用神经网络分类minst的0和7,通过拟合迭代次数曲线n(δ)和准确率曲线p-max(δ),估算得到准确率可以达到0.999网络的训练时间。
实验用minst数据集,将28*28的图片缩小到9*9,网络用一个3*3的卷积核,网络结构是81*49*30*2,画成图
这个网络由两部分组成,左右两边分别向1,0和0,1收敛,左边输入minst的0,右边输入minst的7,让左右两个网络的权重部分共享,实现耦合达到分类的目的。
具体进样顺序 |
|||
δ=0.5 |
迭代次数 |
||
初始化权重 |
|||
minst 0-1 |
1 |
判断是否达到收敛 |
|
minst 7-1 |
2 |
判断是否达到收敛 |
|
梯度下降 |
|||
minst 0-2 |
3 |
判断是否达到收敛 |
|
minst 7-2 |
4 |
判断是否达到收敛 |
|
梯度下降 |
|||
…… |
|||
minst 0-4999 |
9997 |
判断是否达到收敛 |
|
minst 7-4999 |
9998 |
判断是否达到收敛 |
|
梯度下降 |
|||
…… |
|||
如果4999图片内没有达到收敛标准再次从头循环 |
|||
minst 0-1 |
9999 |
判断是否达到收敛 |
|
minst 7-1 |
10000 |
判断是否达到收敛 |
|
…… |
|||
每当网路达到收敛标准记录迭代次数和对应的准确率测试结果 |
|||
将这一过程重复199次 |
|||
δ=0.4 |
|||
… |
收敛条件是
if (Math.abs(f2[0]-y[0])< δ && Math.abs(f2[1]-y[1])< δ )
本文尝试了δ从0.5到4*1e-8在内的41个值,测试集是misnt0和7的前4999张图片。
这个网络简写成
S(minst0)81-(con3*3)49-30-2-(1,0)
S(minst7)81-(con3*3)49-30-2-(0,1)
w=w,w1=w1,w2=w2
进一步简写成
d2(minst0,7)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
测试集中有980个0和1000个7.取199次的平均值得到的数据
δ |
f2[0] |
f2[1] |
迭代次数n |
平均准确率p-ave |
耗时ms/次 |
耗时ms/199次 |
耗时min/199次 |
最大准确率p-max |
0.5 |
0.500624 |
0.500136 |
18.477387 |
0.507484392 |
720.939698 |
143483 |
2.391383333 |
0.788888889 |
0.4 |
0.542874 |
0.457613 |
1482.3216 |
0.758519872 |
1285.25126 |
255768 |
4.2628 |
0.985353535 |
0.3 |
0.602986 |
0.397565 |
1807.8945 |
0.870064971 |
1411.53769 |
280897 |
4.681616667 |
0.989393939 |
0.2 |
0.657201 |
0.342519 |
1978.1859 |
0.91547891 |
1465.53769 |
291642 |
4.8607 |
0.988383838 |
0.1 |
0.663414 |
0.336757 |
2232.1457 |
0.929105122 |
1564.11558 |
311259 |
5.18765 |
0.986868687 |
0.01 |
0.739832 |
0.260164 |
3104.6734 |
0.913217603 |
1906.8593 |
379482 |
6.3247 |
0.986868687 |
0.001 |
0.753366 |
0.246634 |
4367.4472 |
0.916666667 |
2383.22111 |
474277 |
7.904616667 |
0.987878788 |
1.00E-04 |
0.763782 |
0.236218 |
6468.6231 |
0.883122684 |
3217.72362 |
640327 |
10.67211667 |
0.987878788 |
9.00E-05 |
0.708516 |
0.291484 |
6437.6332 |
0.893916552 |
3236.13568 |
643991 |
10.73318333 |
0.98989899 |
8.00E-05 |
0.678371 |
0.321629 |
6564.3568 |
0.898771636 |
2551.54774 |
507774 |
8.4629 |
0.989393939 |
7.00E-05 |
0.703497 |
0.296503 |
6779.5779 |
0.894398761 |
3314.36181 |
659558 |
10.99263333 |
0.988888889 |
6.00E-05 |
0.628131 |
0.371869 |
6887.7739 |
0.907073245 |
3323.72362 |
661421 |
11.02368333 |
0.98989899 |
5.00E-05 |
0.58291 |
0.41709 |
7299.5276 |
0.898002639 |
3470.43719 |
690633 |
11.51055 |
0.989393939 |
4.00E-05 |
0.653257 |
0.346742 |
7553.4774 |
0.885858586 |
3534.61307 |
703388 |
11.72313333 |
0.989393939 |
3.00E-05 |
0.618086 |
0.381914 |
8293.9548 |
0.887477793 |
2956.69347 |
588382 |
9.806366667 |
0.99040404 |
2.00E-05 |
0.628138 |
0.371862 |
8723.6432 |
0.877178823 |
3656.92965 |
727729 |
12.12881667 |
0.988888889 |
1.00E-05 |
0.703515 |
0.296485 |
10555.437 |
0.863994214 |
4407.9598 |
877185 |
14.61975 |
0.984343434 |
9.00E-06 |
0.713565 |
0.286435 |
10476.271 |
0.862659256 |
4351.37688 |
865925 |
14.43208333 |
0.987373737 |
8.00E-06 |
0.723616 |
0.276384 |
10925.467 |
0.875917466 |
4060.24121 |
808003 |
13.46671667 |
0.988383838 |
7.00E-06 |
0.743716 |
0.256284 |
11219.568 |
0.870592863 |
4610.03518 |
917397 |
15.28995 |
0.987373737 |
6.00E-06 |
0.728641 |
0.271359 |
11748.347 |
0.861895335 |
4804.71859 |
956147 |
15.93578333 |
0.988383838 |
5.00E-06 |
0.688441 |
0.311559 |
12474.749 |
0.868242729 |
5049.55779 |
1004873 |
16.74788333 |
0.988383838 |
4.00E-06 |
0.663316 |
0.336684 |
13049.005 |
0.864778438 |
4211.21608 |
838032 |
13.9672 |
0.989393939 |
3.00E-06 |
0.703517 |
0.296483 |
14324.432 |
0.873516573 |
5667.23618 |
1127780 |
18.79633333 |
0.992424242 |
2.00E-06 |
0.592965 |
0.407035 |
16918.784 |
0.897830059 |
6517.77387 |
1297038 |
21.6173 |
0.992424242 |
1.00E-06 |
0.562814 |
0.437186 |
21313.809 |
0.892477539 |
7120.17085 |
1416923 |
23.61538333 |
0.993939394 |
9.00E-07 |
0.628141 |
0.371859 |
21287.422 |
0.894180498 |
7023.47236 |
1397686 |
23.29476667 |
0.991919192 |
8.00E-07 |
0.628141 |
0.371859 |
24145.121 |
0.90640069 |
7850.58794 |
1562283 |
26.03805 |
0.993434343 |
7.00E-07 |
0.643216 |
0.356784 |
27625.457 |
0.891246637 |
9050.57789 |
1801065 |
30.01775 |
0.990909091 |
6.00E-07 |
0.542714 |
0.457286 |
29357.477 |
0.896949393 |
9591.96985 |
1908802 |
31.81336667 |
0.991919192 |
5.00E-07 |
0.673367 |
0.326633 |
40684.06 |
0.898733567 |
12275.5075 |
2442826 |
40.71376667 |
0.993939394 |
4.00E-07 |
0.58794 |
0.41206 |
40085.211 |
0.901317192 |
12461.6784 |
2479874 |
41.33123333 |
0.992929293 |
3.00E-07 |
0.582915 |
0.417085 |
62320.854 |
0.90527892 |
19482.7588 |
3877069 |
64.61781667 |
0.994444444 |
2.00E-07 |
0.557789 |
0.442211 |
74617.935 |
0.913509467 |
22709.0452 |
4519101 |
75.31835 |
0.992929293 |
1.00E-07 |
0.407035 |
0.592965 |
133071.7 |
0.945982437 |
40567.4121 |
8072931 |
134.54885 |
0.995959596 |
9.00E-08 |
0.472362 |
0.527638 |
114357.71 |
0.946269225 |
43659.4774 |
8688252 |
144.8042 |
0.994949495 |
8.00E-08 |
0.477387 |
0.522613 |
134566.49 |
0.939576671 |
45279.7236 |
9010673 |
150.1778833 |
0.994444444 |
7.00E-08 |
0.432161 |
0.567839 |
142171.4 |
0.940269529 |
42553.4724 |
8468172 |
141.1362 |
0.995454545 |
6.00E-08 |
0.492462 |
0.507538 |
182137.55 |
0.93769098 |
54482.0302 |
10841924 |
180.6987333 |
0.994949495 |
5.00E-08 |
0.442211 |
0.557789 |
206749.03 |
0.951748642 |
61953.3668 |
12328735 |
205.4789167 |
0.993939394 |
4.00E-08 |
0.38191 |
0.61809 |
204035.56 |
0.950383229 |
61546.5176 |
12247759 |
204.1293167 |
0.995454545 |
p-ave是199组数据的平均准确率
p-max是199组数据的最大准确率
得到p-ave曲线
这条曲线在6e-6附近有一个谷,再次表明神经网络在训练的过程中平均性能有一个先下降后上升的过程。
比较当δ=0.1和δ=4e-8的数据
δ |
f2[0] |
f2[1] |
迭代次数n |
平均准确率p-ave |
耗时ms/次 |
耗时ms/199次 |
耗时min/199次 |
最大准确率p-max |
0.1 |
0.663414 |
0.336757 |
2232.1457 |
0.929105122 |
1564.11558 |
311259 |
5.18765 |
0.986868687 |
4.00E-08 |
0.38191 |
0.61809 |
204035.56 |
0.950383229 |
61546.5176 |
12247759 |
204.1293167 |
0.995454545 |
可以明显的观察到当将网络的收敛标准设定在δ=0.1时,网络在5.18min内可以实现199次收敛,其中最少有一次的准确率可以达到0.987.或者解释成当δ=0.1时在得到准确率为0.987的概率是5‰,耗时1.564s。
而当将准确率设定在δ=4e-8时,网络在204min内可以实现199次收敛,其中至少有一次的准确率可以达到0.995.或者解释成将网络的收敛标准设定在δ=4e-8时得到准确率0.995的概率是5‰需要耗时61.5s。
所以在实用中如果遇到需要为了训练效率而略微牺牲一些准确率的场景,可以将收敛标准设定在δ=0.1时,通过多次筛选的办法快速得到相对较高的训练结果。
拟合迭代次数曲线n(δ)
x |
δ |
4.00E-08,5.00E-08,6.00E-08,7.00E-08,8.00E-08,9.00E-08,1.00E-07,2.00E-07,3.00E-07,4.00E-07,5.00E-07,6.00E-07,7.00E-07,8.00E-07,9.00E-07,1.00E-06,2.00E-06,3.00E-06,4.00E-06 |
y |
n |
204035.5578,206749.0251,182137.5477,142171.397,134566.4874,114357.7085,133071.7035,74617.93467,62320.85427,40085.21106,40684.0603,29357.47739,27625.45729,24145.1206,21287.42211,21313.80905,16918.78392,14324.43216,13049.00503 |
拟合方程式:y=ax^b |
||
a = 2.55182534870891 |
||
b = -0.664739505322744 |
||
相关系数 R2:0.979422349837314 |
所以n(δ)的表达式为
比较实测值与计算值
δ |
实测迭代次数n |
计算值 |
实测值/计算值 |
0.5 |
18.47738693 |
4.045363 |
4.567547535 |
0.4 |
1482.321608 |
4.692209 |
315.9112178 |
0.3 |
1807.894472 |
5.681056 |
318.2320901 |
0.2 |
1978.18593 |
7.438475 |
265.9397073 |
0.1 |
2232.145729 |
11.79208 |
189.2919269 |
0.01 |
3104.673367 |
54.49165 |
56.97521311 |
0.001 |
4367.447236 |
251.808 |
17.34435699 |
1.00E-04 |
6468.623116 |
1163.614 |
5.559079436 |
9.00E-05 |
6437.633166 |
1248.032 |
5.158226943 |
8.00E-05 |
6564.356784 |
1349.674 |
4.863660981 |
7.00E-05 |
6779.577889 |
1474.954 |
4.596467925 |
6.00E-05 |
6887.773869 |
1634.107 |
4.215006842 |
5.00E-05 |
7299.527638 |
1844.656 |
3.957120345 |
4.00E-05 |
7553.477387 |
2139.614 |
3.53029925 |
3.00E-05 |
8293.954774 |
2590.521 |
3.201655029 |
2.00E-05 |
8723.643216 |
3391.891 |
2.571911094 |
1.00E-05 |
10555.43719 |
5377.104 |
1.963033684 |
9.00E-06 |
10476.27136 |
5767.204 |
1.816525311 |
8.00E-06 |
10925.46734 |
6236.894 |
1.751748019 |
7.00E-06 |
11219.56784 |
6815.817 |
1.646107535 |
6.00E-06 |
11748.34673 |
7551.272 |
1.555810341 |
5.00E-06 |
12474.74874 |
8524.227 |
1.46344634 |
4.00E-06 |
13049.00503 |
9887.236 |
1.319782848 |
3.00E-06 |
14324.43216 |
11970.9 |
1.196604916 |
2.00E-06 |
16918.78392 |
15674.06 |
1.079413126 |
1.00E-06 |
21313.80905 |
24847.8 |
0.857774421 |
9.00E-07 |
21287.42211 |
26650.46 |
0.798763628 |
8.00E-07 |
24145.1206 |
28820.92 |
0.837763598 |
7.00E-07 |
27625.45729 |
31496.15 |
0.877105924 |
6.00E-07 |
29357.47739 |
34894.71 |
0.84131596 |
5.00E-07 |
40684.0603 |
39390.77 |
1.032832225 |
4.00E-07 |
40085.21106 |
45689.29 |
0.877343678 |
3.00E-07 |
62320.85427 |
55317.96 |
1.126593549 |
2.00E-07 |
74617.93467 |
72430.41 |
1.030201719 |
1.00E-07 |
133071.7035 |
114822.6 |
1.15893274 |
9.00E-08 |
114357.7085 |
123152.8 |
0.928583898 |
8.00E-08 |
134566.4874 |
133182.6 |
1.010391113 |
7.00E-08 |
142171.397 |
145544.9 |
0.976821689 |
6.00E-08 |
182137.5477 |
161249.8 |
1.129536768 |
5.00E-08 |
206749.0251 |
182026.2 |
1.135819853 |
4.00E-08 |
204035.5578 |
211131.9 |
0.966388895 |
当δ<1e-5是拟合度都相对较高。
第二步拟合准确率曲线p-max(δ)
x |
-lnδ |
4.605170186,6.907755279,13.81551056,16.11809565 |
y |
n |
0.986868687,0.987878788,0.993939394,0.995959596 |
拟合方程式:y=ax^b |
||
a = 0.974825303673311 |
||
b = 0.00749493648302876 |
||
相关系数 R2:0.958576584249794 |
p-max(δ)的表达式近似为
实测值与计算值比较
错误数量 |
δ |
最大准确率p-max |
-lnδ |
计算δ |
实测δ/计算δ |
29 |
0.4 |
0.985353535 |
0.916291 |
0.015110624 |
26.47144191 |
21 |
0.3 |
0.989393939 |
1.203973 |
7.19E-04 |
417.0819746 |
23 |
0.2 |
0.988383838 |
1.609438 |
0.001808636 |
110.580592 |
26 |
0.01 |
0.986868687 |
4.60517 |
0.005821225 |
1.717851393 |
24 |
0.001 |
0.987878788 |
6.907755 |
0.002742526 |
0.364627293 |
24 |
1.00E-04 |
0.987878788 |
9.21034 |
0.002742526 |
0.036462729 |
12 |
1.00E-06 |
0.993939394 |
13.81551 |
1.61E-06 |
0.621921016 |
8 |
1.00E-07 |
0.995959596 |
16.1181 |
2.53E-08 |
3.949127955 |
10 |
9.00E-08 |
0.994949495 |
16.22346 |
2.32E-07 |
0.388026629 |
11 |
8.00E-08 |
0.994444444 |
16.34124 |
6.31E-07 |
0.126804257 |
9 |
7.00E-08 |
0.995454545 |
16.47477 |
7.95E-08 |
0.880050446 |
10 |
6.00E-08 |
0.994949495 |
16.62892 |
2.32E-07 |
0.258684419 |
12 |
5.00E-08 |
0.993939394 |
16.81124 |
1.61E-06 |
0.031096051 |
9 |
4.00E-08 |
0.995454545 |
17.03439 |
7.95E-08 |
0.502885969 |
0和7之间的外形差异度仅小于0和1之间的外形差异度,因为差异度比较大所以区分的准确率要相对高,所以准确率梯度小些,拟合的精度也受到影响。不过还是用这个表达式估算网络的准确率达到0.999,也就是只错一个或者两个图片,需要
δ= 3.90E-12,
目标准确率 |
计算δ |
计算n |
耗时 min |
耗时 day |
0.999 |
3.90E-12 |
97869735 |
94623.68699 |
65.71089375 |
让p-max=0.999用p-max(δ)解得δ,再用n(δ)得到n,然后根据实验时间的数据得到耗时。
据推算网络d2(minst0,7)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
的准确率要达到0.999可以将收敛标准设定在δ= 3.90E-12,在65天内网络可以收敛199次,其中应该至少有一次的准确率可以达到0.999。或者将网络的收敛标设定在δ= 3.90E-12,准确率达到0.999的概率是5‰,需要时间约为475min。
实验数据 |
学习率 0.1 |
权重初始化方式 |
Random rand1 =new Random(); |
int ti1=rand1.nextInt(98)+1; |
int xx=1; |
if(ti1%2==0) |
{ xx=-1;} |
tw[a][b]=xx*((double)ti1/x); |
第一层第二层和卷积核的权重的初始化的x分别为1000,1000,200 |
http://www.qinms.com/webapp/curvefit/cf.aspx
f2[0] f2[1] 迭代次数n 最大准确率p-max δ 耗时ms/次
0.501388561 0.499863563 33 0.494949495 0.5 1231
0.54846786 0.494237522 1 0.494949495 0.5 813
0.531836001 0.468141868 1 0.494949495 0.5 751
0.499566649 0.515101916 2 0.505050505 0.5 779
0.497015024 0.513528631 2 0.505050505 0.5 731
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143483
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280897
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0.185438007 0.814555129 2518 0.98030303 0.2 1637
0.811215845 0.189681259 1981 0.921212121 0.2 1463
0.156135898 0.841440141 2216 0.974242424 0.2 1620
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0.819378239 0.185157567 2613 0.86010101 0.2 1667
0.81645731 0.183036104 1981 0.847979798 0.2 1565
0.818400474 0.184398987 1685 0.97020202 0.2 1343
0.809524309 0.189222234 1385 0.877272727 0.2 1233
0.808712192 0.189392561 2613 0.892929293 0.2 1685
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0.807497493 0.191792223 2421 0.914141414 0.2 1615
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0.162170978 0.839857039 3654 0.950505051 0.2 2094
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0.191938002 0.807238833 3646 0.941414141 0.2 2097
0.810559076 0.192387159 1685 0.920707071 0.2 1378
0.822212677 0.179373098 1685 0.941414141 0.2 1394
0.807665398 0.194897359 1297 0.871717172 0.2 1254
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0.808615733 0.194613514 1385 0.931818182 0.2 1269
0.828815464 0.170238688 1685 0.966666667 0.2 1330
0.819027974 0.178488289 2147 0.976262626 0.2 1518
0.802952409 0.197708066 3187 0.807575758 0.2 1975
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0.818669564 0.184272362 2935 0.881818182 0.2 1812
0.810327061 0.192430716 1981 0.862121212 0.2 1616
0.822993601 0.171153629 2613 0.920707071 0.2 1690
0.818611203 0.183407216 2975 0.964646465 0.2 1902
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0.814726051 0.181522125 1701 0.853030303 0.2 1333
0.808816521 0.195548047 2145 0.97979798 0.2 1510
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0.176443567 0.827806201 4246 0.962626263 0.2 2286
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0.185494456 0.808293262 1602 0.96010101 0.2 1316
0.812501439 0.1788109 1701 0.849494949 0.2 1331
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0.816601908 0.18036424 1905 0.975252525 0.2 1472
0.807564754 0.195665094 1585 0.864141414 0.2 1344
0.81218061 0.184073619 1373 0.946464646 0.2 1227
0.191599886 0.809782397 1628 0.983333333 0.2 1329
0.809787298 0.192025504 1479 0.946969697 0.2 1233
0.83914959 0.160925865 1685 0.970707071 0.2 1322
0.191144251 0.804210247 1476 0.964646465 0.2 1270
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0.811018537 0.193916846 1479 0.97979798 0.2 1309
0.184814669 0.819266244 1498 0.976262626 0.2 1245
0.191461804 0.811867283 1988 0.980808081 0.2 1424
0.8432941 0.158588306 1585 0.959090909 0.2 1327
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0.853200292 0.150842269 1585 0.948989899 0.2 1282
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0.821465745 0.178227671 1905 0.978787879 0.2 1396
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0.814763758 0.191452714 1685 0.936868687 0.2 1331
0.815469278 0.186302093 2613 0.928787879 0.2 1787
0.838781379 0.165304907 2281 0.79040404 0.2 1549
0.816612365 0.184818567 1385 0.922727273 0.2 1221
0.825285572 0.172535284 1701 0.878787879 0.2 1352
0.120332652 0.878670055 2216 0.965151515 0.2 1508
0.196086645 0.800297787 2586 0.938888889 0.2 1675
0.819682732 0.18362481 1913 0.920707071 0.2 1426
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0.196683249 0.805260893 1602 0.980808081 0.2 1338
0.823660693 0.176051123 1981 0.906060606 0.2 1440
0.813162804 0.183515069 2165 0.911616162 0.2 1505
0.186794489 0.810272442 2060 0.93989899 0.2 1477
0.819413246 0.187886571 1701 0.91969697 0.2 1353
0.811362467 0.192118513 1591 0.955050505 0.2 1346
0.811486497 0.187757736 1569 0.884343434 0.2 1306
0.813926577 0.188498447 2227 0.931818182 0.2 1649
0.81199379 0.190397638 1973 0.88989899 0.2 1460
0.809591737 0.192952621 2371 0.815151515 0.2 1604
0.835675819 0.160150298 1297 0.950505051 0.2 1211
0.804325005 0.197806108 2421 0.922222222 0.2 1631
0.81242916 0.192416337 1603 0.92020202 0.2 1321
0.8240603 0.181743661 2433 0.642424242 0.2 1621
0.812809979 0.18802174 2421 0.959090909 0.2 1586
0.194360129 0.805045802 1080 0.978787879 0.2 1134
0.808537726 0.190857562 1821 0.818686869 0.2 1425
0.814824401 0.188479072 1385 0.921717172 0.2 1222
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0.807745966 0.189372884 1691 0.778282828 0.2 1370
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0.81666095 0.185257812 2157 0.963636364 0.2 1646
0.827402463 0.173281618 1701 0.908080808 0.2 1363
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0.825654562 0.177118562 1981 0.887373737 0.2 1456
0.81868574 0.186463348 1297 0.977272727 0.2 1175
0.802485392 0.191760996 1691 0.891414141 0.2 1339
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0.81188944 0.186515346 1373 0.92020202 0.2 1239
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0.81152524 0.193008462 1981 0.802525253 0.2 1456
0.192625706 0.805202297 1484 0.965151515 0.2 1253
0.809544041 0.190335725 2469 0.866666667 0.2 1600
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0.807734487 0.191879248 1797 0.891919192 0.2 1404
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0.804183199 0.197871724 2047 0.946464646 0.2 1480
0.820980462 0.184000294 2469 0.822727273 0.2 1650
291642
0.096521136 0.902546742 2586 0.958080808 0.1 1644
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0.907211432 0.095044036 1541 0.897474747 0.1 1259
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0.094179628 0.904308778 1834 0.951010101 0.1 1378
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0.099898431 0.900348588 2588 0.958080808 0.1 1740
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0.915024581 0.085917754 3873 0.929292929 0.1 2205
0.903211747 0.094439321 2011 0.980808081 0.1 1456
0.910405346 0.091764183 2577 0.923737374 0.1 1652
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0.088551113 0.913312568 1932 0.93989899 0.1 1410
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0.094662462 0.904656608 3526 0.972727273 0.1 2047
0.910691666 0.087591883 1385 0.904040404 0.1 1238
0.093968965 0.907123938 2148 0.965656566 0.1 1497
0.912357011 0.085171011 2013 0.980808081 0.1 1487
0.073952857 0.927557253 1484 0.942424242 0.1 1299
0.089226854 0.912256162 2350 0.96010101 0.1 1589
0.900528686 0.09736258 1685 0.975757576 0.1 1299
0.09766149 0.903410243 2604 0.933333333 0.1 1727
0.918224559 0.08400099 2613 0.938383838 0.1 1682
0.911365859 0.086528601 2191 0.951010101 0.1 1538
0.904332436 0.096398644 2155 0.967171717 0.1 1674
0.914449449 0.084835542 2195 0.897474747 0.1 1598
0.901267925 0.098819928 1663 0.936868687 0.1 1327
0.930218887 0.068991195 1529 0.964646465 0.1 1335
0.905423789 0.096150672 2613 0.956565657 0.1 1737
0.906684984 0.095179801 2635 0.908080808 0.1 1795
0.913023947 0.087854677 2371 0.891414141 0.1 1600
0.077683748 0.924938406 1484 0.976767677 0.1 1250
0.912174468 0.086422853 1885 0.954545455 0.1 1397
0.906892506 0.092887115 3003 0.823232323 0.1 1846
0.903192217 0.095135691 1913 0.951010101 0.1 1424
0.903980779 0.095849929 2469 0.872222222 0.1 1618
0.084083225 0.914940444 2216 0.977272727 0.1 1532
0.906157418 0.094218414 1913 0.961616162 0.1 1408
0.929443974 0.070711259 1529 0.953535354 0.1 1375
0.900469235 0.09749041 4033 0.784848485 0.1 2267
0.925622302 0.074351918 2673 0.853030303 0.1 1757
0.097373878 0.906162892 1484 0.954040404 0.1 1268
0.913778464 0.084809171 2577 0.951010101 0.1 1673
0.901781482 0.09649746 1585 0.96969697 0.1 1302
0.932915761 0.069026475 1821 0.86969697 0.1 1371
0.904509476 0.09893165 2263 0.905555556 0.1 1569
0.090418037 0.911256694 1932 0.907575758 0.1 1443
0.91653204 0.087689761 2635 0.905050505 0.1 1693
0.907981541 0.089891648 2673 0.896464646 0.1 1699
0.928689003 0.072319964 1685 0.927777778 0.1 1335
0.900706219 0.097109479 1913 0.892929293 0.1 1442
0.080383772 0.921979247 1498 0.980808081 0.1 1318
0.916484229 0.086159939 2577 0.927777778 0.1 1705
0.924742638 0.074424471 1685 0.981818182 0.1 1347
0.902056195 0.09405227 2155 0.973232323 0.1 1529
0.089638242 0.910692454 2174 0.952020202 0.1 1505
0.915137579 0.082333964 2227 0.972727273 0.1 1544
0.917755239 0.081149904 1913 0.972727273 0.1 1443
0.900747876 0.099800222 2037 0.966666667 0.1 1473
0.936335518 0.064352552 2191 0.91010101 0.1 1510
0.097548852 0.901956813 2148 0.968686869 0.1 1488
0.909177867 0.08819607 1707 0.868686869 0.1 1316
0.097888888 0.903629189 1910 0.968686869 0.1 1410
0.914728874 0.086802287 2787 0.882323232 0.1 1792
0.08365362 0.916869493 2204 0.958585859 0.1 1554
0.079300798 0.917546089 2060 0.932323232 0.1 1553
0.069912443 0.931599437 2016 0.974747475 0.1 1504
0.062346848 0.938985477 1988 0.972222222 0.1 1430
0.908542742 0.089629003 1685 0.98030303 0.1 1331
0.902825708 0.096987165 1685 0.966666667 0.1 1364
0.086020157 0.919681533 3902 0.94040404 0.1 2199
0.905044109 0.095042729 1529 0.924242424 0.1 1253
0.937226413 0.062364508 1385 0.952020202 0.1 1252
0.904562572 0.094699462 1701 0.912121212 0.1 1364
0.91762524 0.082880023 2045 0.974747475 0.1 1507
0.908577037 0.094497354 2853 0.807070707 0.1 1827
0.904466915 0.098474237 1385 0.881818182 0.1 1332
0.089917035 0.913152674 2016 0.971212121 0.1 1530
0.906256989 0.094397409 1541 0.946969697 0.1 1320
0.929883496 0.068097603 1905 0.982828283 0.1 1581
0.909992242 0.091344347 2787 0.741414141 0.1 1720
0.916359054 0.084701001 1541 0.915656566 0.1 1291
0.911362913 0.092372431 3169 0.909090909 0.1 1935
0.098989138 0.907073228 2568 0.940909091 0.1 1668
0.904307763 0.097908553 1691 0.958585859 0.1 1300
0.093907556 0.902765891 2204 0.968686869 0.1 1580
0.904407148 0.099070963 2187 0.963131313 0.1 1562
0.902071063 0.095721055 2421 0.891919192 0.1 1652
0.918506206 0.080574412 2227 0.920707071 0.1 1538
0.098630413 0.904059956 1498 0.984848485 0.1 1238
0.917902043 0.081063422 2263 0.777777778 0.1 1574
0.094699391 0.901244204 2350 0.948989899 0.1 1591
0.905373579 0.09377643 2195 0.894949495 0.1 1612
0.926390593 0.07135526 2421 0.921717172 0.1 1618
0.907092813 0.093256363 1885 0.960606061 0.1 1446
0.924040522 0.073855001 2433 0.839393939 0.1 1612
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0.094526399 0.904916059 1712 0.953030303 0.1 1347
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0.916332103 0.087364877 2147 0.972222222 0.1 1526
0.077138854 0.920958945 2350 0.956060606 0.1 1596
0.097865739 0.903942251 1968 0.96969697 0.1 1532
0.091064058 0.906474785 1788 0.952020202 0.1 1377
0.909349753 0.090399494 2857 0.893434343 0.1 1745
0.902488977 0.0976429 2677 0.932323232 0.1 1682
0.065558916 0.934416794 2978 0.945959596 0.1 1802
0.916592424 0.083972011 2371 0.798989899 0.1 1576
0.08779659 0.91238761 2586 0.968686869 0.1 1665
0.09033487 0.907409077 2822 0.958080808 0.1 1735
0.909007828 0.090669589 1981 0.933333333 0.1 1423
0.905224908 0.094501963 2227 0.93989899 0.1 1607
0.091366515 0.906432732 2216 0.977272727 0.1 1644
0.903414863 0.095391264 2435 0.938383838 0.1 1659
0.91023975 0.088591305 1529 0.863636364 0.1 1351
0.909053919 0.09224273 1701 0.871212121 0.1 1389
0.92285271 0.074326435 1603 0.933838384 0.1 1342
0.913185084 0.087036918 1585 0.960606061 0.1 1390
0.913137844 0.090614485 1541 0.864141414 0.1 1289
0.904964476 0.09682673 3395 0.945959596 0.1 2065
0.908462713 0.092087314 1541 0.91969697 0.1 1332
0.90497847 0.09511316 2433 0.709090909 0.1 1738
0.910230891 0.094264013 1685 0.962626263 0.1 1416
0.90827911 0.090628249 2997 0.907070707 0.1 1886
0.084240434 0.914684331 1988 0.986868687 0.1 1504
0.078611612 0.918509324 1932 0.973232323 0.1 1418
0.91614285 0.082045748 1691 0.83989899 0.1 1353
311259
0.991634408 0.008240038 2421 0.933838384 0.01 1608
0.991098169 0.009011174 2733 0.904545455 0.01 1778
0.991057439 0.008977802 2241 0.969191919 0.01 1571
0.992490624 0.007479069 3557 0.931818182 0.01 2097
0.995151903 0.004947088 2433 0.534848485 0.01 1616
0.993497348 0.006502729 3533 0.981313131 0.01 2087
0.991551625 0.008455672 3003 0.791414141 0.01 1970
0.005806864 0.994333548 2232 0.912626263 0.01 1615
0.991662148 0.00835886 2421 0.985353535 0.01 1663
0.009805232 0.990046942 2022 0.974747475 0.01 1577
0.994601595 0.005406837 3343 0.974242424 0.01 1980
0.991245317 0.008625625 3107 0.973737374 0.01 1878
0.993556762 0.006496074 2433 0.635353535 0.01 1649
0.991081197 0.008475945 2147 0.984848485 0.01 1531
0.005736511 0.994078064 3526 0.947979798 0.01 2082
0.009296469 0.990530005 3174 0.966161616 0.01 1967
0.992743656 0.007475986 3615 0.96969697 0.01 2160
0.992770702 0.007485378 4107 0.737878788 0.01 2419
0.990644395 0.009058978 2433 0.727777778 0.01 1674
0.990398163 0.009623519 5459 0.656060606 0.01 2866
0.99129405 0.008733028 3139 0.981313131 0.01 1912
0.994126254 0.005761022 2191 0.952020202 0.01 1565
0.992194787 0.008109739 3139 0.973232323 0.01 1981
0.994674258 0.005345461 3187 0.875757576 0.01 1912
0.990761144 0.009379683 2421 0.958585859 0.01 1647
0.991856621 0.008194569 4819 0.934343434 0.01 2579
0.993889245 0.006131212 2787 0.745454545 0.01 1786
0.991573422 0.008519313 3873 0.908585859 0.01 2385
0.990050488 0.009802058 3359 0.969191919 0.01 1977
0.007412738 0.992429287 2216 0.982323232 0.01 1560
0.99418603 0.006072667 2613 0.984343434 0.01 1778
0.993190652 0.00678989 3395 0.979292929 0.01 2080
0.007023229 0.993154178 3312 0.86969697 0.01 1987
0.99322879 0.006879647 2673 0.911616162 0.01 1771
0.990579301 0.009678331 4351 0.895454545 0.01 2408
0.991666492 0.008423139 3947 0.905050505 0.01 2227
0.008193524 0.992150068 2586 0.933333333 0.01 1751
0.009854233 0.990285538 3308 0.971717172 0.01 2034
0.99029804 0.009572556 2421 0.960606061 0.01 1787
0.9906537 0.009544047 3181 0.939393939 0.01 2007
0.991249994 0.00882355 3395 0.901010101 0.01 2041
0.991850871 0.008224246 2263 0.901515152 0.01 1578
0.992370328 0.007474781 2433 0.761616162 0.01 1622
0.991058123 0.008676105 3531 0.883333333 0.01 2065
0.992428866 0.00742216 4207 0.961111111 0.01 2366
0.004937054 0.995033842 2798 0.977272727 0.01 1817
0.992150918 0.007706901 3545 0.879292929 0.01 2037
0.991623289 0.008180968 2823 0.98030303 0.01 1771
0.991332349 0.008634689 2699 0.894444444 0.01 1787
0.990916482 0.009069344 3747 0.978282828 0.01 2222
0.007642474 0.992506951 1988 0.957575758 0.01 1454
0.994827845 0.005217394 3557 0.856565657 0.01 2053
0.007533867 0.992513646 2798 0.935858586 0.01 1754
0.992151638 0.007865531 4843 0.849494949 0.01 2496
0.009621318 0.990194431 3942 0.926767677 0.01 2203
0.993817221 0.006028932 3959 0.723737374 0.01 2265
0.990145732 0.00991472 3107 0.957575758 0.01 1889
0.005463814 0.994386976 2208 0.977777778 0.01 1550
0.990972069 0.008980851 3187 0.916161616 0.01 1927
0.994079525 0.00586232 2421 0.948484848 0.01 1739
0.005307427 0.994678355 4376 0.943434343 0.01 2368
0.996241478 0.003754329 3343 0.960606061 0.01 1959
0.008997739 0.990611321 2262 0.92979798 0.01 1578
0.008654805 0.991300353 2978 0.893939394 0.01 1807
0.009939257 0.990230452 3468 0.947979798 0.01 2030
0.008428506 0.991741232 2756 0.979292929 0.01 1758
0.991927158 0.008186036 2677 0.942424242 0.01 1685
0.005782116 0.99439727 3110 0.849494949 0.01 1868
0.991852094 0.007763705 2433 0.714141414 0.01 1585
0.990855795 0.009151041 2613 0.968686869 0.01 1685
0.997840051 0.002149854 3557 0.861111111 0.01 2164
0.992550795 0.007770957 3395 0.963636364 0.01 2030
0.993906698 0.006133224 3181 0.923232323 0.01 1906
0.990612377 0.009219057 3909 0.975757576 0.01 2140
0.991726001 0.008044021 2147 0.986868687 0.01 1532
0.008943023 0.991228161 3380 0.969191919 0.01 1936
0.990419175 0.009637065 2669 0.972222222 0.01 1667
0.99135204 0.008345866 3257 0.952020202 0.01 1938
0.994865098 0.005164087 3343 0.939393939 0.01 1955
0.991772724 0.008482317 3701 0.976767677 0.01 2075
0.990637377 0.009729898 2433 0.911111111 0.01 1609
0.99051089 0.009302357 3139 0.953535354 0.01 1982
0.008248208 0.991470693 3526 0.950505051 0.01 2091
0.992304508 0.007776676 2263 0.886868687 0.01 1590
0.99293407 0.007133525 2613 0.955555556 0.01 1716
0.007489418 0.992664774 3726 0.917676768 0.01 2149
0.992191684 0.007489961 3501 0.881818182 0.01 2052
0.007647684 0.99221792 2798 0.955555556 0.01 1738
0.990782462 0.009193615 3395 0.880808081 0.01 2057
0.991987891 0.007984134 3019 0.951515152 0.01 1851
0.992287831 0.00751522 2613 0.953535354 0.01 1687
0.993128501 0.006875488 3395 0.937373737 0.01 2005
0.990346924 0.009630402 2191 0.934343434 0.01 1547
0.00975787 0.990283559 3526 0.963636364 0.01 2007
0.990560616 0.009584664 3947 0.83989899 0.01 2195
0.004585398 0.995565953 2978 0.916666667 0.01 1885
0.990953641 0.009370614 2613 0.982828283 0.01 1677
0.990395253 0.009476332 4485 0.945959596 0.01 2388
0.991075465 0.009075044 3343 0.922727273 0.01 2000
0.994190555 0.005816134 3343 0.975252525 0.01 2000
0.991938657 0.008020823 3257 0.977272727 0.01 1971
0.007963254 0.992271081 3380 0.970707071 0.01 2041
0.990785888 0.00941952 2435 0.901010101 0.01 1614
0.991726484 0.008170259 5271 0.827777778 0.01 2800
0.004381469 0.995675043 4592 0.895454545 0.01 2495
0.995414484 0.004523516 3627 0.79040404 0.01 2084
0.991228656 0.008337171 2433 0.843434343 0.01 1646
0.993862466 0.006127208 2677 0.926767677 0.01 1693
0.006761003 0.993388343 2960 0.885858586 0.01 1809
0.990832289 0.009028462 3897 0.971717172 0.01 2204
0.991345706 0.0082392 3299 0.962626263 0.01 1937
0.994121474 0.005765387 3343 0.96969697 0.01 1941
0.990325065 0.009804199 3257 0.968686869 0.01 1961
0.995277539 0.004991406 2191 0.914141414 0.01 1614
0.990449015 0.009319543 2191 0.878787879 0.01 1530
0.991279698 0.008727438 2613 0.986363636 0.01 1714
0.990927843 0.009181241 3671 0.91969697 0.01 2131
0.0079059 0.992254133 3526 0.97020202 0.01 2062
0.009232944 0.990283945 6076 0.961616162 0.01 3055
0.991869666 0.007964874 3557 0.925252525 0.01 2008
0.993528175 0.006477831 2433 0.843939394 0.01 1609
0.006733248 0.993208359 2798 0.939393939 0.01 1774
0.992041854 0.007829469 2191 0.935858586 0.01 1505
0.991012049 0.009238085 2263 0.927272727 0.01 1552
0.99198331 0.008005818 2677 0.826262626 0.01 1810
0.006989127 0.993059878 2216 0.982323232 0.01 1553
0.990356065 0.009421667 2577 0.94040404 0.01 1702
0.006594017 0.993481816 2216 0.97979798 0.01 1550
0.990502598 0.009661076 2263 0.868686869 0.01 1591
0.993502042 0.006567666 2433 0.857070707 0.01 1598
0.99292672 0.006920709 2421 0.986363636 0.01 1582
0.991568583 0.008179449 2733 0.861111111 0.01 1778
0.008569745 0.991256526 2822 0.971212121 0.01 1745
0.00768543 0.992418901 3350 0.97020202 0.01 1950
0.994779896 0.005195327 2677 0.825252525 0.01 1729
0.992886141 0.007171465 2549 0.93030303 0.01 1673
0.009835712 0.990102966 3216 0.957070707 0.01 1985
0.990971477 0.00901836 3615 0.951010101 0.01 2136
0.991431401 0.008466751 3747 0.96010101 0.01 2188
0.990835192 0.008837369 3187 0.93989899 0.01 1943
0.99143639 0.008507805 3561 0.783838384 0.01 2092
0.990591678 0.009331948 2787 0.92020202 0.01 1762
0.993758019 0.006224216 3557 0.916666667 0.01 2036
0.99015705 0.009990504 3257 0.968686869 0.01 1932
0.00975847 0.990218818 2630 0.982323232 0.01 1679
0.991936551 0.008246768 3015 0.905050505 0.01 1831
0.992893717 0.006916347 2421 0.981818182 0.01 1620
0.990489094 0.009617126 3557 0.943939394 0.01 2145
0.990622955 0.009365288 3219 0.947474747 0.01 1993
0.993008685 0.006991306 5519 0.70959596 0.01 2770
0.007429007 0.992395524 1932 0.983333333 0.01 1445
0.007686226 0.992151565 2798 0.96969697 0.01 1770
0.993272775 0.006852548 2613 0.976262626 0.01 1700
0.992000802 0.008030865 2433 0.627272727 0.01 1592
0.991425963 0.008551462 3257 0.97979798 0.01 1954
0.991178603 0.009213257 2191 0.909090909 0.01 1525
0.99088127 0.009187375 2613 0.972727273 0.01 1682
0.9907739 0.009321513 2433 0.842929293 0.01 1576
0.991274605 0.009003602 3181 0.918686869 0.01 1966
0.992359297 0.007921716 3003 0.80959596 0.01 1822
0.991136285 0.008816987 2733 0.863131313 0.01 1781
0.993934507 0.005833335 1685 0.966161616 0.01 1367
0.994519135 0.005708958 3615 0.957575758 0.01 2085
0.990852585 0.009346892 2433 0.745454545 0.01 1627
0.990366905 0.00956448 3709 0.574242424 0.01 2102
0.99324461 0.006527329 2787 0.896969697 0.01 1720
0.009630749 0.990200947 4058 0.936363636 0.01 2226
0.990515371 0.009021661 3257 0.977272727 0.01 1926
0.992525021 0.007437457 2433 0.679292929 0.01 1653
0.993532783 0.006259264 4843 0.881313131 0.01 2666
0.991872943 0.007952179 3181 0.905050505 0.01 1904
0.008800368 0.991189174 3380 0.954545455 0.01 1970
0.990494731 0.00921118 3441 0.901515152 0.01 2047
0.990636834 0.009305713 3905 0.915151515 0.01 2192
0.993675861 0.006352522 3019 0.970707071 0.01 1820
0.009552184 0.99037861 4592 0.956565657 0.01 2480
0.991308572 0.008672814 2613 0.972222222 0.01 1664
0.990457355 0.00949313 3839 0.948989899 0.01 2167
0.009895666 0.990151876 3980 0.808080808 0.01 2227
0.993794074 0.006226914 2733 0.859090909 0.01 1777
0.99397601 0.0061493 2227 0.959090909 0.01 1657
0.99218839 0.007922634 2263 0.832828283 0.01 1596
0.007159706 0.993132703 4246 0.932828283 0.01 2411
0.008660527 0.991146912 3110 0.903030303 0.01 1870
0.006963677 0.993131676 3412 0.852525253 0.01 1968
0.991819725 0.008268735 2613 0.983838384 0.01 1695
0.993387767 0.006611297 3557 0.927272727 0.01 2093
0.009871911 0.990164188 2798 0.97979798 0.01 1823
0.990469252 0.009730528 2623 0.927272727 0.01 1724
0.991380189 0.008569952 2191 0.936868687 0.01 1527
0.99115435 0.008952706 3139 0.941414141 0.01 1921
0.008209925 0.991767096 3174 0.982828283 0.01 2039
0.992101649 0.007725783 2433 0.566666667 0.01 1660
0.007222983 0.992941095 3174 0.978282828 0.01 1951
0.008513942 0.991406419 3174 0.976767677 0.01 1951
0.99110232 0.009302572 3627 0.92979798 0.01 2370
0.993001588 0.0068664 3343 0.98030303 0.01 2434
0.009506885 0.990717922 2822 0.975252525 0.01 1762
0.991150068 0.008923827 3343 0.983838384 0.01 2007
379482
0.999019786 9.40E-04 3343 0.952020202 0.001 2018
0.999410161 6.05E-04 3343 0.940909091 0.001 1990
8.46E-04 0.999175086 3526 0.977777778 0.001 2105
0.999269325 7.21E-04 3627 0.88989899 0.001 2185
0.999109227 9.00E-04 3919 0.846464646 0.001 2273
0.999291177 7.06E-04 3875 0.983333333 0.001 2170
0.999024835 9.76E-04 5271 0.61010101 0.001 2700
0.99937229 6.31E-04 4951 0.87979798 0.001 2570
0.999041925 9.71E-04 3615 0.985353535 0.001 2071
0.999439986 5.62E-04 4677 0.903030303 0.001 2491
0.99912106 8.80E-04 4677 0.955555556 0.001 2454
6.83E-04 0.999315511 3646 0.952020202 0.001 2135
0.999171481 8.14E-04 3919 0.960606061 0.001 2254
0.999248231 7.35E-04 3993 0.980808081 0.001 2212
0.999299766 6.92E-04 4819 0.968686869 0.001 2580
0.999375728 6.26E-04 4677 0.905050505 0.001 2512
0.999053507 9.50E-04 3897 0.980808081 0.001 2222
0.999129437 8.34E-04 3533 0.96010101 0.001 2067
7.52E-04 0.999242438 3980 0.84040404 0.001 2213
0.999344374 6.46E-04 4723 0.83989899 0.001 2536
0.999215771 7.69E-04 4951 0.82020202 0.001 2650
7.61E-04 0.999228856 5778 0.963131313 0.001 2997
0.999223169 8.02E-04 4819 0.937878788 0.001 2504
0.999155391 8.29E-04 3931 0.960606061 0.001 2229
0.999362021 6.27E-04 3947 0.857575758 0.001 2180
5.24E-04 0.999481723 4246 0.946969697 0.001 2348
0.999040903 9.66E-04 3627 0.827272727 0.001 2130
0.999566853 4.32E-04 3993 0.951515152 0.001 2234
0.999241938 7.77E-04 4351 0.954040404 0.001 2396
0.999014393 9.97E-04 3395 0.98030303 0.001 2027
0.999137344 8.92E-04 3993 0.943939394 0.001 2268
0.999404537 6.01E-04 4291 0.889393939 0.001 2319
0.999466687 5.34E-04 3343 0.958080808 0.001 1958
2.71E-04 0.999731524 4236 0.926767677 0.001 2314
0.999036931 9.57E-04 3343 0.971212121 0.001 1994
3.94E-04 0.99961107 4236 0.90959596 0.001 2367
0.9990257 9.74E-04 3875 0.980808081 0.001 2181
8.24E-04 0.99921553 4114 0.965151515 0.001 2212
0.999460238 5.40E-04 4819 0.963131313 0.001 2620
0.999249451 7.47E-04 4723 0.839393939 0.001 2582
0.999336761 6.61E-04 3875 0.985858586 0.001 2197
0.999067192 9.19E-04 4723 0.618686869 0.001 2559
0.999212597 7.89E-04 4949 0.674242424 0.001 2605
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12247759