无k聚类法

无k聚类法

前言

众所周知的k-means聚类算法必须在k给定的条件下才能给出无监督学习结果，简单讲就是必须事先知道有几个类别方能完成聚类，而我们大多时候不能知道或者很难知道具体数据中有多少个类。因此寻找一个在无给定k条件下（即不知道有多少类别的情况下）的聚类算法显得尤为重要。

       在这里本人试探性地给出一种自认为可行的方法（希望读者与我一同探讨该方法的正确性）。

算法简析

       首先我们必须先给出一个限定条件，该限定条件限定了，每组分类中分类点（简单讲就是k-mean中的均值点，某种意义上讲也可认为是质点）到该分组个点的最大距离。

有了以上给定前提后我们就可以往下分析问题了：

简单二分法：

1.首先考虑，当前数据组是否可以作为一个组，若可以则将该分组插入结果分组集。（其考虑标准为，先算出分类点坐标，然后把各个点到该分类点的距离逐一计算，并比较得是否所有数据点到分类点的距离都小于给定的最大距离，若是则该为一个可行分组，若否则不可）。

2.把所有数据点利用2-means算法二等分，则得到2组数据，每组数据递归地调用该方法（也就是把这两组数据集分别从第1步开始迭代）。

3.输出结果分组集。

 

初步解释：

由于任何的非负整数都可以通过二进制表示，因此能保证所有可能分组数可达。而以上的过程实际上是一个二进制表示的过程，我们可以吧递给看成是二叉树的模样，而其分类种也就是叶子节点数量，如图1。

图1

其中可以清晰的看到第一次迭代吧数据集分成了2组，而后再前一组（A1）中由于已经达到标准，所以作为结果集的一项被保留了下来，而后一组（A2），由于仍然不满足要求仍需迭代，后面一次迭代把改组分成了2个合格的可行组（B1,B2）

由此迭代结束，输出结果集（{A1,B1,B2}）。

 

并组优化：

       在得到以上结果集后，我们会发现有些组本可以合并为一组但却因为上述做法而分别对应到了两个分组，若下图2。

图 2

在这里我们本应该吧中间两组作为一组，然而由于随机选择初始迭代点的原因，会导致如上这种过度分组的现象，为了解决上述现象，我做了一个优化，其思路待我慢慢讲来。

       我们先把以上的结果集中的分组尝试进行合并。任意取2个结果集进行如下操作。

1判断结果集中是否存在两个可以合并的分组（即把该两个分组合并为一个后仍然满足最大距离要求）若有则转2，若无则输出结果，算法终止。

2.把两个分组S1.，S2合并为一个分组S，用S替代S1,S2，并更新结果集，转1。

完成这样的任务后我们就解决了上面的问题了，很开心得到如下结果，如图3

图3

哈哈哈！还没完呢？优化继续。。。。。

分组优化：

       这里有这样的问题：是否某些组可以拆解为其他分组的一部分呢？这样的话这个分组就不复存在了完全归为其他分组的一部分，这样也可以减少分组数量。

       基于这个思想，我们得出这样的算法：

1、       判断是否存在某个分组其完全可以拆解为其他分组的一部分（这个判断略微复杂，你需要做的可不只是所把每一个试着放入其他分组中这么简单，你要考虑到某一元素放入其他分组后整个结果集也变了，该被放入分组的分组点也变了，所以简单判断一个分组各个元素独立的属于其他分组是毫无意义的，这其中是一个动态变化着的问题，不能静态考虑），若没有则输出结果。若有转2。

2、       将该分组解开，依次放入结果集的其他分组中，并从结果集中删除该分组。转1。

其现象大致若下图4

 

实验代码及运行结果：

实验数据为如下：

{{0.4,0},{1,0},{2.5,0},{3.1,0},{1.5,0},{ 1.55,0 },{2,0},{1.95,0}}

 

#include <iostream>#include <string>#include <cstring>#include <fstream>#include <functional>#include <algorithm>#include <ctime>#include <cmath>#include <vector>#include <limits>#include <unordered_set>#include <memory>using namespace std;const double eps = 0.00001;unordered_set<shared_ptr<vector<double>>> tos;unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>> midres;unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>> realres;unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>> nextres;unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>> finalres;double stddis;double maxdis(const shared_ptr<unordered_set<shared_ptr<vector<double>>>> &s, shared_ptr<vector<double>> &p1, shared_ptr<vector<double>> &p2);double dis(const shared_ptr<vector<double>> &p1, const shared_ptr<vector<double>> &p2);shared_ptr<vector<double>> getmid(shared_ptr<unordered_set<shared_ptr<vector<double>>>> s);double nrom(const shared_ptr<vector<double>> &p);shared_ptr<vector<double>> operator-(const shared_ptr<vector<double>> &p);shared_ptr<vector<double>> operator+(const shared_ptr<vector<double>> &p1, const shared_ptr<vector<double>> &p2);shared_ptr<vector<double>> operator-(const shared_ptr<vector<double>> &p1, const shared_ptr<vector<double>> &p2);ostream& operator<<(ostream& o, const shared_ptr<vector<double>> &p);void get2(const shared_ptr<unordered_set<shared_ptr<vector<double>>>> &s);bool getClass();double dis(const shared_ptr<vector<double>> &p1, const shared_ptr<vector<double>> &p2) {double res = 0;for (int i = 0; i < p1->size(); ++i) {res += ((*p1)[i] - (*p2)[i])*((*p1)[i] - (*p2)[i]);}return sqrt(res);}double maxdis(const shared_ptr<unordered_set<shared_ptr<vector<double>>>> &s, shared_ptr<vector<double>> &p1, shared_ptr<vector<double>> &p2) {double mmax = 0;double res = 0;shared_ptr<vector<double>> mid = getmid(s);for (shared_ptr<vector<double>> pv : *s) {for (shared_ptr<vector<double>> pn : *s) {double tem = dis(pv, pn);if (tem > mmax) {mmax = tem;p1 = pv;p2 = pn;}}res = max(res, dis(mid, pv));}return res;}shared_ptr<vector<double>> getmid(shared_ptr<unordered_set<shared_ptr<vector<double>>>> s) {shared_ptr<vector<double>> res = shared_ptr<vector<double>>(new vector<double>((*(s->begin()))->size()));for (const shared_ptr<vector<double>> &p : *s) {for (int i = 0; i < p->size(); ++i) {(*res)[i] += (*p)[i]/s->size();}}return res;}double nrom(const shared_ptr<vector<double>> &p) {double res = 0;for (double td : *p) {res += td*td;}return sqrt(res);}shared_ptr<vector<double>> operator-(const shared_ptr<vector<double>> &p) {shared_ptr<vector<double>> res = shared_ptr<vector<double>>(new vector<double>(p->size()));for (int i = 0; i < p->size(); ++i) {(*res)[i] = -(*p)[i];}return res;}shared_ptr<vector<double>> operator+(const shared_ptr<vector<double>> &p1, const shared_ptr<vector<double>> &p2) {if (p1->size() != p2->size())return nullptr;shared_ptr<vector<double>> res = shared_ptr<vector<double>>(new vector<double>(p1->size()));for (int i = 0; i < p1->size(); ++i) {(*res)[i] = (*p1)[i]+ (*p2)[i];}return res;}shared_ptr<vector<double>> operator-(const shared_ptr<vector<double>> &p1, const shared_ptr<vector<double>> &p2) {return p1 + (-p2);}ostream& operator<<(ostream& o, const shared_ptr<vector<double>> &p) {for (double td : *p) {o << td << " ";}return o;}void get2(const shared_ptr<unordered_set<shared_ptr<vector<double>>>> &s) {shared_ptr<vector<double>> p1;shared_ptr<vector<double>> p2;if (maxdis(s,p1,p2) <= stddis) {midres.insert(s);return;}shared_ptr<unordered_set<shared_ptr<vector<double>>>> s1 = shared_ptr<unordered_set<shared_ptr<vector<double>>>>(new unordered_set<shared_ptr<vector<double>>>());shared_ptr<unordered_set<shared_ptr<vector<double>>>> s2 = shared_ptr<unordered_set<shared_ptr<vector<double>>>>(new unordered_set<shared_ptr<vector<double>>>());for (shared_ptr<vector<double>> p : *s) {if (dis(p, p1) < dis(p, p2)) {s1->insert(p);}else {s2->insert(p);}}shared_ptr<vector<double>> np1 = getmid(s1);shared_ptr<vector<double>> np2 = getmid(s2);while (nrom(np1 - p1) > eps || nrom(np2 - p2) > eps) {s1->clear();s2->clear();for (shared_ptr<vector<double>> p : *s) {if (dis(p, p1) < dis(p, p2)) {s1->insert(p);}else {s2->insert(p);}}p1 = np1;p2 = np2;shared_ptr<vector<double>> np1 = getmid(s1);shared_ptr<vector<double>> np2 = getmid(s2);}get2(s1);get2(s2);}bool isSum(const shared_ptr<unordered_set<shared_ptr<vector<double>>>> &ps, const shared_ptr<unordered_set<shared_ptr<vector<double>>>> &psn, shared_ptr<unordered_set<shared_ptr<vector<double>>>> &outping, shared_ptr<unordered_set<shared_ptr<vector<double>>>> &outfloat) {shared_ptr<unordered_set<shared_ptr<vector<double>>>> tempres = shared_ptr<unordered_set<shared_ptr<vector<double>>>>(new unordered_set<shared_ptr<vector<double>>>(*ps));tempres->insert(psn->begin(), psn->end());shared_ptr<vector<double>> mid = getmid(tempres);bool flag = true;for (shared_ptr<vector<double>> ptd : *tempres) {if (dis(ptd, mid) > stddis) {outfloat->insert(ptd);flag = false;}else {outping->insert(ptd);}}return flag;}int pingClass(const shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>> &s) {shared_ptr<unordered_set<shared_ptr<vector<double>>>> floatTemp = nullptr;shared_ptr<unordered_set<shared_ptr<vector<double>>>> pingTemp = nullptr;shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>> tempres = shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>>(new unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>(*s));shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>> firstout = shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>>(new unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>());while (!tempres->empty()) {bool flag = false;shared_ptr<unordered_set<shared_ptr<vector<double>>>> spt = *(tempres->begin());for (const shared_ptr<unordered_set<shared_ptr<vector<double>>>> sptn : *tempres) {if (spt == sptn)continue;floatTemp = shared_ptr<unordered_set<shared_ptr<vector<double>>>>(new unordered_set<shared_ptr<vector<double>>>());pingTemp = shared_ptr<unordered_set<shared_ptr<vector<double>>>>(new unordered_set<shared_ptr<vector<double>>>());if (isSum(spt, sptn, pingTemp, floatTemp)) {spt->insert(sptn->begin(), sptn->end());tempres->erase(sptn);flag = true;break;}}if (!flag) {tempres->erase(spt);firstout->insert(spt);}}nextres = *firstout;return nextres.size();}bool add(const shared_ptr<unordered_set<shared_ptr<vector<double>>>> &ps, const shared_ptr<vector<double>>& pd) {ps->insert(pd);shared_ptr<vector<double>> mid = getmid(ps);for (shared_ptr<vector<double>> ptd : *ps) {if (dis(ptd, mid) > stddis) {ps->erase(pd);return false;}}return true;}bool openClass(shared_ptr<unordered_set<shared_ptr<vector<double>>>> pt,shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>> &s) {shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>> b = shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>>(new unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>());for (shared_ptr<unordered_set<shared_ptr<vector<double>>>> apt : *s) {shared_ptr<unordered_set<shared_ptr<vector<double>>>> tpt(new unordered_set<shared_ptr<vector<double>>>(*apt));if (apt == pt) {pt = tpt;}b->insert(shared_ptr<unordered_set<shared_ptr<vector<double>>>>(tpt));}b->erase(pt);while (!pt->empty()){shared_ptr<vector<double>> nowpt = *(pt->begin());bool flag = false;for (const shared_ptr<unordered_set<shared_ptr<vector<double>>>> &ptd : *b) {if (add(ptd,nowpt)) {flag = true;break;}}if (flag) {pt->erase(nowpt);}else {return false;}}s = b;return true;}void deepPingClass(shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>> s) {while (true) {bool flag = false;for (shared_ptr<unordered_set<shared_ptr<vector<double>>>> pt : *s) {if (openClass(pt, s)) {flag = true;break;}}if (!flag) {break;}}finalres = *s;}bool getClass() {get2(shared_ptr<unordered_set<shared_ptr<vector<double>>>>(new unordered_set<shared_ptr<vector<double>>>(tos)));pingClass(shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>>(new unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>(midres)));deepPingClass(shared_ptr<unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>>(new unordered_set<shared_ptr<unordered_set<shared_ptr<vector<double>>>>>(nextres)));return false;}int main() {vector<vector<double>> solve = { {0.4,0},{1,0},{2.5,0},{3.1,0} ,{1.5,0},{ 1.55,0 },{2,0},{1.95,0} };for (const vector<double> & v : solve) {tos.insert(shared_ptr<vector<double>>(new vector<double>(v)));}stddis = 0.6;getClass();for (shared_ptr<unordered_set<shared_ptr<vector<double>>>> p : finalres) {for(shared_ptr<vector<double>> pv:*p) {for (double i : *pv) {cout << i << " ";}cout << endl;}cout << "==========" <<endl;}cin >> stddis;return 0;}

测试数据一

1000组二维数据（数据大小在0-100之间，保留2位有效数字，组内距分类点最大距离为6.0）

=============================
mid point:12.209 94.258 
14.03 93.69 
9.69 90.99 
13.78 92.69 
13.5 97.62 
13.84 92.64 
13.51 94.43 
11.23 96.17 
9.91 91.65 
12.15 95.44 
10.45 97.26 
=============================
=============================
mid point:51.5286 42.4957 
49.07 47.69 
45.68 43.05 
50.46 40.93 
48.76 45.24 
56.92 40.17 
53.57 37.7 
56.24 42.69 
=============================
=============================
mid point:88.514 49.39 
85.46 51.22 
87.43 48.82 
90.91 47.38 
86.19 51.62 
92.58 47.91 
=============================
=============================
mid point:65.6171 42.2271 
65.95 44.81 
66.23 42.05 
62.58 38.42 
68.85 41.01 
69.01 40.58 
62.29 41.27 
64.41 47.45 
=============================
=============================
mid point:26.6288 79.9513 
23.75 80.82 
30.54 75.47 
25.12 74.52 
30.09 78.75 
24.73 84.07 
29.52 82.04 
24.46 84.21 
24.82 79.73 
=============================
=============================
mid point:46.44 11.5178 
50.25 7.07 
41.39 11.9 
44.82 7.61 
45.21 15.14 
47.81 13.34 
49.52 14.02 
47.14 10.29 
43.89 11.28 
47.93 13.01 
=============================
=============================
mid point:32.8633 33.6 
33.86 33.05 
30.16 29.04 
34.57 38.71 
=============================
=============================
mid point:43.6025 29.5713 
47.34 29.55 
41.8 29.68 
45.83 27.85 
41.31 32.09 
43.45 34.03 
41.84 31.38 
46.66 26.75 
40.59 25.24 
=============================
=============================
mid point:87.4122 43.7522 
89.96 39.45 
82.94 44.23 
87.73 44.1 
89.81 44.1 
89.42 38.7 
85.3 46.19 
84.11 45.05 
90.55 46.48 
86.89 45.47 
=============================
=============================
mid point:87.5778 4.31444 
91.61 7.97 
87.35 8.8 
89.72 0.04 
89.15 3.82 
85.96 0.66 
83.87 0.43 
86.57 5.6 
86.21 4.23 
87.76 7.28 
=============================
=============================
mid point:3.83167 11.1867 
6.51 9.51 
3.75 11.88 
5.5 12.82 
4.16 12.4 
0.28 10.49 
2.79 10.02 
=============================
=============================
mid point:41.876 44.432 
45.98 44.97 
45.7 45.26 
38.22 44.29 
41.53 41.98 
37.95 45.66 
=============================
=============================
mid point:56.36 3.94077 
54.21 5.11 
57.93 6.2 
55.66 3.46 
56.81 3.77 
59.07 5.42 
55.14 2.29 
52.31 0.95 
53.05 0.33 
58.47 0.15 
52.55 6.29 
59.6 7.62 
60.15 8.4 
57.73 1.24 
=============================
=============================
mid point:10.3964 59.7743 
8.19 57.09 
9.48 56.35 
7.81 58.68 
9.29 58.02 
5.31 59.03 
6.75 59.59 
8.97 61.07 
9.99 62.3 
13.73 58.53 
13.84 58.63 
14.79 56.58 
12.92 64.44 
12.6 60.98 
11.88 65.55 
=============================
=============================
mid point:25.2143 17.2836 
24.52 22.13 
26.69 20.75 
25.45 12.2 
25.88 12.27 
27 14.73 
22.87 18.79 
27.38 19.07 
25.51 13 
21.46 17.99 
24.72 15.9 
25.8 16.85 
24.13 22.48 
25.44 15.82 
26.15 19.99 
=============================
=============================
mid point:78.7791 53.3273 
78.71 51.65 
78.65 52.13 
78.86 54.34 
74.37 57.23 
78.91 48.88 
81.09 53.57 
81.78 55.26 
81.56 56.28 
76.46 58.09 
77.32 51.5 
78.86 47.67 
=============================
=============================
mid point:62.8813 80.9988 
62.38 78.98 
60.79 80 
58.76 79.71 
64.55 79.14 
65.38 81.16 
62.5 79.59 
65.72 84.98 
62.97 84.43 
=============================
=============================
mid point:59.354 72.128 
61.56 76.43 
59.94 70.4 
56.77 67.23 
59.09 66.85 
57.84 76.84 
58.21 68.78 
64.1 72.43 
60.96 70.58 
59.23 76.42 
55.84 75.32 
=============================
=============================
mid point:45.9617 50.785 
43.73 51.61 
48.86 48.77 
45.97 47.11 
45.5 48.95 
45.44 53.01 
46.27 55.26 
=============================
=============================
mid point:1.966 25.954 
0.88 22.48 
0.66 28.94 
2.08 24.43 
2.57 25.22 
3.64 28.7 
=============================
=============================
mid point:26.6443 28.8643 
29.09 26.68 
25.92 29.48 
24.07 26.99 
26.55 33.4 
28.48 29.84 
22.51 31.53 
29.89 24.13 
=============================
=============================
mid point:16.587 70.283 
16.59 66.72 
13.76 71.39 
18.72 71.82 
17.57 70.77 
20.9 72.71 
13.86 70 
19 69.57 
17.77 72.84 
13.7 68.43 
14 68.58 
=============================
=============================
mid point:95.7237 42.2013 
93 44.59 
99.38 38.24 
97.71 46.53 
99.84 40.78 
92.8 39.07 
93.53 45.24 
93.92 46.2 
95.61 36.96 
=============================
=============================
mid point:94.7933 60.5422 
91.18 63.66 
91.64 62.09 
98.79 56.35 
95.61 58.28 
98.45 57.53 
99.26 63.6 
89.65 60.57 
92.91 62.79 
95.65 60.01 
=============================
=============================
mid point:87.7033 83.8667 
83.71 86.17 
88.56 81.96 
90.84 83.47 
=============================
=============================
mid point:36.4471 82.3 
38.68 82.63 
39.47 78.39 
32.85 81.97 
34.24 85.66 
30.6 81.47 
41.63 83.88 
37.66 82.1 
=============================
=============================
mid point:63.5375 57.71 
63.65 59.87 
59.98 59.06 
65.46 59.83 
65.06 52.08 
=============================
=============================
mid point:9.96357 6.58929 
14.22 5.38 
9.78 8.36 
11.77 7.87 
11.98 9.95 
13.3 10.42 
11.22 2.47 
7.98 2.53 
8.51 6.27 
6.65 2.49 
14.2 2.99 
8.4 7.18 
5.66 6.57 
7.66 8.42 
8.16 11.35 
=============================
=============================
mid point:89.7536 66.9745 
87.86 65.49 
86.48 69.09 
89.27 68.96 
88.06 69.37 
90 71.39 
89.07 62.7 
91.88 67.11 
91.73 65.31 
90.26 66.74 
87.53 62.41 
95.15 68.15 
=============================
=============================
mid point:14.2825 38.7888 
10.76 39.13 
10.97 39.55 
15.1 43.55 
9.7 36.13 
12.97 36.59 
18.79 38.85 
19.54 38.94 
16.43 37.57 
=============================
=============================
mid point:77.1417 62.0267 
77.42 62.51 
74 62.95 
78.68 61.99 
78.99 65.33 
73.87 59.28 
79.89 60.1 
=============================
=============================
mid point:3.14545 43.1891 
0.57 46.53 
0.37 45.5 
0.34 47.25 
5.46 46.58 
5.43 41.76 
4.72 42.62 
2.6 44.84 
7.57 40.74 
3.89 37.91 
1.2 43.32 
2.45 38.03 
=============================
=============================
mid point:77.1057 43.1671 
77.95 41.42 
75.98 42.94 
80.33 44.2 
74.62 38.03 
76.02 46.37 
74.38 42.39 
80.46 46.82 
=============================
=============================
mid point:80.1283 3.335 
80.02 4.03 
77.78 0.26 
78.77 3.81 
79.1 6.26 
82.62 4.58 
82.48 1.07 
=============================
=============================
mid point:23.8967 49.9975 
23.8 47.44 
27.18 48.81 
24.44 51.71 
20.84 49.37 
23.12 54.07 
20.78 49.68 
27.46 49.76 
25.29 52.08 
20.62 45.48 
22.33 54.54 
22.42 50.05 
28.48 46.98 
=============================
=============================
mid point:60.6086 15.0014 
64.11 15.52 
55.56 14.35 
63.02 14.36 
63.63 10.65 
58.42 15.12 
59.82 11.35 
61.47 15.21 
61.91 10.26 
59.83 19.15 
62.93 12.53 
61.74 18.01 
60.97 20.97 
58.89 18.17 
56.22 14.37 
=============================
=============================
mid point:19.978 93.242 
16.92 93.4 
18.31 91.64 
21.84 97.99 
19.51 92.25 
23.31 90.93 
=============================
=============================
mid point:36.3942 53.1558 
38.35 58.41 
34.92 53.58 
40.46 54.61 
32.96 51.79 
36.99 54.41 
35.73 48.78 
36.86 50.14 
41.75 55.07 
35.21 54.99 
34.45 53.67 
37.58 51.5 
31.47 50.92 
=============================
=============================
mid point:37.3383 32.5083 
35.3 31.9 
37.21 27.21 
38.48 32.96 
39.25 37.32 
39.18 37.92 
34.61 27.74 
=============================
=============================
mid point:27.378 57.127 
31.81 56.55 
26.01 60.19 
26.61 52.93 
28.82 55.13 
25.69 59.54 
24.38 57.29 
28.75 60.95 
26.61 60.1 
26.09 56.66 
29.01 51.93 
=============================
=============================
mid point:68.2478 55.6022 
68.87 55.55 
71.06 53.52 
70.63 55.13 
68.56 52.66 
62.81 56.56 
62.64 55.87 
72.54 59.76 
69.3 55.54 
67.82 55.83 
=============================
=============================
mid point:35.9356 64.0178 
35.51 61.71 
31.6 67.16 
34.18 59.7 
35.11 62.13 
39.13 60.92 
34.84 64.85 
35.33 65.66 
38.78 67.09 
38.94 66.94 
=============================
=============================
mid point:54.4578 61.0544 
53.81 63.66 
57.94 62.8 
55.41 57.63 
53.06 60.89 
56.83 61.61 
57.66 61.62 
55.74 62.41 
48.95 61.89 
50.72 56.98 
=============================
=============================
mid point:96.2585 22.0531 
94.65 23 
94.83 19.97 
93.61 22.54 
97.04 19.45 
95.95 18.59 
97.57 18.68 
98.5 26.09 
98.26 25.71 
93.54 25.52 
97.32 23.87 
94.91 20.93 
95.2 22.88 
99.98 19.46 
=============================
=============================
mid point:52.0733 97.2211 
56.62 99.57 
51.34 98.59 
54.92 99.26 
51.48 94.94 
55.61 97.62 
49.59 96.7 
51.98 97.1 
46.9 98.12 
50.22 93.09 
=============================
=============================
mid point:3.916 52.356 
8.23 55.21 
0.85 54.76 
2.75 49.82 
2.79 50.38 
4.96 51.61 
=============================
=============================
mid point:24.3633 97.8811 
24.88 99.59 
23 94.72 
25.42 98.36 
26.85 96.19 
26.46 98.51 
25.45 95.24 
23.83 99.13 
22.96 99.84 
20.42 99.35 
=============================
=============================
mid point:30.625 6.79167 
30.36 1.67 
28.61 2.63 
32 10.93 
28.7 7.87 
32.19 5.8 
31.89 11.85 
=============================
=============================
mid point:69.6071 17.5357 
70.12 14.38 
71.34 18.08 
70.51 19.68 
64.63 20.63 
72 15.57 
69.98 16.86 
68.67 17.55 
=============================
=============================
mid point:84.3583 95.0067 
87.12 95.29 
85.54 95.4 
86.45 96.26 
81.48 92.47 
84.28 97.97 
81.28 92.65 
=============================
=============================
mid point:46.1578 2.36778 
49.62 1.14 
45.42 0.45 
49.12 2.67 
41.93 1.51 
42.88 3.98 
45.97 4.03 
49.65 0.95 
45.58 3.12 
45.25 3.46 
=============================
=============================
mid point:90.1909 17.2355 
93.22 15.81 
90.32 13.81 
91.06 14.85 
87.36 18.45 
89.54 12.44 
89.18 20.7 
92.29 15.67 
87.34 19.04 
92.03 21.21 
90.39 19.44 
89.37 18.17 
=============================
=============================
mid point:24.9611 67.5356 
25.88 72.02 
21.57 68.05 
20.77 63.8 
29.54 67.62 
28.69 65.81 
29.48 67.64 
23.7 65.58 
23.58 70.31 
21.44 66.99 
=============================
=============================
mid point:60.87 92.76 
63.65 91.63 
58.05 94.33 
60.91 92.32 
=============================
=============================
mid point:4.99375 80.6613 
7.33 80.86 
3.18 79.96 
9.62 84.22 
8.21 83.2 
4.62 83.23 
3 75.81 
0.56 83.04 
3.43 74.97 
=============================
=============================
mid point:59.2867 49.8842 
62.23 52.5 
60.09 45.68 
58.97 50.1 
57.46 46.21 
61.47 48.54 
57.2 51.98 
58.47 47.76 
56.79 50.8 
62.99 54.05 
53.52 48.86 
60.97 50.21 
61.28 51.92 
=============================
=============================
mid point:46.1317 88.6908 
47.95 83.76 
50.25 84.56 
43.28 90.1 
42.94 89.92 
47.66 86.71 
42.09 91.2 
49.01 85.75 
45.24 88.83 
49.63 85.49 
46.2 90.57 
44.75 94.31 
44.58 93.09 
=============================
=============================
mid point:26.9962 87.0962 
27.85 91.21 
27.97 84.37 
27.29 86.13 
24.85 87.56 
31.96 86.3 
25.35 86.04 
24.29 85.48 
26.41 89.68 
=============================
=============================
mid point:24.6545 7.17364 
28.32 7.78 
26.71 7.13 
27.46 8.33 
20.76 7.18 
23.04 5.46 
27.01 1.68 
23.15 10.26 
24.84 5.29 
21.88 7.45 
25.35 7.75 
22.68 10.6 
=============================
=============================
mid point:82.8927 66.4645 
82.35 66.96 
85.24 67.53 
80.23 65.24 
84.74 67.81 
83.63 68.23 
82.89 68.8 
84 68.18 
82.53 62.61 
81.24 66.22 
81.19 66.45 
83.78 63.08 
=============================
=============================
mid point:6.5 98.34 
9.14 97.83 
3.86 98.85 
=============================
=============================
mid point:71.9625 83.275 
69.24 83.88 
76.01 79.3 
70.25 88.12 
72.35 81.8 
=============================
=============================
mid point:84.604 33.87 
82.47 32.24 
86.84 32.32 
85.28 32.37 
85.42 37.05 
83.01 35.37 
=============================
=============================
mid point:94.3633 97.3533 
94.72 95.09 
94.87 98.51 
91.14 96.03 
88.92 96.11 
98.84 98.97 
97.69 99.41 
=============================
=============================
mid point:55.1812 86.4712 
55.67 82.39 
51.56 81.7 
59.44 88.64 
55.95 89.37 
55.36 87.84 
59.05 82.16 
51.84 91 
52.58 88.67 
=============================
=============================
mid point:68.09 36.1838 
68 34.41 
71.85 36.26 
72.12 37.71 
64.09 37.22 
69.67 35.34 
69.06 34.03 
67.03 36.74 
62.9 37.76 
=============================
=============================
mid point:17.58 24.7081 
20.35 23.85 
20.06 24.56 
17.76 26.3 
16.71 26.93 
14.98 24.45 
19.47 25.1 
17.99 23.96 
14.23 23.77 
18.13 26.46 
22.35 23.14 
13.07 21.81 
17.28 27 
13.38 23.08 
14 22.91 
17.68 21.85 
14.54 24.25 
13.42 21.62 
21.72 25.01 
20.86 27.96 
22.12 27.85 
19.08 27.01 
=============================
=============================
mid point:75.84 87.2311 
78.74 87.71 
74.29 90.12 
80.73 86.37 
74.68 84.59 
79.12 90.67 
78.47 86.21 
74.14 85.53 
71.62 85.81 
70.77 88.07 
=============================
=============================
mid point:45.0317 63.8 
50.23 64.24 
41.12 67.66 
47.34 67.28 
45.87 61.34 
43.83 61.71 
41.8 60.57 
=============================
=============================
mid point:3.4925 90.9537 
0.11 86.04 
4.16 92.83 
1 94.73 
1.66 92.45 
7.38 87.19 
8.44 89.32 
4.45 91.34 
0.74 93.73 
=============================
=============================
mid point:33.9771 18.0871 
29.33 20.42 
33.68 21.59 
37.18 17.44 
33.99 16.52 
32.82 15.83 
37.57 16.09 
33.27 18.72 
=============================
=============================
mid point:70.122 75.116 
70.34 74.58 
72.39 74.2 
72.39 74.47 
75.16 76.79 
67.76 75.35 
70.79 78.08 
73.57 77.7 
67.61 72.15 
65.89 72.74 
65.32 75.1 
=============================
=============================
mid point:46.3857 73.7914 
46.71 70.62 
42.88 71.89 
46.4 79.52 
51.24 73.96 
50.71 77.13 
43.25 70.91 
43.51 72.51 
=============================
=============================
mid point:48.655 37.898 
49.53 37.3 
51.37 37.92 
43.13 37.72 
49.42 39.61 
47.64 40.33 
50.99 36.32 
52.1 39 
50.81 34.68 
46.92 34.68 
44.64 41.42 
=============================
=============================
mid point:67.407 95.638 
65.58 95.84 
68.68 93.82 
69.86 95.86 
69.92 98.23 
66.4 98.58 
62.42 96.67 
69.17 90.99 
62.15 95.91 
69.12 99.72 
70.77 90.76 
=============================
=============================
mid point:80.905 12.7675 
82.84 13.36 
80.18 15.08 
78.48 13.1 
81.59 9.53 
80.75 11.02 
82.51 12.82 
80.69 14.44 
80.86 9.25 
79.14 12.26 
82.14 13.32 
81.87 15.57 
79.81 13.46 
=============================
=============================
mid point:18.0864 3.73818 
15.34 7.42 
19.62 0.95 
18.11 9.2 
15.91 1.47 
18.77 4.17 
14.76 3.7 
15.57 4.03 
20.51 2.07 
22.87 3.65 
18.78 1.37 
18.71 3.09 
=============================
=============================
mid point:57.7085 34.0769 
53.3 35.17 
61.24 36.78 
54.75 34.26 
57.27 37.62 
57.67 36.8 
57.89 32.61 
57.5 34.04 
61.75 36.5 
52.44 34.94 
60.37 34.23 
60.68 29.69 
58.19 30.56 
57.16 29.8 
=============================
=============================
mid point:38.472 73.434 
41.43 73.81 
39.59 72.97 
34.91 72.48 
34.21 76.17 
42.22 71.74 
=============================
=============================
mid point:75.15 95.752 
72.67 91.35 
77.12 93.07 
75.83 97.66 
78.3 99.44 
73.7 94.55 
77.95 97 
73.52 99.47 
74.06 97.16 
77.78 95.24 
70.57 92.58 
=============================
=============================
mid point:1.27667 3.61556 
0.1 4.15 
0.51 1.65 
2.29 2.63 
1.71 7.6 
4.26 4.48 
0.19 0.06 
0.02 2.08 
1.12 5.95 
1.29 3.94 
=============================
=============================
mid point:39.3867 14.2767 
42.07 19.61 
39.41 11.51 
36.87 11.12 
38.37 16.66 
39.21 13.64 
40.39 13.12 
=============================
=============================
mid point:36.9971 2.73714 
40.2 0.45 
35.57 5.62 
37.59 8.54 
35.4 0.59 
33.59 0.3 
37.78 1.25 
38.85 2.41 
=============================
=============================
mid point:87.8145 77.7655 
88.31 79.35 
86.16 82.33 
85.7 77.6 
87.49 79.05 
89.92 77.7 
90.56 73.93 
87.08 80.92 
86.36 81.94 
87.09 74.84 
86.95 73.55 
90.34 74.21 
=============================
=============================
mid point:6.06429 32.5914 
6.06 34.27 
1.91 34.97 
8.89 30.61 
5.51 30.28 
6.06 27.61 
6.91 30.85 
6.57 30.54 
10.38 32.63 
4.76 30.86 
6.03 37.86 
1.15 33.73 
9.2 32.93 
1.35 34.51 
10.12 34.63 
=============================
=============================
mid point:94.4667 29.4675 
97.08 31.56 
98.63 32.48 
89.23 27.35 
90.85 26.68 
99.37 29.13 
98.38 32.58 
96.05 30.65 
95.26 33.61 
90.17 27.38 
90.23 25.85 
91.45 27.74 
96.9 28.6 
=============================
=============================
mid point:94.7418 3.21 
95.5 2.55 
91.75 2.48 
92.94 0.52 
95.57 2.98 
92.38 1.45 
90.66 5.26 
96.39 0.69 
91.88 0.91 
99.71 3.62 
98.65 6.15 
96.73 8.7 
=============================
=============================
mid point:16.086 33.426 
13.97 33.44 
15.7 34.98 
19 30.65 
14.63 34 
17.13 34.06 
=============================
=============================
mid point:72.59 10.234 
68.63 13.15 
72.54 6.82 
72.76 11.04 
75.06 5.56 
73.96 14.6 
=============================
=============================
mid point:46.789 18.992 
50.87 23.33 
50.7 21.03 
45.77 16.18 
42.26 16.17 
48.38 21.37 
44.71 16.41 
48.42 15.61 
43.94 20.37 
51.29 21.28 
41.55 18.17 
=============================
=============================
mid point:67.4513 65.4688 
66.86 67.11 
65.69 63.79 
70.58 62.73 
67.22 67.93 
66.4 65.66 
65.93 68.66 
67.99 65.47 
68.94 62.4 
=============================
=============================
mid point:19.67 76.4575 
18.19 80.43 
17 74.3 
24 73.41 
19.49 77.69 
=============================
=============================
mid point:93.477 53.381 
90.39 52.92 
94.73 52.38 
96.26 52.83 
90.47 55.58 
94.22 49.35 
90.86 54.49 
97.34 55.09 
96.2 51.42 
92.58 57.05 
91.72 52.7 
=============================
=============================
mid point:21.2129 42.9943 
21.71 41.2 
22.47 45.81 
19.94 39.09 
22.89 43.19 
22.66 45.89 
21.1 40.3 
17.72 45.48 
=============================
=============================
mid point:74.4544 24.2444 
72.48 26.57 
76.55 21.66 
75.57 21.85 
73.23 26.41 
71.05 25.2 
72.59 20.53 
75.55 24.71 
77.7 27.01 
75.37 24.26 
=============================
=============================
mid point:37.076 88.35 
36.07 86.06 
35.46 86.56 
39.41 84.99 
38.07 90.29 
41.33 86.98 
37.03 87.8 
38.41 89.42 
31.8 89.34 
36.95 89 
36.23 93.06 
=============================
=============================
mid point:37.8933 96.1283 
36.71 99.89 
40.72 95.35 
36.4 93.76 
38.13 97.22 
40.5 95.59 
34.9 94.96 
=============================
=============================
mid point:77.574 81.272 
80.09 81.24 
77.51 79.88 
78.58 83.24 
78 77.76 
73.69 84.24 
=============================
=============================
mid point:65.5192 5.35692 
68.78 4.47 
69.15 2.15 
67.45 4.2 
63.97 6.99 
67.74 2.67 
63.08 8.24 
70.21 6.63 
66.81 9.61 
62.12 9.26 
63.88 1.26 
61.39 9.44 
63.47 3.71 
63.7 1.01 
=============================
=============================
mid point:9.988 74.217 
10.23 72.13 
11.68 76.66 
15.31 74.46 
11.9 74.8 
6.94 73.78 
7.24 74.57 
11.86 75.06 
10.66 77.8 
7.48 71.65 
6.58 71.26 
=============================
=============================
mid point:97.7567 14.2367 
98.97 9.94 
98.61 16.39 
99.63 13.77 
99.91 18.7 
95.8 15.8 
93.62 10.82 
=============================
=============================
mid point:10.9564 49.5773 
12.57 51.26 
9.88 53.71 
11.83 49.35 
7.69 48.94 
11.9 48.32 
7.73 47.46 
8.89 51.59 
7.59 52.76 
12.73 44.66 
13.07 46.51 
16.64 50.79 
=============================
=============================
mid point:2.45667 18.64 
1.78 15.69 
0.33 18.19 
1.68 18.19 
3.87 19.52 
3.84 20.09 
3.24 20.16 
=============================
=============================
mid point:8.72286 15.7857 
12.31 17.6 
11 12.8 
12.19 11.26 
13.58 13.61 
9.41 17 
7.76 18.55 
8.83 16.96 
8.98 17.37 
8.55 13.19 
6.18 16.59 
3.58 16.93 
4.98 18.3 
8.45 16.09 
6.32 14.75 
=============================
=============================
mid point:18.5267 86.2527 
13.51 82.99 
20.35 82.53 
15.98 89.42 
17.75 81.72 
16.17 88.09 
20.32 84.96 
18.37 90.19 
19.84 84.31 
16.13 83.77 
21.66 88.41 
19.18 87.11 
16.42 89.6 
19.69 89.44 
19.02 85.81 
23.51 85.44 
=============================
=============================
mid point:29.5622 41.69 
31.94 38.64 
33.62 40.44 
33.39 42.81 
24.01 43.27 
33.01 43.48 
32.88 42.04 
25.9 41.85 
25.48 41.74 
25.83 40.94 
=============================
=============================
mid point:79.1771 31.1843 
78.05 29.56 
84.86 29.79 
80.03 31.47 
80.6 34.47 
78 30.11 
75.44 32.85 
77.26 30.04 
=============================
=============================
mid point:5.36 65.326 
7.72 63.86 
1.43 62.97 
5.21 68.82 
7.94 63.51 
4.5 67.47 
=============================
=============================
mid point:19.542 59.743 
18.81 63.65 
18.78 58.93 
24.52 59.68 
23.53 58.4 
19.15 60.63 
21.63 59.14 
18.4 61.72 
16.12 58.18 
16.25 54.88 
18.23 62.22 
=============================
=============================
mid point:96.2967 89.0667 
96.06 86.85 
99.28 88.76 
93.55 91.59 
=============================
=============================
mid point:83.345 24.3375 
82.06 20.58 
85.32 22.53 
84.48 23.83 
80.39 19.28 
82.41 26.62 
82.66 25.74 
82.99 27.8 
86.45 28.32 
=============================
=============================
mid point:65.2325 26.5488 
61.23 23.1 
65.78 27.83 
67.77 30.72 
66.55 26.85 
67.59 27.05 
65.64 21.65 
64.33 25.29 
62.97 29.9 
=============================
=============================
mid point:18.8691 14.1591 
18.63 19.64 
15.98 15.09 
18.17 11.3 
17.46 12.76 
20.26 15.01 
20.1 16.35 
21.29 12.05 
17.99 15.42 
22.47 12.59 
18.46 13.49 
16.75 12.05 
=============================
=============================
mid point:53.6914 23.1857 
56.97 19.89 
53.71 21.95 
53.43 21.45 
52.31 23.29 
53.4 26.74 
53.02 23.26 
53 25.72 
=============================
=============================
mid point:8.96857 26.0543 
7.79 28.22 
12.39 30.26 
10.81 23.51 
5.1 22.9 
12.14 26.38 
3.97 24.83 
10.58 26.28 
=============================
=============================
mid point:80.046 73.532 
80.6 74.61 
77.19 70.12 
79.68 77.32 
80.42 70.42 
82.15 73.05 
83.47 75.27 
77.68 75.15 
77.19 74.21 
80.94 71.55 
81.14 73.62 
=============================
=============================
mid point:97.0133 78.4117 
96.89 77.33 
99.68 75.79 
92.29 79.04 
94.15 78.26 
99.77 78.59 
99.3 81.46 
=============================

实验数据二

1000组五维数据（数据大小在0-100之间，保留2位有效数字，组内距分类点最大距离为60.0）

=============================
mid point:27.3429 55.3209 56.7018 30.8544 80.7938 
7.72 78.29 46.75 8.62 77.27 
21.38 63.68 80.94 28.87 93.44 
20.86 61.82 43.19 73.55 99.71 
10.05 89.36 16.19 24.16 59.48 
31.45 66.89 59.19 81.18 75 
0.04 45.02 74.99 15.34 60.37 
17.62 31.97 67.61 10.98 90.04 
2.68 44.75 70.15 1.67 78.81 
12.21 39.43 78.05 14.13 63.05 
32.33 70.89 40.57 29.51 65.91 
50.14 34.47 41.04 12.54 83.01 
1.04 39.33 70.72 4.24 91.47 
13.22 83.43 28.05 13.36 70.51 
24.89 73.44 46.62 21.81 88.38 
0.09 69.39 51.73 20.88 68.12 
2.99 18.55 72.91 13.92 88.68 
33.44 89.57 31.44 19.7 94.11 
27.62 85.31 87.33 8.61 98.17 
59.73 42.81 55.78 11.17 89.28 
66.96 45.71 91.71 5.82 74.35 
62.34 66.49 95.9 25.31 79.98 
63.25 78.31 71.79 28.37 58.83 
50.98 68.37 32.33 17.32 98.29 
54.48 88.65 77.2 13.76 78.06 
24.11 37.75 54.33 39.31 94.77 
3.87 23.65 39 49.56 99.37 
54.35 63.82 32.18 69.77 83.22 
25.6 38.84 36.12 57.14 96.93 
8.7 34.56 21.5 58.65 93.41 
57.29 64.6 81.51 63.66 83.26 
31.67 37.91 59.41 55.72 71.68 
38.78 32.77 53.52 51.24 82.13 
6.43 61.33 52.77 77.09 60.16 
11.35 9.75 65.34 22.09 57.74 
=============================
=============================
mid point:22.1062 36.8395 68.5501 33.5422 32.0751 
2.61 76.24 79.14 40.8 12.79 
11.47 16.66 95.59 32.27 71.63 
58.17 56.22 89.96 28.56 48.22 
4.04 24.54 96.46 3.38 3.5 
5.97 7.81 84.82 20.89 20.31 
50.74 45.88 85.88 49.02 40.54 
21.03 75.82 93.21 13.17 9.98 
60.07 57.22 69.06 27.09 19.88 
16.04 47.08 54.56 5.65 18.66 
8.35 74.08 71.34 67.08 49.79 
34.66 11.6 76.89 12.71 46.22 
26.23 27.68 93.4 4.47 55.22 
8.47 1.48 85.5 32.59 3.52 
43.63 22.21 62.76 19.79 49.43 
29.14 64.45 99.73 40.04 11.95 
7.35 5.03 60.26 60.94 8.76 
6.33 17.04 94.14 24.72 63.86 
55.51 32.46 84.45 27.21 50.88 
23.34 23.39 61.04 15.19 24.68 
34.78 23.61 78.53 7.28 54.22 
17.83 67.25 98.63 13.58 10.4 
12.88 25.8 86.62 9.01 8.23 
12.55 6.78 66.73 4.08 19.81 
6.86 39.74 96.34 21.76 45.31 
17.75 29.54 89.79 24.75 7.45 
25.69 54.9 89.01 38.28 15.21 
54.19 30.32 79.39 30.37 55.06 
34.28 22.68 56.74 20.01 52.67 
51.27 62.91 74.62 40.09 41.4 
29.44 28.35 81.63 5.67 16.33 
16.15 36.8 27.71 30.28 7.92 
19.73 23.2 86.62 45.46 75.59 
33.56 68.39 73.41 2.49 7.32 
12.78 2.44 79.69 56.12 10.28 
27.42 33.19 88.55 35.71 20.24 
3.71 31.4 95.88 13.03 76.69 
16.97 21.14 90.42 15.62 78.44 
51.38 41.92 41.51 25.11 69.12 
6.72 75.89 69.65 5.4 10.11 
23.24 68.03 92.98 25.17 3.95 
42.16 47.44 75.54 25.47 78.77 
35.4 35.08 93.24 47.93 53.28 
22.59 30.87 96.66 8.86 29.19 
5.33 25.36 62.21 16.83 36.35 
5.54 76.95 64.97 54.35 41.39 
3.81 7.97 56.04 27.47 65.97 
10.2 52.46 43.18 47.79 18.02 
5.16 54.09 82.57 43.29 25.77 
11.46 71.87 99.47 53.39 60.19 
10.81 42.54 72.31 52.33 63.36 
6.94 77.69 89.07 45.83 19.8 
8.34 84.71 81.4 21.97 5.28 
19.37 25.3 64.98 29.54 27.27 
14.98 35.92 71.03 42.59 72.14 
9.77 56.82 54.6 39.71 22.75 
8.71 83.38 67.15 35.84 9.84 
24.72 46.83 62.41 30.54 23.3 
11.02 74 85.04 65.79 38.39 
7.67 29.1 60.39 30.37 19.61 
2.79 73.93 48.04 33.7 0.43 
8.95 20.28 42.2 6.45 4.97 
18.36 8.41 53.35 44.34 4.48 
4.25 0.07 65.69 30.76 16.33 
9.76 21.27 32.59 24.9 18.3 
16.72 42.98 37.14 22.37 16.87 
39.63 57.44 98.76 16.48 67.25 
38.25 42.32 81.28 23.32 78.98 
11.95 6.1 43.47 39.68 58.75 
36.67 28.37 29.7 23.63 24.1 
16.66 9.31 57.31 19.93 61.04 
13.59 17.93 44.9 62.55 22.1 
2.46 5.76 57.91 66.01 8.9 
6.17 45.12 35.43 43.96 40.98 
2.07 6.77 49.11 62.41 25.92 
3.32 13.89 33.72 55.78 17.26 
46.37 9.68 35.22 44.99 28.26 
24.45 6.04 21.66 20.84 22.78 
20.9 2.03 49.57 31.64 21.26 
20.81 9.24 18.41 38.76 20.1 
15.1 3.2 67.69 65.31 24.44 
42.88 26.7 65.29 2.7 58.64 
12.39 29.57 64.43 30.4 78.5 
34.17 44.58 76.13 59.48 61.5 
16.89 44.18 43.32 83.55 27.14 
15.94 19.22 97.65 74.49 11.08 
22.59 38.81 90.65 82.1 23.61 
3.12 36.57 72.27 74.72 0.14 
31.46 39 10.91 40.75 31.17 
24.92 79.93 51.28 55.32 47.94 
63.87 50.93 72.44 23.73 5.44 
60.09 38.28 34.37 54.6 18.38 
59.34 51.49 68.94 22.38 13.78 
62.68 57.12 59.43 22.66 15.92 
=============================
=============================
mid point:67.0251 73.7153 23.3935 80.5837 60.7172 
91.52 71.32 13.62 58.38 51.98 
91.59 89.02 7.22 63.73 43.39 
78.03 48.92 7.62 96.01 88.72 
90.62 43.36 6.43 97.77 78.62 
65.82 87.93 40.77 54.97 33.44 
99.07 83.08 7.74 96.11 17.9 
98.38 79.86 9.89 82.33 26.39 
85.53 52.83 44.63 72.11 71.46 
61.56 78.21 19.65 71.54 70.43 
31.99 49.81 34.57 91.7 94.91 
98.11 70.13 25.42 80.36 78.38 
81.61 24.37 7.16 98.41 78.93 
90.63 43.39 10.15 89.15 72.05 
79.92 56.77 10.78 92.33 78.24 
98.28 59.48 8.59 93.88 90.4 
92.84 80.75 19.72 55.64 57.86 
90.69 80.64 36.52 67.68 64.53 
94.32 71.17 15.55 54.71 65.17 
30.64 82.14 29.09 60.08 27.09 
95.31 60.12 16.71 73.26 50.4 
58.65 75.66 68.5 98.03 79.19 
86.89 92.99 7.21 86 19.69 
44.25 81.08 8.47 92.02 63.69 
67.45 80.34 31.66 98.41 33.94 
49.55 93.63 5.79 82.85 96.3 
28.42 88.12 34.59 53.5 80.57 
77.61 89.96 53.02 84.44 61.54 
44.86 97.35 19.34 65.85 53.64 
51.47 87.08 49.86 64.73 72.21 
36.43 60.59 45.37 75.38 50.83 
79.66 96.1 35.81 94.57 92.1 
32.85 82.91 25.51 96.95 48.11 
50.09 86.86 16.07 92.29 61.09 
38.16 83.5 40.91 54.02 70.38 
66.5 99.62 3.22 97.29 35.48 
65.38 99.98 29.19 94.71 90.68 
62.57 98.62 16.3 95.8 25.43 
44.77 66.31 22.98 80.13 90.18 
63.22 37.26 33.41 89.23 95.84 
57.35 56.69 1.19 93.92 27.12 
26.48 70.6 41.2 68.69 51.04 
15.49 53.63 9.92 85.9 60.98 
87.52 77.58 34.57 70.24 10.52 
=============================
=============================
mid point:60.0918 24.2139 42.2464 74.8882 24.4418 
25.44 21.85 68.67 84.96 13.37 
85.03 19.61 39.96 98.67 34.15 
48.58 31.48 53.66 77.25 23.9 
47.68 30.12 49.82 75.26 1.44 
45.69 13.59 38.82 86.91 3.47 
47.88 42.48 64.5 95.25 10.51 
73 3.51 88.72 89.66 3.83 
15.8 20.59 56.23 92.88 7.58 
52.29 54.73 64.01 75.5 51.67 
80.58 25.31 16.62 52.11 42.18 
69.72 4.42 59.05 78.29 46.19 
30.11 13.88 49.31 73.16 14.56 
59.9 16.41 62.04 83.82 15.28 
58.49 49.03 40.81 75.21 17.32 
69.37 11.32 29.11 47.65 44.03 
34.19 32.17 64.15 93.27 2.92 
85.68 13.3 29.02 32.86 19.66 
90.51 9.73 20.12 66.53 0.59 
73.94 30.59 20.16 39.77 19.38 
57.24 2.05 35.6 56.17 4.09 
67.95 9.15 24.87 69.51 33.13 
40.16 14.36 46.4 95.93 0.82 
93.13 6.36 16.51 97.55 0.94 
41.92 19.61 16.96 97.5 27.39 
73.16 10.44 31.28 94.07 2.08 
31.04 28.08 41.29 88.06 22.18 
33.82 14.54 2.78 84.47 2.11 
45.27 51.52 53.32 81.81 37.99 
46.08 20.8 47.53 81.72 9.46 
55.08 32.86 39.41 80.41 15.27 
69.4 9.86 16.13 98.54 37.6 
94.4 41.2 74.15 85.19 36.69 
32.83 26.18 60.94 82.66 26.09 
89.95 22.4 25.39 85.63 11.97 
73.77 13.05 44.92 63.25 15.21 
69.99 13.95 34.43 58.82 46.37 
90.25 2.3 41.87 56.79 20.28 
72.48 22.35 52.87 71.31 4.85 
77.18 11.05 8.13 35.27 10.36 
98.99 25.81 6.93 70.47 20.3 
61.5 38.02 32.38 60.76 12.61 
58.39 3.57 43.05 89 4.4 
57.16 25.47 35.37 57.65 24.52 
81.47 12.16 9.69 81.41 8.4 
67.76 14.39 54.4 88.93 36.76 
81.37 22.16 81.14 88.04 47.02 
64.07 0.03 57.34 60.71 14.31 
49.54 47.54 52.66 95.42 17.77 
78.39 24.15 19.47 67.38 18.48 
56.35 20.08 42.03 93.31 3.89 
74.6 17.24 19.63 31.44 39.28 
83.6 45.65 16.62 72.04 17.88 
66.29 32.19 43.45 70.03 22.13 
86.91 15.12 42.84 69.35 13.91 
56.59 9.8 63.63 84.65 18.38 
47.55 17.09 60.26 81.3 35.84 
85.33 9.78 15.86 62.52 26.67 
51.01 24.74 7.78 98.09 43.91 
53.7 17.03 47.24 74.94 59.56 
49.76 42.68 14.56 97.11 6.87 
32.95 14.93 21.79 78.02 54.12 
52.24 22.41 19.16 89.2 26.48 
53.82 53.76 30.42 81.74 4.83 
68.06 16.83 11.1 87.66 0.31 
25.47 1.56 19.44 94.4 52.67 
43.61 12.18 26.97 74.84 12.44 
93.1 37.14 65.03 98.77 40.06 
62.97 46.79 82.22 88.83 45.64 
77.52 27.63 75.36 79.62 57.26 
56.66 46.47 64.61 88.43 67.86 
40.8 20.89 27.21 71.49 54.57 
55.38 58.81 39.22 94.69 29.51 
11.92 6.88 38.01 54.86 5.63 
24.91 5.03 69.26 73.66 6.61 
40.65 12.54 18.01 30.22 35.66 
18.84 3.42 24.22 62.03 6.44 
28.88 41.37 29.82 71.71 65.46 
65.71 51.91 50.48 79.11 68.84 
50.68 35.13 63.46 87.48 74.79 
48.85 30.32 57.55 66.27 49.04 
87.01 69.02 51.8 60.12 21.33 
44.88 27.17 66.9 85.52 55.08 
69.4 38.81 20.8 74.77 25.07 
70.15 7.88 4.17 85.9 17.06 
61.5 12.51 19.64 64 20.38 
8 34.74 63.43 77.55 16.11 
22.81 26.18 72.59 60.94 11.53 
7.96 49.4 47.1 73.39 39.34 
96.42 45.89 38.35 76.97 5.93 
85.04 5.12 51.39 35.73 4.31 
84.14 12.76 91.81 64.27 24.33 
93.11 39.01 47.37 41.11 24.01 
79.8 52.69 71.85 43.1 41.86 
95.31 7.7 84.23 59.62 22.66 
90.86 44.51 52.75 80.14 4.95 
=============================
=============================
mid point:37.1516 29.0156 82.6472 70.4925 79.415 
48.67 13.55 81.07 76.51 66.42 
71.91 52.8 89.33 76.36 91.01 
39.43 15.4 90.4 21.52 89.07 
43.8 43.86 85.42 86.5 95.28 
8.22 32.5 99.13 66.91 49.15 
54.2 25.23 43.32 96.28 98.59 
24 5.2 97.46 81.92 85.33 
55.44 56.92 82.65 83.08 80.65 
64.95 33.69 92.54 53.6 67.65 
83.85 11.52 95.33 95.44 97.46 
38.53 53.17 89.67 81.78 97.43 
47.22 29.42 83.83 61.79 95.52 
52.88 8.13 87.97 87.07 84.02 
64.75 19.31 84.68 62.33 93.56 
62.96 36.78 95.11 53.41 35.26 
45.82 41.62 99.61 48.01 89.88 
59.16 46.16 96.59 40.91 65.74 
70.54 17.44 55.92 81.81 92.15 
27.76 36.36 90.93 74.26 93.27 
15.91 41.07 91.05 87.33 98.9 
17.65 18.38 53.02 33.85 70.68 
13.62 48.24 87.29 77.19 55.12 
23.1 37.73 85.31 61.15 90.52 
28.6 18.25 72.54 50.84 28.12 
14.11 8.24 59.5 81.09 91.11 
14.13 5.15 91.98 63.81 74.71 
8.34 22.43 61.83 75.26 89.19 
3.27 15.38 98.37 75.72 86.33 
30.32 20.74 28.52 88.76 74.41 
9.4 45.37 94.11 74.86 73.81 
27.91 31.29 84.19 82.65 56.09 
18.4 37.17 96.04 73.76 84.85 
=============================
=============================
mid point:29.2486 73.7364 59.4398 14.9174 52.7071 
12.01 82.34 73.45 20.46 59.69 
40.48 79.24 95.64 0.71 40.29 
11.74 86.45 60.94 26.92 13.27 
4.21 29.82 58.59 11.62 51.34 
13.2 63.27 78.26 14.21 64.07 
21.56 68.24 38.82 18.28 45.68 
20.22 92.92 66.2 22.59 88.23 
72.17 98.88 70.36 12.97 69.96 
15.05 88.57 77.65 12.56 72.12 
10.38 98.38 49.15 25.79 34.29 
29.7 95.71 21.86 24.18 72.59 
35.11 86.82 85.88 14.31 45.3 
48.13 82.82 98.13 7.41 65.61 
31.58 86.51 51.4 9.73 68.7 
9.22 52.9 30.58 16.19 60.53 
24.33 77.63 73.05 15.73 78.3 
22.43 72.15 87.98 23.45 47.41 
12.83 77.83 74.09 17.82 95.77 
23.74 79.05 95.58 41.84 72.97 
31.5 71.71 60.69 14.7 74.95 
25.59 93.42 27.48 27.25 36.01 
22.2 75.37 83.12 26.87 56.48 
16.72 86.24 51.67 21.9 33.21 
21.97 75.41 59.45 36.32 51.74 
21.62 77.39 82.21 0.33 58.99 
54.76 77.53 40.6 1.9 57.98 
38.65 46.31 44.27 40.49 43.6 
47.67 74.94 89.2 4.32 43.03 
61.07 58.01 68.96 18.18 36.8 
14.43 81.4 51.57 4.61 26.75 
18.99 66.85 39.42 0.68 0.14 
9.74 36.24 49.36 8.77 78.91 
35.98 93.74 53.65 2.98 22.52 
30.86 74.27 39.56 1.63 5.92 
15.71 79.73 14.27 13.09 60.33 
38.43 74.99 27.76 11.72 74.19 
23.02 64.55 38.86 1.79 50.16 
39.56 48.28 51.96 14.65 47.44 
57.35 51.72 55.35 2.33 54.47 
20.08 70.93 58.52 16.61 13.55 
61.72 56.39 38.28 9.77 46.04 
62.73 61.98 82.65 8.87 94.37 
=============================
=============================
mid point:72.2953 28.2917 41.5894 72.407 57.3338 
40.65 44.62 77.35 99.99 73.69 
70.32 2.26 75.42 90.07 45.82 
75.27 19.67 42.43 94.08 85.92 
28.19 15.26 29.86 44.27 45.9 
51.12 70.76 63.44 79.75 70.48 
77.61 23.63 46.26 21.73 59.02 
93.82 22.68 29.33 38.07 64.68 
93.08 6.45 51.37 38.77 48.32 
77.87 17.77 40.17 82.95 96.55 
74.68 37.36 47.18 68.64 26.54 
82.3 33.31 8.29 70.7 49.72 
76.5 5.96 9.6 96.99 93 
77.04 11.47 68.78 96.52 76.68 
80.76 9.4 39.04 91.77 69.15 
84 8.03 70.92 99.08 79.64 
74.2 34.08 1.85 77.46 71.48 
87.62 25.24 64.52 73.26 39.14 
86.89 35.94 43.86 57.47 37.47 
90.76 8.47 67.12 62.08 43.51 
75.24 44.53 69.68 82.83 90.86 
94.58 12.89 55.24 72.68 54.25 
77.44 23.11 42.43 91.76 96.91 
62.02 53.25 14.03 62.03 23.53 
95.86 10.3 13.28 51.11 59.7 
91.38 9.8 18.65 62.99 70.1 
96.54 52.53 44.54 68.87 28.4 
90.24 22.97 69.07 92.34 12.28 
66.03 50.48 39.75 91.07 42.58 
55.22 26.21 44.88 98.76 90.8 
71.9 64.34 46.58 90.49 53.56 
63.65 46.19 8.02 71.9 18.08 
99.93 22.98 64.42 47.55 77.44 
64.42 65.71 69.84 98.79 60.39 
84.4 14.59 57.93 89.84 91.81 
45.98 45.7 15.57 95.95 42.15 
76.97 56.17 65.03 84.54 80.06 
67.65 47.03 50.05 26.45 73.32 
66.75 9.68 54.36 56.39 42.74 
74.82 19.36 40.49 19.52 43.5 
53.95 5.62 52.31 62.17 94.02 
92.79 26.23 2.58 72.78 31.5 
67.48 2.02 75.66 75.48 81.79 
78.81 6.91 56.23 74.12 75.85 
58.76 22.61 17.97 82.24 52.14 
35.45 9.8 27.5 73.89 43.79 
51.63 15.08 30.2 63.91 35.02 
73.66 51.71 8.36 87.56 52.39 
57.57 50.26 7.21 72.96 26.44 
83.44 66.42 4.31 77.18 38.67 
50.47 32.47 28.09 50.75 47.03 
31.29 18.37 25.25 89.98 40.44 
54.21 27.47 37.97 83.77 46.15 
98.44 34.31 69.97 31.27 44.29 
=============================
=============================
mid point:64.9233 54.9117 13.877 55.1313 70.3028 
94.38 99.35 16.76 51.31 91.17 
26.41 73.85 37.38 66.33 75.17 
67.59 58.52 17.64 62.6 91.78 
63.01 66.6 0.28 19.76 84.91 
94.25 62.47 7.83 35.29 91.57 
94.15 65.98 42.46 38.02 98.93 
71.14 29.1 36.55 69.69 86.07 
47.84 96.2 18.56 29.98 94.13 
71.08 58.89 10.83 64.1 19.9 
99.15 70.04 2.48 23.16 68.27 
62.64 30.01 8.31 56.76 23.55 
58.56 47.26 18.95 92.41 96.62 
48.57 96.69 13.74 40.6 86.14 
55.81 90.28 19.66 36.64 78.94 
69.43 94.54 22.67 61.07 58.96 
36.41 27.6 26.13 80.14 56.87 
76.79 56.42 20.18 51.89 86.63 
94.56 66.8 4.71 44.04 64.65 
84.16 92.22 11.54 56.08 79.89 
91.49 67.9 7.55 80.85 96.04 
85.27 54.67 12.11 70.87 99.89 
94.37 62.64 13.45 25.23 95.64 
76.99 69.63 6.79 78.57 81.08 
55.55 50.43 11.63 53.84 83.38 
87.49 34.39 2.04 40.89 51.45 
75.13 41.9 19.18 40.98 63.97 
93.47 62.28 11.68 60.81 24.84 
91.8 11.23 12.21 59.81 78.22 
56.88 34.78 17.07 63.79 69.47 
83.35 83.58 4.76 70.54 26.01 
42 34.82 2.79 50.29 68.45 
65.24 58.7 7.45 34.32 44.42 
45.01 6.66 23.17 48.5 63.47 
58.78 24.85 3.09 38.67 70.69 
78.86 46.7 6.95 52.18 55 
75.44 49.38 2.71 50.72 33.77 
77.78 38.52 27.37 22.97 91.92 
82.7 25.28 17.68 6.97 78.12 
42.16 52.39 24.82 96.7 81.73 
49.3 64.94 42.04 63.17 71.34 
89.19 56.78 45.15 87.59 88.03 
33.9 65.68 5.82 31.92 68.11 
65.72 15.12 11.93 76.75 60.51 
56.13 14.5 6.66 81.31 91.96 
71 36.98 14.35 51.57 16.42 
37.42 10.99 2.81 61.7 57.53 
37 39.36 11.06 51.97 46.34 
43.33 91.49 2.22 48.89 76.82 
52.15 39.26 10.02 91.55 86.84 
58.15 26.49 15.43 59.84 64.92 
14.94 77.8 5.7 58.49 75.31 
45.58 78.47 3.46 62.49 77.04 
20.76 65.22 0.03 68.95 63.21 
55.6 88.6 1.52 53.53 60.26 
=============================
=============================
mid point:46.1898 19.7051 19.9192 36.5166 69.3831 
46.18 26.28 33.95 29.75 89.32 
40.12 10.93 18.36 40.19 84.45 
57.08 39.2 0.06 8.96 98.38 
42.74 6.37 19.42 44.67 77.14 
39.99 1.73 32.21 55.08 90.93 
41.03 8.59 2.98 41.06 46.61 
56.53 4.55 14.86 13.8 35.47 
28.04 21.61 5.85 19.92 67.12 
59.3 30.01 44.56 39.23 76.64 
68.7 25.38 34.92 20.83 95.81 
60.07 42.3 7.55 43.36 96.76 
40.13 56.01 23.98 25.38 74.22 
51.91 1.45 34.6 80.84 91.32 
22.1 5.11 12.6 48.67 65.69 
33.63 41.17 17.08 25.17 95.38 
70.82 5.23 38.32 51.51 91.07 
44.39 22.22 43.21 13.28 72.09 
56.12 19.46 3.77 23.73 61.7 
52.87 14.28 44.37 7.77 87.53 
54.73 10.55 5.11 62.1 29.63 
57.67 0.12 10.86 8.7 28.24 
76.08 9.21 10.28 9.7 46.44 
61 21.33 10.81 25.37 62.43 
78.24 7.73 11.78 41.9 95.14 
36.02 21.76 18.96 2.32 99.7 
49.12 31.67 22.54 14.37 64.94 
63.17 19.7 31.48 20.36 90.82 
68.2 19.91 23.95 46.47 97.88 
25.37 27.88 14.37 2.03 75.87 
26.06 31.5 27.1 87.56 68.43 
21.61 6.85 19.17 68.21 84.41 
24.05 65.63 10.51 46.49 51.98 
39.12 26.68 4.17 69.93 96.39 
86.47 6.76 6.84 11.11 57.07 
57.91 8.9 4.06 26 78.37 
34.76 0.45 10.91 17.46 94.11 
46.97 31.02 26.41 40.35 61.62 
47.89 25.83 0.59 5.29 54.85 
75 19.89 47.55 42.67 69.99 
80.94 0.24 1.54 24.5 63.86 
20.62 12.75 11.29 66.04 55 
50.91 37.62 29.56 29.03 61.59 
74.98 19.28 2.56 22.06 99.51 
36.7 6.23 19.29 4.26 75.12 
37.27 2.19 7.55 44.37 68.43 
47.55 11.26 20.51 21.87 91.13 
70.76 2.39 23.68 15.11 93.32 
6.61 23.96 58.91 32.77 81.47 
58.32 28.39 56 40.21 85.67 
88.93 5.86 41.51 27.7 97.85 
36.04 22.07 24.88 37.78 63.69 
45.87 6.79 32.1 34.65 24.08 
22.5 0.78 17.47 63.89 69.11 
36.05 14.09 32.36 28.55 60.27 
44.47 26.5 21.94 44.66 89.19 
1.72 1.54 23.86 36.51 48.52 
33.15 14.36 10.49 26.02 23.49 
23.7 32.81 20.19 35.86 24.03 
16 23.41 11.93 57.41 38.59 
40.87 10.73 2.55 86.74 82.91 
42.44 34 21.95 49.57 28.8 
52.23 48.27 2.46 61.05 41.17 
29.39 24.71 19.18 88.53 57.4 
23.47 27.08 15.79 59.85 30.06 
39.66 68.27 15.1 53 49.7 
=============================
=============================
mid point:76.5572 20.9108 73.8075 32.6108 63.48 
83.95 5.75 55.46 20.35 58.7 
73.31 37.71 80.89 35.08 79.07 
52 7.38 54.38 27.34 59.4 
93.38 6.33 67.69 52.74 61.75 
92.95 3.02 81.38 26.21 20.52 
53.98 3.8 67.72 14.09 62.06 
92 8.49 79.72 34 23.82 
71.17 49.51 89.03 2.74 93.26 
54.45 21.77 93.54 39.54 56.92 
60.76 24.14 98.36 8.65 68.96 
58.79 11.01 94.45 21.29 85.3 
55.2 2.58 64.86 52.33 23.67 
53.43 36.86 57.6 63.88 79.99 
97.95 5.46 93.48 44.27 50.04 
77.6 18.35 83.89 16.68 47.68 
84.34 32.58 82.66 55.36 78.11 
57.91 15.9 51.6 68.81 86.68 
47.69 9.91 71.07 22.91 67.67 
80.18 24.67 83.59 38.64 25.74 
92.66 1.13 88.16 53.55 39.55 
54.64 8.33 71.23 40.07 57.89 
99.19 1.07 43.36 18.28 49.06 
75.5 11.31 94.92 59.6 21.48 
90.9 14.28 81.25 21.19 86.17 
69.5 26 99.73 27.55 80.15 
58.89 7.53 79.92 34.97 47.86 
96.17 9.12 91.4 53.01 97.35 
88.36 3.3 35.57 14.29 73.79 
84.62 19.36 74.65 46.9 61.92 
92.47 1.24 87.29 25.22 75.19 
95.27 5.63 88.02 7.34 44.03 
86.39 22.74 96.33 44.82 59.4 
95.35 16.63 82.4 86.35 70.58 
99.74 21.83 86.04 67.87 71.32 
92.65 53.79 75.32 2.96 96.75 
69.3 67.11 68.78 28.68 82.58 
78.39 29.78 87.42 48.82 93.02 
66.06 49.83 77.4 54.09 78.77 
93.6 9.83 51.16 1.26 77.04 
75.92 48.66 58.46 23.54 94.41 
63.81 22.69 74.23 39.88 82.42 
82.72 42.27 74.43 32.38 19.9 
82.53 22.73 55.19 13.51 96.88 
81.83 49.26 60.04 6.24 48.79 
72.84 23.02 54.39 10.61 56.06 
72.13 28.73 83.31 23.71 71.2 
78.4 23.24 59.66 15.01 82.13 
82.41 31.98 62.83 2.14 68.48 
68.01 29.5 49.59 4.91 40.46 
34.55 12.6 72.27 30.54 83.67 
65.91 20.87 63.26 58.5 92.25 
85.5 12.82 66.75 54.28 10.76 
90.28 34.84 65.67 31.39 23.79 
=============================
=============================
mid point:20.7316 32.0689 18.6955 25.1482 35.8057 
2.17 27.61 36.96 2.51 43.44 
8.78 15.43 6.93 14.84 38.57 
30.85 26.49 45.86 16.57 51.26 
10.2 33.72 16.37 46.26 19.19 
33.57 50.83 26.58 17.18 26.57 
27.85 31.55 22.86 63.65 16.64 
24.4 38.75 24.29 51.65 50.73 
53.7 30.72 26.69 8.91 21.97 
18.54 58.45 22.09 27.94 34.32 
22.98 59.93 4.05 8.71 73.94 
42.94 28.95 30.66 0.86 30.49 
16.83 39.65 26.71 7.81 51.87 
44.76 2.89 3.11 1.01 23.43 
27.26 25.84 0.69 37.27 33.71 
18.15 2.54 12.33 14.06 53.33 
23.93 51.77 8.6 13.23 26.19 
5.89 11.26 20 36.37 22.79 
27.91 27.77 14.79 70.7 23.91 
16.58 46.5 0.48 20.94 20.24 
37.89 41.28 10.7 2.88 20.4 
25.23 25.74 12.05 10.55 11.53 
8.26 12.06 17.5 22.23 55.74 
30.61 62.46 3.06 0.33 32.61 
1.92 54.82 29.36 6.2 52.91 
28.66 21.04 22.75 0.93 27.02 
0.95 32.69 1.16 49.9 18.33 
3.64 18.72 16.31 14.24 56.34 
0.61 42.34 29 5.99 12.27 
3.16 21.56 40.06 4.56 45.1 
52.1 40.62 24.08 5.98 27.65 
7.04 45.24 37.29 59.86 42.07 
7.02 52.98 15.44 26.45 72.99 
22.31 65.4 17.3 14.86 29.63 
21.73 63.44 8.34 23.91 60.12 
15.47 44.25 9.3 53.88 61.54 
55.31 9.76 9.82 40.33 8.55 
19.74 14.05 51.9 6.7 53.53 
0.65 23.38 43.23 1.33 73.92 
24.98 18.05 8.85 12.37 7.83 
1.38 4.02 24.12 37.7 33.24 
51.55 6.57 12.39 45.42 7.53 
26.02 27.17 18.86 58.74 14.2 
4.73 20.8 6.82 66.69 45.93 
3.94 31.94 2.86 74.02 41.88 
=============================
=============================
mid point:57.3343 22.9679 73.0224 18.7929 19.0531 
48.7 44.98 79.86 31.11 20.14 
52.86 1.68 35.24 24.09 21.12 
52.17 12.39 19.37 19.38 11.68 
62.15 20.96 84.12 8.8 8.13 
28.34 16.22 56.18 27.71 23.72 
83.27 24.53 68.56 11.93 16.54 
63.76 22.88 74.09 1.47 1.51 
82.97 15.34 95.72 0.14 41.44 
58.19 42.64 92.37 38.54 25.45 
72.77 45.72 97.36 29.73 16.94 
23.62 4.76 75.88 5.13 17.89 
56.98 2.63 85.04 6.61 40.16 
32.04 38.77 67.92 0.9 3.57 
30.08 31.81 46.31 12.87 16.28 
65.17 20.62 91.72 18.21 20.54 
65.89 12.41 85.86 9.87 47.94 
49.99 15.98 92.72 2.71 18.48 
79.45 0.28 80.95 6.61 9.8 
59.8 41.83 67.82 3.39 24.36 
54.59 24.76 64.57 11.75 15.32 
48.26 44.34 59.87 12.69 4.65 
60.72 31.47 73.62 34.55 35.69 
54.46 1.25 75.1 39.96 24.24 
81.76 40.61 96.59 6.11 11.52 
18.81 6.31 72.49 25.19 8.2 
51.68 7.02 58.43 11.38 31.47 
49.42 30.4 86.7 37.79 7.38 
65.19 20.34 67.52 41.51 27.39 
63.79 19.92 64.02 11.71 40.2 
53.98 6.46 78.09 55.96 8.09 
93.51 56.84 73.29 39.35 9.94 
42.63 38.72 75.57 6.64 29.25 
96.39 32.69 81.91 8.52 17.54 
73.04 21.13 54.02 25.13 36.58 
27.52 8.83 65.99 8.49 23.4 
88.03 1.52 59.66 16.11 10.15 
26.21 38.86 78.19 3.86 5.49 
61.21 18.38 93.84 26.67 13.86 
62.85 9.24 72.61 4.97 3.34 
10.94 1.57 85.97 44.69 22.05 
78.06 52.89 89.28 6.13 26.19 
76.79 34.67 42.52 50.94 2.6 
=============================
=============================
mid point:16.6665 73.9715 54.0924 68.5665 71.8697 
3.9 85.68 43.24 46.18 42.8 
19.89 83.89 47.5 66.85 94.25 
21.08 83.21 66.49 50.5 81.17 
9.38 98.87 52 80.49 43.55 
46.86 83.96 83.5 70.62 95.12 
4.99 81.3 77.4 36.27 66.15 
5.33 85.52 73.87 93.27 98.06 
21.55 66.87 57.4 66.95 64.34 
28.97 96.99 95.46 68.33 87.38 
2.26 92.39 45.41 49.09 40.7 
23.94 45.14 75.91 61.08 99.65 
24.54 70.28 62.45 93.17 84.78 
6.17 81.7 87.51 57.81 88.15 
7.57 97 93.18 58.55 62.61 
3.38 92.2 13.93 69.44 64 
8.31 67.02 67.32 78.39 78.74 
23.99 26.19 49.06 93.53 84.95 
24.01 85.74 49.23 39.15 80.71 
22.22 94.61 25.57 24.79 69.54 
13.09 89.54 60.85 41.41 56.7 
14.52 77.08 31.87 49.17 61.1 
7.12 35.02 38.01 84.64 68.82 
21.7 21.27 56.68 69.34 87.16 
17.57 55.42 21.42 71.21 81.3 
35.49 29.62 49.49 82.65 97.78 
17.88 75.64 23.71 70.79 25.76 
10.17 81.26 34.22 81.65 86.34 
17.36 84.89 50.34 95.91 77.79 
13 71.4 85.19 78.8 80.58 
20.37 47.36 85.28 87.3 57.1 
47.91 79.23 43.73 95.81 99.32 
2.61 96.09 25.16 55.83 73.2 
13.56 59.39 37.05 78.53 39.5 
5.97 93.26 29.71 83.76 24.47 
=============================
=============================
mid point:18.7733 14.8688 41.9988 19.3046 84.7904 
34.22 15.85 42.95 7.1 62.31 
25.05 14.34 33.73 19.05 97.57 
23.56 29.79 12.38 0.41 96.9 
34.99 38.24 35.86 7.45 92.8 
16.48 5.44 14.5 31.22 98.14 
15.35 8.55 25.22 30.36 64.39 
25 25.43 29.39 9.06 83.6 
24.37 33.13 39.21 10.5 72.41 
25.72 10.48 30.56 44.02 77.38 
19.07 8.81 20.21 21.48 81.62 
12.15 3.69 36.71 27.36 78.3 
22.16 28.1 66.61 1.94 75.34 
2.3 14.21 21.85 31.36 70.93 
5.22 20.78 58.59 0.68 83.26 
17.29 25.87 68.01 10.58 98.59 
8.12 8.59 3.96 9.54 90.71 
11.1 7.44 8 30.38 76.48 
11.65 5.56 39.66 30.61 82.82 
24.31 9.83 54.67 6.35 79.1 
1.21 4.92 81.43 4.16 91.21 
29.77 4.15 30.78 41.89 99.82 
14.17 3.01 90.73 26.77 83.94 
21.95 2.94 87.47 46.09 98.1 
25.35 27.7 75.49 14.95 99.25 
=============================
=============================
mid point:17.8432 15.49 67.6939 81.6887 56.3052 
17.26 0.92 31.88 69.93 56.24 
12.21 10.66 98.86 66.34 66.39 
24.74 0.45 81.24 89.35 1.14 
17.12 14.89 96.65 68.37 65.25 
45.41 3.57 80.85 86.9 60.98 
0.16 18.17 74.51 68.95 62.95 
17.06 20.61 43 77.35 53.16 
19.12 8.4 54.09 82.19 44.44 
36.28 24.76 97.3 87.7 39.6 
22.2 9.49 96.89 88.14 18.55 
20 49 85.32 87.51 97.38 
35.79 2.68 59.97 79.45 48.9 
18.94 21.12 18.09 94.74 59.55 
29.89 27.05 80.91 92.3 29.76 
8.72 13.32 98.79 67.93 65.12 
35.76 6.69 78.76 92.24 61.12 
0.89 29.98 46.47 92.11 60.85 
6.31 31.67 96.96 72.83 55.43 
17.46 1.42 16.48 77.1 62.17 
18.25 3.42 88.28 85.04 63.95 
46.19 4.72 90.73 94.81 45.41 
5.73 1.65 91.41 60.1 75.3 
6.04 9.35 60.16 96.87 7.49 
31.4 1.24 22.63 85.76 63 
9.23 10.58 84.71 88.72 61.52 
1.35 6.17 80.34 61.69 60.61 
22.07 19.15 97.24 61.26 91.77 
2.95 25.75 24.92 88.56 40.07 
9.2 24.51 29.84 83.95 82.24 
9.4 28.13 35.68 90.1 99.13 
6.01 50.67 55.55 94.06 45.99 
=============================
=============================
mid point:26.04 51.8562 13.0021 83.0676 19.889 
1.49 35.97 3.62 95.04 33.83 
23.5 27.2 1.67 94.03 33.07 
0.05 82.92 8.81 56.28 1.03 
35.73 47.97 2.31 79.26 2.12 
24.46 78.16 0.85 99.04 12.3 
21.75 81.93 19.64 77.85 23.93 
40.79 64.97 20.91 88.78 21.39 
16.19 40.81 26.33 59.3 15.9 
32.86 71.56 11.79 94.57 3.68 
7.88 68.72 43.68 95.19 35.13 
17.15 34.33 18.94 97.44 40.26 
7.45 36.57 9.15 55.94 9.96 
54.46 72.98 16.7 84.14 5.08 
38.93 52.86 7.25 75.89 5.12 
10.8 39.65 16.01 79.78 5.72 
60.76 89.44 2.33 97.15 2.29 
17.38 32.32 18.09 52.03 8.12 
59.14 89.09 10.73 89.57 33.94 
35.4 89.88 27.5 81.53 33.93 
39.82 45.74 28.4 75.28 3.96 
5.63 16.95 14.32 94.59 1.27 
1.19 50.21 6.51 96.8 55.25 
0.27 24.49 7.24 94.99 14.75 
35.66 16.46 13.54 99.52 25.09 
44.35 0.83 11.62 67.39 6.81 
32.26 17.39 3.95 98.73 33.7 
13.58 5.09 19.41 87.83 33.89 
32.16 91.13 2.76 77.09 54.95 
44.07 98.21 3 63.93 20.31 
=============================
=============================
mid point:85.7673 34.5086 28.8018 21.1332 19.9882 
97.99 0.04 55.87 10.56 2.35 
94.47 23.72 0.63 6.23 15.13 
77.47 11.49 6.71 4.57 10.68 
91.58 44.22 21.92 56.18 9.4 
92.24 83.91 51.26 37 37.36 
89.76 49.65 27.44 2.2 31.29 
90.72 50.04 22.78 16.91 6.24 
81.47 7.74 41.46 20.48 8.83 
77.07 46.36 32.59 23.42 19.79 
82.43 32.27 26.04 3.97 39.8 
93.4 49.09 32.78 5.43 3.01 
80.3 26.52 7.52 25.67 8.1 
99.34 15.79 50.59 26.06 9.98 
96.71 31.31 32.21 26.56 29.01 
84.81 47.75 44.41 7.4 7.52 
87.48 68.76 47.41 13.27 49.27 
79.61 49.3 58.53 10.49 31.22 
82.54 38.83 17.07 34.16 11.91 
73.29 3.75 2.26 36.38 10.85 
79.91 56.38 45.51 30.63 69.56 
78.09 10.28 6.78 22.03 20.31 
76.2 11.99 1.87 45.33 8.13 
=============================
=============================
mid point:84.7412 56.9341 79.64 76.4671 18.56 
83.9 21.77 87.49 80 9.75 
81.96 22.96 85.85 82.55 4.94 
72.74 59.7 71.09 66.06 24.28 
71.98 80.55 70.38 74.91 8.99 
91.31 58.77 81.89 76.17 51.95 
87.19 26.86 78.38 83.92 12.59 
60.43 65.56 79.19 69.45 20.63 
89.52 63.44 98.08 71.2 58.33 
93.77 64.67 78.68 74.18 35.22 
85.97 54.78 79.46 93.99 7.25 
74.57 31.1 91.5 94.36 2.88 
93.22 57.46 87.42 84.2 1.35 
99.64 53.9 82.78 97.66 10.47 
72.47 77.74 65.08 93.35 19.4 
98.29 66.08 72.74 74.2 31.76 
94.21 91.55 53.58 58.34 8.62 
89.43 70.99 90.29 25.4 7.11 
=============================
=============================
mid point:45.9212 69.0947 16.0837 33.4073 15.2855 
66.59 45.81 22.11 31.01 38.87 
33.47 88.07 22.41 30.44 26.91 
86.1 78.74 12.14 39.23 2.49 
75.81 54.31 12.59 55.61 0.81 
35.12 62.28 34.33 15.14 6.83 
54.28 58.57 5.73 16.93 1.46 
70.76 51.87 16 51.91 15.63 
23.09 54.94 10.14 29.86 38.12 
10.48 69.8 2.6 28.94 24.02 
66.9 88.19 15.9 74.32 10.72 
66.62 81.83 22.93 22.79 12.18 
78.95 85.56 1.25 39.14 2.72 
62.03 29.39 2.05 20.04 7.62 
80.85 53.8 5.82 0.05 1.49 
79.38 97.65 18.3 34.79 3.94 
58.89 45.76 28.91 10.46 5.29 
72.2 87.97 22.88 59.37 15.87 
41.59 80.47 24.71 34.18 40.91 
23.85 70.2 2.59 48.69 18.05 
25.17 70.41 3.23 20.88 19.97 
23.33 91.61 5.11 34.53 40.72 
45.11 20.1 17 18.8 2.31 
58.88 99.36 24.28 35.38 16.53 
22.54 87.1 5.79 36.96 49.41 
69.78 56.82 33.22 26.47 5.96 
25.84 44.94 31.5 34.48 14.18 
37.89 29.67 19.92 33.49 4.95 
47.63 29.32 22.35 41.18 12.02 
71.1 78.18 4.37 11.68 15.92 
70.88 53.92 23.76 11.06 18.44 
55.65 68.86 10.98 50.76 22.64 
50.67 90.09 1.74 42.22 35.26 
48.33 53.18 27.13 47.51 28.15 
26.69 77.33 18.92 45.58 25.54 
68.17 83.64 1.35 68.39 5.46 
49.34 70.67 1.56 10.19 9.72 
28.19 75.24 8.01 10.52 2.9 
11.51 53.6 29.71 32.82 0.52 
46.32 88.4 15.7 60.52 13.74 
68.02 88.75 11.06 72.42 15.82 
27 47.15 8.09 25.91 10.58 
66.46 36.1 1.84 8.93 15.18 
30.59 60.61 32.31 22.15 20.26 
4.19 87.45 31.08 25.72 1.06 
37.82 97.8 20.24 35.84 6.24 
15.21 99.27 36.96 30.62 8.97 
32.66 68.08 24.22 32.85 2.06 
28.9 44.71 3.16 30.97 5.6 
16.92 97.58 11.94 16.64 11.01 
36.46 90.83 43.41 47.72 17.27 
7.77 97.85 6.94 37.68 47.24 
=============================
=============================
mid point:74.5596 86.2713 73.6178 31.9296 29.4835 
78.9 87.71 90.26 0.7 4.21 
84.66 79.16 93.24 44.69 29.1 
58.16 66.99 59.03 45.89 0.01 
95.13 90.05 99.76 24.54 2.04 
94.41 95.74 70.31 25.82 47.13 
91.03 68.21 34.87 25.76 9.46 
89.32 97.87 99.67 49.5 2.36 
98.8 94.67 69.62 57.4 35.99 
80.95 99.39 73.07 63.17 1.39 
55.64 76.45 84.89 14.84 7.07 
57.87 99.9 50.41 27.94 35.55 
44.25 72.27 80.78 44.43 25.94 
86.9 99.82 51.85 45.74 17 
49.83 81.24 48.96 25.67 50.21 
75.09 97.53 78.46 42.45 33.22 
65.81 82.61 77.74 34.43 55.04 
78.18 77.88 79.72 50.41 64.15 
48.87 97.81 57.51 14.22 45.14 
76.66 88.43 66.62 46.05 55.2 
94.18 81.41 99.85 4.14 54.86 
91.69 84.4 64.12 1.35 76.32 
32.53 98.14 66.73 42.45 24.6 
86.01 66.56 95.74 2.79 2.13 
=============================
=============================
mid point:36.34 64.1327 19.47 25.0087 87.8393 
45.94 69.2 22.1 42.12 97.28 
86.31 48.02 21.45 9.14 90.28 
49.64 64.39 27.95 4.89 95.83 
5.39 49.97 15.56 69.97 80.38 
13.53 90.69 6.23 7.83 92.74 
4.74 65.58 24.53 21.84 86.35 
11.97 55.07 30.62 44.76 92.92 
4.4 54.35 30.7 34.3 89.67 
5.02 64.82 25.49 30.83 78.84 
86.97 48.24 20.38 2.79 95.08 
61.37 52.76 9.6 3.44 98.93 
44.93 88.8 3.06 13.42 95.91 
49.67 51.8 39.99 35.11 59.78 
51.98 64 7.67 21.92 87.67 
23.24 94.3 6.72 32.77 75.93 
=============================
=============================
mid point:62.9012 89.3071 64.5365 72.5982 67.11 
87.26 82.08 80.62 47.51 99.34 
78.55 81.29 80.52 64.68 68.95 
63.37 97.25 45 78.38 48.48 
65.56 91.84 16.4 54.62 52.8 
72.37 96.82 34.07 66.63 45.47 
67.07 92.49 55.22 53.12 62.13 
39.93 83.52 69.84 51.62 48.67 
46.07 90.22 43.1 47.51 51.86 
27.48 99.87 92.24 98.19 60.03 
60.14 97.37 76.98 72.13 69.68 
38.95 98.38 70.15 72.3 63.58 
59.9 98.2 65.9 84.26 43.98 
98.5 88.49 76.29 91.54 79.22 
69.2 94.78 88.54 87 87.3 
72.03 95.38 74.03 82.56 94.29 
43.91 59.05 35.54 90.68 84.1 
79.03 71.19 92.68 91.44 80.99 
=============================
=============================
mid point:38.5617 78.5681 64.1488 73.9556 17.8473 
79.17 82.31 81.54 79.81 46.11 
48.63 80.13 68.32 18.29 17.87 
27.07 42.52 67.43 68.61 5.98 
65.57 76.34 73.83 74.81 45.13 
49.32 77.93 93.27 74.78 13.88 
80.81 83.34 81.72 73.46 42.41 
8.54 71.27 24.87 85.87 2.61 
43.72 95.38 79.73 57.34 10.28 
39.3 70.69 98.1 99.15 55.26 
45.29 39.11 73.53 81.83 19.19 
20.51 79.03 93.99 97.38 42.22 
17.23 84.31 64.74 99.72 15.09 
69.39 70.82 89.23 91.2 46.33 
6.37 69.62 65.18 73.19 6.69 
55.6 80.78 93.05 74.71 13.85 
85.01 97.57 77.36 93.95 30.39 
75.32 87.46 94.89 81.66 14.72 
13.46 89.02 40.98 62.78 8.84 
18.57 69.07 49.68 40.32 20.78 
37.51 66.76 44.2 85.55 7.24 
58.06 96 82.63 40.26 5.02 
54.41 45.17 85.75 72.53 3.09 
29.89 65.97 43.03 65.72 15.24 
2.15 95.47 63.76 52.83 5.08 
3.65 93.91 52.94 94.87 5.74 
47.47 84.65 33.23 79.45 28.71 
8.73 71.85 59.37 73.33 37.93 
13.45 98.11 72.75 93.73 27.61 
5.86 98.92 43.1 92.74 22.89 
26.11 90.99 41.05 90.53 27.1 
17.84 59.71 45.24 46.63 4.69 
47.71 84.82 77.15 70.65 8.9 
50.66 84.99 30.02 72.44 17.96 
85.01 82.41 51.42 98.49 11.65 
40.25 66.74 71.32 74.22 15.96 
66.26 79.8 63.62 73.74 17.84 
7.2 79.11 74.53 63.96 17.56 
71.68 90.32 60.55 64.91 0.88 
6.56 85.13 86.62 92.6 6.92 
27.56 99.69 85.31 61.26 26.8 
74.29 98.94 48.53 55.05 12.81 
25.93 79.69 47.97 81.3 5.29 
47.64 78.53 33.45 65.6 8.03 
17.18 73.59 69.21 63.33 3 
31.56 84.04 49.49 99.54 22.71 
23.79 33.02 52.46 69.22 8.07 
17.1 92.79 24 86.07 11.11 
56.57 63.45 75 40.46 13.21 
=============================
=============================
mid point:80.0021 82.0426 26.8372 23.5303 42.4469 
98.13 88.56 11.02 50.85 42.1 
94.67 93.24 7.01 32.46 1.86 
75.39 85.86 35.33 22.71 32.74 
88.88 84.39 19.4 59.01 42.28 
84.26 87.4 23.93 12.84 88.51 
51.55 59.89 37.55 39.15 56.04 
94.12 81.21 20.4 6.74 68.82 
41.38 90.36 8.91 31.62 55.07 
83.32 75.41 2.02 24.43 53.97 
82.88 69.44 30.38 6.49 36.68 
47.03 86.21 16.02 24.67 47.86 
55.75 88.11 9.57 28.44 63.01 
89.85 93.41 7.57 48.29 43.93 
84.02 69.13 33.9 11.93 49.91 
85.06 76.12 51.74 11.39 27.2 
84.21 82.73 13.03 46.35 49.21 
81.38 56.61 32.77 1.48 33.49 
92.41 87.46 34.97 14.85 76.92 
65.24 75.2 13.76 38.32 43.27 
60.45 72.24 31.26 13.77 35.67 
96.75 81.75 10.3 7.6 48.61 
77.96 86.32 37.11 54.77 35.04 
59.58 92.86 12.89 47.26 57.88 
79.58 84.24 25.96 27.63 68.81 
79.82 87.26 60.18 28.65 23.49 
92.53 56 20.73 8.32 51.87 
67.72 82.43 70.74 10.56 40.73 
90.52 74.88 39.62 33.74 14.22 
80.32 93.23 21.95 36.54 32.73 
91.58 93.2 5.4 5.34 1.22 
95.6 93 62.6 17.39 6.87 
98.16 97.74 21.1 19.85 47.65 
77.56 94.29 30.2 5.96 28.33 
45.49 87.59 13.23 22.28 52.57 
81.84 87.97 24.03 21.13 54.96 
94.85 91.11 55.44 12.61 9.17 
90.65 94.51 52.58 17.7 67.83 
92.89 49 1.56 0.75 16.37 
86.7 69.3 40.49 13.81 48.54 
=============================