,
3643,
9920,
2588,
89,
6241,
3357,
5033,
6154,
1944,
5030,
1910,
2134,
2359,
2803,
9024,
403,
184,
8653,
3604,
1620,
3072,
4659,
1323,
1122,
2465,
2573,
2215,
2818,
6889,
6335,
3346,
1974,
7792,
8073,
7858,
9936,
250,
641,
6673,
9114,
191,
1560,
3369,
2230,
3657,
4768,
2247,
6787,
6791,
412,
5381,
9082,
4978,
5461,
2188,
1691,
1691,
9400,
9805,
1924,
8606,
1603,
2780,
1009,
8170,
5547,
3106,
7576,
9260,
5879,
6652,
7675,
9933,
5799,
6569,
2187,
1006,
5671,
9082,
805,
2721,
6920,
5120,
1982,
9074,
7471,
5649,
5802,
2403,
4778,
7862,
3324,
3168,
8586,
2779,
7923,
6028,
1504,
4959,
7079,
7666,
4098,
2681,
9437,
146,
5167,
9995,
3537,
756,
9817,
1333,
2495,
2713,
8307,
7224,
6506,
2801,
3381,
8123,
2899,
6562,
2817,
370,
3450,
5837,
5548,
703,
6906,
6353,
7514,
8109,
4774,
198,
4422,
2652,
2529,
2465,
1524,
1949,
7366,
9801,
5407,
5826,
2951,
1207,
3641,
9715,
6129,
7811,
2258,
3610,
1007,
2627,
6745,
4513,
2974,
424,
6090,
4926,
9052,
7867,
812,
4524,
8644,
6496,
3637,
3788,
723,
3727,
3589,
6806,
5683,
8694,
9119,
3997,
3896,
2621,
1921,
3491,
2888,
3405,
1731,
2959,
279,
3629,
7818,
1279,
7554,
3488,
7261,
5083,
9200,
9125,
9355,
5398,
1540,
4169,
1340,
6933,
8826,
9891,
2740,
2914,
2604,
4064,
9508,
1558,
5892,
3954,
8225,
5593,
3813,
1808,
8325,
1104,
8707,
9861,
770,
5911,
1183,
7390,
2703,
336,
2996,
9796,
4413,
7313,
5009,
3994,
7305,
7776,
560,
983,
5479,
1883,
5797,
4352,
8900,
3385,
1140,
1161,
269,
5737,
2660,
4120,
8729,
6851,
9524,
9160,
2879,
5538,
3116,
4319,
20,
7753,
2839,
1571,
8922,
2675,
9590,
5031,
3846,
8867,
702,
5191,
751,
3644,
3620,
2290,
8386,
9566,
8792,
4844,
6167,
285,
6114,
2897,
7589,
9613,
7184,
368,
3178,
427,
4438,
641,
3762,
7376,
6406,
5533,
8748,
5379,
9490,
8314,
5322,
7417,
1634,
1427,
3280,
3478,
4259,
2980,
3097,
1054,
7657,
4364,
7687,
8175,
3033,
9508,
7120,
7716,
3022,
9030,
3057,
3903,
5544,
1110,
4156,
9754,
1536,
7662,
2947,
4376,
7889,
6879,
506,
8076,
861,
5383,
883,
7171,
2398,
2311,
3453,
9083,
6845,
1554,
9692,
2627,
2045,
4201,
3329,
4890,
5601,
716,
9672,
2234,
8711,
3489,
8043,
5444,
7958,
8883,
2700,
2682,
5194,
9448,
4872,
9165,
4045,
5625,
1883,
546,
7188,
3367,
9103,
1172,
969,
9953,
7501,
9441,
3308,
5546,
8039,
1979,
7953,
4418,
8040,
1702,
8926,
8212,
7609,
9366,
1638,
9368,
2531,
9838,
2290,
9261,
3977,
4766,
5365,
5146,
7930,
4758,
5141,
9973,
1070,
2303,
7283,
2071,
7004,
1642,
3627,
5325,
3022,
5149,
2605,
2853,
1737,
1321,
110,
9197,
483,
1510,
8947,
6595,
3595,
1912,
4847,
9557,
2345,
8224,
549,
6618,
4762,
6693,
8256,
1490,
6013,
7406,
5460,
1936,
5335,
3206,
653,
7873,
1539,
8491,
1604,
9047,
7525,
2516,
8935,
7638,
7826,
7262,
5392,
8445,
4856,
660,
8414,
6450,
6571,
2295,
4149,
5174,
7965,
6488,
668,
3154,
6022,
7553,
1173,
5843,
2939,
6453,
517,
3612,
8274,
5853,
2047,
6388,
7599,
7253,
6623,
78,
1724,
6944,
7295,
1874,
7054,
3548,
6673,
3628,
3761,
287,
429,
7545,
1539,
5782,
2405,
5160,
6269,
1808,
6314,
3121,
8121,
9224,
40,
621,
6756,
1271,
7096,
9880,
1974,
6986,
4136,
986,
2314,
2506,
3916,
4089,
2508,
3846,
7333,
7651,
8667,
2150,
6103,
720,
3968,
1389,
1507,
3527,
5247,
1518,
8620,
8184,
7181,
5722,
3906,
2035,
2594,
8919,
3733,
4586,
112,
9683,
1667,
7019,
4258,
6681,
3511,
9943,
6441,
6156,
2087,
1549,
747,
9069,
5496,
1972,
9565,
8351,
9323,
4431,
4779,
6668,
9026,
6224,
2884,
7941,
4215,
1457,
3217,
1764,
1800,
4737,
2106,
8760,
9173,
261,
8427,
9001,
8263,
3973,
3404,
7116,
5066,
6122,
2381,
8468,
9502,
220,
3907,
9683,
1783,
7428,
8874,
1624,
9292,
4809,
9075,
7564,
7458,
1845,
7062,
1125,
812,
4110,
527,
8183,
668,
2716,
8230,
2666,
2954,
2012,
2605,
503,
1829,
6676,
937,
4486,
8415,
6329,
1229,
5612,
1194,
6557,
2882,
1581,
6619,
1141,
1800,
1939,
7317,
2863,
1680,
3440,
53,
7424,
4280,
123,
6286,
5197,
8485,
7504,
9320,
2131,
6540,
4333,
4606,
8479,
432,
8745,
1813,
353,
4172,
4765,
3175,
8710,
5891,
4193,
6591,
4907,
4384,
3125,
5701,
6890,
8833,
5483,
2690,
5557,
7296,
6768,
1966,
9098,
6512,
7723,
4292,
2633,
3192,
7604,
9016,
7183,
7641,
7307,
4072,
4248,
3529,
310,
3652,
4660,
3290,
6489,
9648,
7664,
3423,
5813,
1484,
7676,
520,
9816,
2463,
5991,
4551,
2955,
5471,
5308,
5953,
5850,
5040,
6692,
5923,
7226,
5847,
1214,
3234,
8930,
1116,
2117,
5534,
3169,
8208,
8178,
4144,
1476,
8081,
6844,
7453,
1162,
405,
4571,
78,
3822,
7197,
7720,
2432,
487,
2621,
2228,
1557,
4014,
4003,
8177,
111,
938,
8896,
2980,
7707,
7661,
5748,
1168,
4571,
7364,
2376,
9189,
5622,
1963,
9478,
17,
8825,
2859,
3635,
273,
6943,
5621,
8664,
2897,
2037,
198,
2615,
7852,
9630,
275,
8904,
2496,
6762,
7246,
4972,
5668,
9479,
442,
1810,
3873,
3533,
530,
3221,
4033,
8449,
9818,
7426,
7751,
6970,
474,
1923,
6767,
9319,
6593,
6850,
2805,
3447,
3698,
3531,
8067,
1740,
7443,
2664,
8494,
1843,
8533,
7399,
3580,
7241,
2334,
670,
5718,
4989,
7072,
6354,
9107,
7321,
8814,
4847,
358,
8994,
599,
8413,
8047,
7842,
6524,
5489,
4265,
5619,
4503,
8334,
5371,
386,
593,
5512,
5407,
4533,
9522,
803,
6778,
7462,
7924,
7629,
3063,
2495,
1869,
1735,
4993,
954,
320,
6692,
7914,
7463,
8007,
3117,
4088,
4969,
844,
5627,
5544,
8197,
5967,
53,
4558,
564,
6255,
6009,
4414,
2151,
4610,
1815,
635,
5994,
1720,
9273,
3805,
8460,
2797,
9833,
4045,
2627,
2647,
9060,
7448,
6116,
2218,
5947,
8091,
3835,
9632,
1083,
7279,
9571,
8703,
4385,
9958,
3239,
7169,
738,
290,
8837,
3837,
7260,
6932,
2226,
4984,
6658,
4133,
2300,
900,
70,
6893,
7830,
4213,
4365,
7946,
9249,
1200,
2965,
4745,
331,
2428,
5267,
1223,
8287,
9095,
8801,
2436,
440,
9832,
581,
105,
2106,
7051,
8895,
6473,
8950,
634,
8024,
1474,
8422,
7032,
372,
196,
8777,
9732,
7516,
2662,
3241,
9477,
5711,
4119,
4180,
7950,
7821,
3076,
304,
3749,
480,
4165,
2441,
5525,
7209,
2704,
9571,
9531,
8738,
3173,
8868,
5682,
4456,
3234,
3871,
1782,
9112,
6392,
1837,
1476,
8999,
8649,
2550,
1359,
157,
5996,
9452,
2162,
3229,
6542,
7970,
6972,
1301,
5446,
6109,
9718,
1998,
1910,
6074,
5987,
992,
9276,
336,
7857,
5029,
8828,
62,
5470,
3288,
4916,
628,
6189,
62,
8791,
4170,
3519,
9293,
2131,
8451,
5581,
1514,
510,
102,
3003,
2220,
2287,
4008,
5671,
6659,
5980,
904,
5362,
2234,
8868,
3647,
3835,
2519,
8698,
1092,
1382,
2432,
3027,
2523,
8368,
8621,
1723,
9436,
3437,
138,
4980,
655,
316,
8641,
4993,
5681,
8571,
2726,
5588,
7644,
62,
3346,
2389,
2781,
2058,
9490,
8483,
1992,
7483,
3124,
5873,
4153,
1337,
552,
7960,
9854,
8629,
5820,
8296,
7323,
3151,
422,
254,
6956,
4115,
3236,
6495,
7237,
214,
7966,
5092,
1531,
4683,
5833,
920,
120,
1224,
2759,
2256,
5851,
5524,
2926,
6348,
9034,
8785,
2966,
2827,
3804,
2188,
945,
6507,
6801,
2894,
6681,
3758,
1268,
8884,
7872,
1058,
4122,
2213,
8674,
2757,
2498,
1709,
9205,
9188,
6799,
7744,
7418,
7863,
5566,
5903,
1514,
4705,
828,
3701,
567,
2992,
9433,
2392,
7854,
2390,
348,
2897,
2927,
769,
116,
5395,
4512,
1272,
630,
4600,
5626,
6010,
470,
7795,
7493,
187,
2816,
4506,
7933,
4630,
7330,
4868,
4419,
6329,
980,
3645,
3726,
9808,
1477,
9210,
8387,
7849,
3259,
7989,
6173,
4560,
7500,
5091,
1517,
2468,
7063,
8318,
4906,
921,
2625,
3160,
8803,
4858,
2604,
3496,
2993,
9300,
3028,
8782,
6538,
6826,
9168,
776,
4110,
508,
8265,
973,
7814,
3181,
8686,
1465,
7673,
1352,
5031,
8914,
6594,
9483,
4916,
2078,
5762,
3751,
5200,
9557,
5192,
9659,
3334,
4766,
9273,
4872,
7728,
24,
2980,
5448,
8425,
6571,
2110,
2862,
9558,
3695,
6567,
1080,
8000,
743,
2505,
7227,
9228,
9078,
4486,
6614,
4052,
4066,
8162,
1359,
1559,
6778,
7942,
6794,
7369,
5003,
2160,
2350,
7684,
7138,
3391,
9946,
8677,
1048,
3310,
7269]
nums = heap_sort(nums)
test(nums)
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