MatCarlo
From FarmShare
Matlab and Monte Carlo simulations
This example shows one possible way to run monte carlo simulations on the barley cluster using matlab. The example was lifted from http://en.literateprograms.org/Monte_Carlo_simulation_%28Matlab%29. The technique outlined here is actually much more general than this, as the essence of it is just to run many jobs with different parameters.
The technique shown below makes use of a python "driver script" to generate all of the unique files needed to run all of the jobs. If you follow the steps you can see where the python script creates a directory for a job, populates it with a matlab source file and a qsub script, and then executes qsub. Doing it this way has the advantage that the source code and the output are all kept as a unit. This makes it very easy to analyze later and to reproduce any given result.
Also listed below is an example of saving the matlab variables to a .mat file so that at some future time you can run matlab, load up the .mat file and manipulate the data.
setup
To run this example, create a directory for your results.
mkdir /mnt/glusterfs/bishopj/mattest cd /mnt/glusterfs/bishopj/mattest
save this python script as 'driver.py':
import os n = 0 for mymu in [ 0.05, 0.06, 0.07, 0.08, 0.09 ]: for myT in range(10,50,10): n += 1 matlabstartup = ''' S0 = 1000 mu = %f sigma = .12 T = %d nb_traj = 100 step = 1/255 [S, t] = simplest_montecarlo0( sigma, T, nb_traj, S0, mu, step); listOfVariables = {'S', 't'}; save('run%d/mydata.mat', listOfVariables{:}); mcplot = figure('Color',[0.9412 0.9412 0.9412 ]); plot(t,S, 'linewidth',2); axis([t(1) t(end) min(S(:)) max(S(:))]); xlabel('time');ylabel('value'); title(sprintf('%%d trajectories', size(S,2))); print(mcplot,'-dpng','run%d/figure.png') ''' % (mymu, myT, n, n) qsubscript = ''' #$ -N run%d #$ -o run%d/job.out #$ -e run%d/job.error #$ -cwd #$ -S /bin/bash ##$ -l testq=1 /mnt/glusterfs/software/non-free/MATLAB-R2012b/bin/matlab -nodesktop -singleCompThread < run%d/run.m ''' % (n,n,n,n) os.mkdir('run%d' % n) runfile = open('run%d/run.m' % n, 'w') runfile.write(matlabstartup) runfile.close() qsubfile = open('run%d/run.submit' % n, 'w') qsubfile.write(qsubscript) qsubfile.close() os.system('qsub run%d/run.submit' % n)
save this file as 'simplest_montecarlo0.m':
function [S, t] = simplest_montecarlo0( sigma, T, nb_traj, S0, mu, step) % SIMPLEST_MONTECARLO - the simplest Monte Carlo simulation with Matlab % use: % S = simplest_montecarlo( sigma, T, nb_traj, S0, mu, step) % example: % [S, t] = simplest_montecarlo( .12, 5, 50, 100, .05, 1/255); nT = ceil(T/step); W = sigma * sqrt(step) * cumsum(randn(nT, nb_traj)); c = repmat((mu - sigma^2/2) *step * (1:nT)',1,nb_traj); S = [repmat(S0,1,nb_traj); S0 * exp( c + W)]; if nargout > 1 t = [0;step * (1:nT)']; end
running
Lets run it
bishopj@corn08:/mnt/glusterfs/bishopj/mattest$ python driver.py Your job 669323 ("run1") has been submitted Your job 669324 ("run2") has been submitted Your job 669325 ("run3") has been submitted Your job 669326 ("run4") has been submitted Your job 669327 ("run5") has been submitted Your job 669328 ("run6") has been submitted Your job 669329 ("run7") has been submitted Your job 669330 ("run8") has been submitted Your job 669331 ("run9") has been submitted Your job 669332 ("run10") has been submitted Your job 669333 ("run11") has been submitted Your job 669334 ("run12") has been submitted Your job 669335 ("run13") has been submitted Your job 669336 ("run14") has been submitted Your job 669337 ("run15") has been submitted Your job 669338 ("run16") has been submitted Your job 669339 ("run17") has been submitted Your job 669340 ("run18") has been submitted Your job 669341 ("run19") has been submitted Your job 669342 ("run20") has been submitted bishopj@corn08:/mnt/glusterfs/bishopj/mattest$ qstat job-ID prior name user state submit/start at queue slots ja-task-ID ----------------------------------------------------------------------------------------------------------------- 669323 0.25000 run1 bishopj r 02/19/2013 14:08:10 test.q@barley-testq.stanford.e 1 669324 0.25000 run2 bishopj r 02/19/2013 14:08:10 test.q@barley-testq.stanford.e 1 669325 0.25000 run3 bishopj r 02/19/2013 14:08:10 test.q@barley-testq.stanford.e 1 669326 0.25000 run4 bishopj r 02/19/2013 14:08:10 test.q@barley-testq.stanford.e 1 669327 0.25000 run5 bishopj qw 02/19/2013 14:08:07 1 669328 0.25000 run6 bishopj qw 02/19/2013 14:08:08 1 669329 0.25000 run7 bishopj qw 02/19/2013 14:08:10 1 669330 0.25000 run8 bishopj qw 02/19/2013 14:08:11 1 669331 0.25000 run9 bishopj qw 02/19/2013 14:08:12 1 669332 0.25000 run10 bishopj qw 02/19/2013 14:08:13 1 669333 0.25000 run11 bishopj qw 02/19/2013 14:08:14 1 669334 0.25000 run12 bishopj qw 02/19/2013 14:08:16 1 669335 0.25000 run13 bishopj qw 02/19/2013 14:08:17 1 669336 0.25000 run14 bishopj qw 02/19/2013 14:08:18 1 669337 0.25000 run15 bishopj qw 02/19/2013 14:08:19 1 669338 0.25000 run16 bishopj qw 02/19/2013 14:08:20 1 669339 0.25000 run17 bishopj qw 02/19/2013 14:08:22 1 669340 0.25000 run18 bishopj qw 02/19/2013 14:08:23 1 669341 0.25000 run19 bishopj qw 02/19/2013 14:08:24 1 669342 0.00000 run20 bishopj qw 02/19/2013 14:08:25 1
Since job run1 is started, lets see if things are running as expected:
bishopj@corn08:/mnt/glusterfs/bishopj/mattest/run1$ cd run1 bishopj@corn08:/mnt/glusterfs/bishopj/mattest/run1$ cat job.out Warning: No display specified. You will not be able to display graphics on the screen. Warning: No window system found. Java option 'MWT' ignored. < M A T L A B (R) > Copyright 1984-2012 The MathWorks, Inc. R2012b (8.0.0.783) 64-bit (glnxa64) August 22, 2012 To get started, type one of these: helpwin, helpdesk, or demo. For product information, visit www.mathworks.com. >> >> S0 = 1000 >> mu = 0.0500 >> sigma = 0.1200 >> T = 10 >> nb_traj = 100 >> step = 0.0039 >> >> >> >> >> >> >>
Wait for some time for the jobs to finish. Then we can examine the job directory in detail:
bishopj@corn24:/mnt/glusterfs/bishopj/mattest/run18$ ls -l total 3736 -rw-r--r-- 1 bishopj root 22803 Feb 19 14:13 figure.png -rw-r--r-- 1 bishopj root 52 Feb 19 14:13 job.error -rw-r--r-- 1 bishopj root 762 Feb 19 14:13 job.out -rw-r--r-- 1 bishopj root 3781664 Feb 19 14:13 mydata.mat -rw-r--r-- 1 bishopj root 475 Feb 19 14:08 run.m -rw-r--r-- 1 bishopj root 195 Feb 19 14:08 run.submit
the run.submit file contains the commands to start matlab:
bishopj@corn24:/mnt/glusterfs/bishopj/mattest/run18$ cat run.submit #$ -N run18 #$ -o run18/job.out #$ -e run18/job.error #$ -cwd #$ -S /bin/bash #$ -l testq=1 /mnt/glusterfs/software/non-free/MATLAB-R2012b/bin/matlab -nodesktop -singleCompThread < run18/run.m
the run.m file contains the matlab source program. Note that the save function is used to save the state of the S and t arrays as well as a plot of the data is saved to figure.png
bishopj@corn24:/mnt/glusterfs/bishopj/mattest/run18$ cat run.m S0 = 1000 mu = 0.090000 sigma = .12 T = 20 nb_traj = 100 step = 1/255 [S, t] = simplest_montecarlo0( sigma, T, nb_traj, S0, mu, step); listOfVariables = {'S', 't'}; save('run18/mydata.mat', listOfVariables{:}); mcplot = figure('Color',[0.9412 0.9412 0.9412 ]); plot(t,S, 'linewidth',2); axis([t(1) t(end) min(S(:)) max(S(:))]); xlabel('time');ylabel('value'); title(sprintf('%d trajectories', size(S,2))); print(mcplot,'-dpng','run18/figure.png')
We can look at the png via:
bishopj@corn08:/mnt/glusterfs/bishopj/mattest/run18$ display figure.png
And
bishopj@corn08:/mnt/glusterfs/bishopj/mattest/run18$ matlab -nodesktop bishopj@corn24:/mnt/glusterfs/bishopj/mattest/run18$ matlab -nodesktop Warning: No display specified. You will not be able to display graphics on the screen. Warning: No window system found. Java option 'MWT' ignored. < M A T L A B (R) > Copyright 1984-2012 The MathWorks, Inc. R2012b (8.0.0.783) 64-bit (glnxa64) August 22, 2012 No window system found. Java option 'MWT' ignored. To get started, type one of these: helpwin, helpdesk, or demo. For product information, visit www.mathworks.com. >> whos -file mydata Name Size Bytes Class Attributes S 5101x100 4080800 double t 5101x1 40808 double >> load mydata >> t t = 0 0.0039 0.0078 0.0118 0.0157 0.0196 0.0235 0.0275 0.0314 0.0353 0.0392 0.0431 0.0471 0.0510 0.0549 0.0588 0.0627 0.0667 0.0706 0.0745 0.0784 0.0824 0.0863 0.0902 0.0941 0.0980 0.1020 0.1059 0.1098 0.1137 0.1176 0.1216 0.1255 0.1294 0.1333 0.1373 0.1412 0.1451 0.1490 0.1529 0.1569 0.1608 0.1647 0.1686 0.1725 0.1765 0.1804 0.1843 0.1882 0.1922 0.1961 0.2000 0.2039 0.2078 0.2118 0.2157 0.2196 0.2235 0.2275 0.2314 0.2353 0.2392 0.2431 0.2471 0.2510 0.2549 0.2588 0.2627 0.2667 0.2706 0.2745 0.2784 0.2824 0.2863 0.2902 0.2941 0.2980 0.3020 0.3059 0.3098 0.3137 0.3176 0.3216 0.3255 0.3294 0.3333 0.3373 0.3412 0.3451 0.3490 0.3529 0.3569 0.3608 0.3647 0.3686 0.3725 0.3765 0.3804 0.3843 0.3882 0.3922 0.3961 0.4000 0.4039 0.4078 0.4118 0.4157 0.4196 0.4235 0.4275 0.4314 0.4353 0.4392 0.4431 0.4471 0.4510 0.4549 0.4588 0.4627 0.4667 0.4706 0.4745 0.4784 0.4824 0.4863 0.4902 0.4941 0.4980 0.5020 0.5059 0.5098 0.5137 0.5176 0.5216 0.5255 0.5294 0.5333 0.5373 0.5412 0.5451 0.5490 0.5529 0.5569 0.5608 0.5647 0.5686 0.5725 0.5765 0.5804 0.5843 0.5882 0.5922 0.5961 0.6000 0.6039 0.6078 0.6118 0.6157 0.6196 0.6235 0.6275 0.6314 0.6353 0.6392 0.6431 0.6471 0.6510 0.6549 0.6588 0.6627 0.6667 0.6706 0.6745 0.6784 0.6824 0.6863 0.6902 0.6941 0.6980 0.7020 0.7059 0.7098 0.7137 0.7176 0.7216 0.7255 0.7294 0.7333 0.7373 0.7412 0.7451 0.7490 0.7529 0.7569 0.7608 0.7647 0.7686 0.7725 0.7765 0.7804 0.7843 0.7882 0.7922 0.7961 0.8000 0.8039 0.8078 0.8118 0.8157 0.8196 0.8235 0.8275 0.8314 0.8353 0.8392 0.8431 0.8471 0.8510 0.8549 0.8588 0.8627 0.8667 0.8706 0.8745 0.8784 0.8824 0.8863 0.8902 0.8941 0.8980 0.9020 0.9059 0.9098 0.9137 0.9176 0.9216 0.9255 0.9294 0.9333 0.9373 0.9412 0.9451 0.9490 0.9529 0.9569 0.9608 0.9647 0.9686 0.9725 0.9765 0.9804 0.9843 0.9882 0.9922 0.9961 1.0000 1.0039 1.0078 1.0118 1.0157 1.0196 1.0235 1.0275 1.0314 1.0353 1.0392 1.0431 1.0471 1.0510 1.0549 1.0588 1.0627 1.0667 1.0706 1.0745 1.0784 1.0824 1.0863 1.0902 1.0941 1.0980 1.1020 1.1059 1.1098 1.1137 1.1176 1.1216 1.1255 1.1294 1.1333 1.1373 1.1412 1.1451 1.1490 1.1529 1.1569 1.1608 1.1647 1.1686 1.1725 1.1765 1.1804 1.1843 1.1882 1.1922 1.1961 1.2000 1.2039 1.2078 1.2118 1.2157 1.2196 1.2235 1.2275 1.2314 1.2353 1.2392 1.2431 1.2471 1.2510 1.2549 1.2588 1.2627 1.2667 1.2706 1.2745 1.2784 1.2824 1.2863 1.2902 1.2941 1.2980 1.3020 1.3059 1.3098 1.3137 1.3176 1.3216 1.3255 1.3294 1.3333 1.3373 1.3412 1.3451 1.3490 1.3529 1.3569 1.3608 1.3647 1.3686 1.3725 1.3765 1.3804 1.3843 1.3882 1.3922 1.3961 1.4000 1.4039 1.4078 1.4118 1.4157 1.4196 1.4235 1.4275 1.4314 1.4353 1.4392 1.4431 1.4471 1.4510 1.4549 1.4588 1.4627 1.4667 1.4706 1.4745 1.4784 1.4824 1.4863 1.4902 1.4941 1.4980 1.5020 1.5059 1.5098 1.5137 1.5176 1.5216 1.5255 1.5294 1.5333 1.5373 1.5412 1.5451 1.5490 1.5529 1.5569 1.5608 1.5647 1.5686 1.5725 1.5765 1.5804 1.5843 1.5882 1.5922 1.5961 1.6000 1.6039 1.6078 1.6118 1.6157 1.6196 1.6235 1.6275 1.6314 1.6353 1.6392 1.6431 1.6471 1.6510 1.6549 1.6588 1.6627 1.6667 1.6706 1.6745 1.6784 1.6824 1.6863 1.6902 1.6941 1.6980 1.7020 1.7059 1.7098 1.7137 1.7176 1.7216 1.7255 1.7294 1.7333 1.7373 1.7412 1.7451 1.7490 1.7529 1.7569 1.7608 1.7647 1.7686 1.7725 1.7765 1.7804 1.7843 1.7882 1.7922 1.7961 1.8000 1.8039 1.8078 1.8118 1.8157 1.8196 1.8235 1.8275 1.8314 1.8353 1.8392 1.8431 1.8471 1.8510 1.8549 1.8588 1.8627 1.8667 1.8706 1.8745 1.8784 1.8824 1.8863 1.8902 1.8941 1.8980 1.9020 1.9059 1.9098 1.9137 1.9176 1.9216 1.9255 1.9294 1.9333 1.9373 1.9412 1.9451 1.9490 1.9529 1.9569 1.9608 1.9647 1.9686 1.9725 1.9765 1.9804 1.9843 1.9882 1.9922 1.9961 2.0000 2.0039 2.0078 2.0118 2.0157 2.0196 2.0235 2.0275 2.0314 2.0353 2.0392 2.0431 2.0471 2.0510 2.0549 2.0588 2.0627 2.0667 2.0706 2.0745 2.0784 2.0824 2.0863 2.0902 2.0941 2.0980 2.1020 2.1059 2.1098 2.1137 2.1176 2.1216 2.1255 2.1294 2.1333 2.1373 2.1412 2.1451 2.1490 2.1529 2.1569 2.1608 2.1647 2.1686 2.1725 2.1765 2.1804 2.1843 2.1882 2.1922 2.1961 2.2000 2.2039 2.2078 2.2118 2.2157 2.2196 2.2235 2.2275 2.2314 2.2353 2.2392 2.2431 2.2471 2.2510 2.2549 2.2588 2.2627 2.2667 2.2706 2.2745 2.2784 2.2824 2.2863 2.2902 2.2941 2.2980 2.3020 2.3059 2.3098 2.3137 2.3176 2.3216 2.3255 2.3294 2.3333 2.3373 2.3412 2.3451 2.3490 2.3529 2.3569 2.3608 2.3647 2.3686 2.3725 2.3765 2.3804 2.3843 2.3882 2.3922 2.3961 2.4000 2.4039 2.4078 2.4118 2.4157 2.4196 2.4235 2.4275 2.4314 2.4353 2.4392 2.4431 2.4471 2.4510 2.4549 2.4588 2.4627 2.4667 2.4706 2.4745 2.4784 2.4824 2.4863 2.4902 2.4941 2.4980 2.5020 2.5059 2.5098 2.5137 2.5176 2.5216 2.5255 2.5294 2.5333 2.5373 2.5412 2.5451 2.5490 2.5529 2.5569 2.5608 2.5647 2.5686 2.5725 2.5765 2.5804 2.5843 2.5882 2.5922 2.5961 2.6000 2.6039 2.6078 2.6118 2.6157 2.6196 2.6235 2.6275 2.6314 2.6353 2.6392 2.6431 2.6471 2.6510 2.6549 2.6588 2.6627 2.6667 2.6706 2.6745 2.6784 2.6824 2.6863 2.6902 2.6941 2.6980 2.7020 2.7059 2.7098 2.7137 2.7176 2.7216 2.7255 2.7294 2.7333 2.7373 2.7412 2.7451 2.7490 2.7529 2.7569 2.7608 2.7647 2.7686 2.7725 2.7765 2.7804 2.7843 2.7882 2.7922 2.7961 2.8000 2.8039 2.8078 2.8118 2.8157 2.8196 2.8235 2.8275 2.8314 2.8353 2.8392 2.8431 2.8471 2.8510 2.8549 2.8588 2.8627 2.8667 2.8706 2.8745 2.8784 2.8824 2.8863 2.8902 2.8941 2.8980 2.9020 2.9059 2.9098 2.9137 2.9176 2.9216 2.9255 2.9294 2.9333 2.9373 2.9412 2.9451 2.9490 2.9529 2.9569 2.9608 2.9647 2.9686 2.9725 2.9765 2.9804 2.9843 2.9882 2.9922 2.9961 3.0000 3.0039 3.0078 3.0118 3.0157 3.0196 3.0235 3.0275 3.0314 3.0353 3.0392 3.0431 3.0471 3.0510 3.0549 3.0588 3.0627 3.0667 3.0706 3.0745 3.0784 3.0824 3.0863 3.0902 3.0941 3.0980 3.1020 3.1059 3.1098 3.1137 3.1176 3.1216 3.1255 3.1294 3.1333 3.1373 3.1412 3.1451 3.1490 3.1529 3.1569 3.1608 3.1647 3.1686 3.1725 3.1765 3.1804 3.1843 3.1882 3.1922 3.1961 3.2000 3.2039 3.2078 3.2118 3.2157 3.2196 3.2235 3.2275 3.2314 3.2353 3.2392 3.2431 3.2471 3.2510 3.2549 3.2588 3.2627 3.2667 3.2706 3.2745 3.2784 3.2824 3.2863 3.2902 3.2941 3.2980 3.3020 3.3059 3.3098 3.3137 3.3176 3.3216 3.3255 3.3294 3.3333 3.3373 3.3412 3.3451 3.3490 3.3529 3.3569 3.3608 3.3647 3.3686 3.3725 3.3765 3.3804 3.3843 3.3882 3.3922 3.3961 3.4000 3.4039 3.4078 3.4118 3.4157 3.4196 3.4235 3.4275 3.4314 3.4353 3.4392 3.4431 3.4471 3.4510 3.4549 3.4588 3.4627 3.4667 3.4706 3.4745 3.4784 3.4824 3.4863 3.4902 3.4941 3.4980 3.5020 3.5059 3.5098 3.5137 3.5176 3.5216 3.5255 3.5294 3.5333 3.5373 3.5412 3.5451 3.5490 3.5529 3.5569 3.5608 3.5647 3.5686 3.5725 3.5765 3.5804 3.5843 3.5882 3.5922 3.5961 3.6000 3.6039 3.6078 3.6118 3.6157 3.6196 3.6235 3.6275 3.6314 3.6353 3.6392 3.6431 3.6471 3.6510 3.6549 3.6588 3.6627 3.6667 3.6706 3.6745 3.6784 3.6824 3.6863 3.6902 3.6941 3.6980 3.7020 3.7059 3.7098 3.7137 3.7176 3.7216 3.7255 3.7294 3.7333 3.7373 3.7412 3.7451 3.7490 3.7529 3.7569 3.7608 3.7647 3.7686 3.7725 3.7765 3.7804 3.7843 3.7882 3.7922 3.7961 3.8000 3.8039 3.8078 3.8118 3.8157 3.8196 3.8235 3.8275 3.8314 3.8353 3.8392 3.8431 3.8471 3.8510 3.8549 3.8588 3.8627 3.8667 3.8706 3.8745 3.8784 3.8824 3.8863 3.8902 3.8941 3.8980 3.9020 3.9059 3.9098 3.9137 3.9176 3.9216 3.9255 3.9294 3.9333 3.9373 3.9412 3.9451 3.9490 3.9529 3.9569 3.9608 3.9647 3.9686 3.9725 3.9765 3.9804 3.9843 3.9882 3.9922 3.9961 4.0000 4.0039 4.0078 4.0118 4.0157 4.0196 4.0235 4.0275 4.0314 4.0353 4.0392 4.0431 4.0471 4.0510 4.0549 4.0588 4.0627 4.0667 4.0706 4.0745 4.0784 4.0824 4.0863 4.0902 4.0941 4.0980 4.1020 4.1059 4.1098 4.1137 4.1176 4.1216 4.1255 4.1294 4.1333 4.1373 4.1412 4.1451 4.1490 4.1529 4.1569 4.1608 4.1647 4.1686 4.1725 4.1765 4.1804 4.1843 4.1882 4.1922 4.1961 4.2000 4.2039 4.2078 4.2118 4.2157 4.2196 4.2235 4.2275 4.2314 4.2353 4.2392 4.2431 4.2471 4.2510 4.2549 4.2588 4.2627 4.2667 4.2706 4.2745 4.2784 4.2824 4.2863 4.2902 4.2941 4.2980 4.3020 4.3059 4.3098 4.3137 4.3176 4.3216 4.3255 4.3294 4.3333 4.3373 4.3412 4.3451 4.3490 4.3529 4.3569 4.3608 4.3647 4.3686 4.3725 4.3765 4.3804 4.3843 4.3882 4.3922 4.3961 4.4000 4.4039 4.4078 4.4118 4.4157 4.4196 4.4235 4.4275 4.4314 4.4353 4.4392 4.4431 4.4471 4.4510 4.4549 4.4588 4.4627 4.4667 4.4706 4.4745 4.4784 4.4824 4.4863 4.4902 4.4941 4.4980 4.5020 4.5059 4.5098 4.5137 4.5176 4.5216 4.5255 4.5294 4.5333 4.5373 4.5412 4.5451 4.5490 4.5529 4.5569 4.5608 4.5647 4.5686 4.5725 4.5765 4.5804 4.5843 4.5882 4.5922 4.5961 4.6000 4.6039 4.6078 4.6118 4.6157 4.6196 4.6235 4.6275 4.6314 4.6353 4.6392 4.6431 4.6471 4.6510 4.6549 4.6588 4.6627 4.6667 4.6706 4.6745 4.6784 4.6824 4.6863 4.6902 4.6941 4.6980 4.7020 4.7059 4.7098 4.7137 4.7176 4.7216 4.7255 4.7294 4.7333 4.7373 4.7412 4.7451 4.7490 4.7529 4.7569 4.7608 4.7647 4.7686 4.7725 4.7765 4.7804 4.7843 4.7882 4.7922 4.7961 4.8000 4.8039 4.8078 4.8118 4.8157 4.8196 4.8235 4.8275 4.8314 4.8353 4.8392 4.8431 4.8471 4.8510 4.8549 4.8588 4.8627 4.8667 4.8706 4.8745 4.8784 4.8824 4.8863 4.8902 4.8941 4.8980 4.9020 4.9059 4.9098 4.9137 4.9176 4.9216 4.9255 4.9294 4.9333 4.9373 4.9412 4.9451 4.9490 4.9529 4.9569 4.9608 4.9647 4.9686 4.9725 4.9765 4.9804 4.9843 4.9882 4.9922 4.9961 5.0000 5.0039 5.0078 5.0118 5.0157 5.0196 5.0235 5.0275 5.0314 5.0353 5.0392 5.0431 5.0471 5.0510 5.0549 5.0588 5.0627 5.0667 5.0706 5.0745 5.0784 5.0824 5.0863 5.0902 5.0941 5.0980 5.1020 5.1059 5.1098 5.1137 5.1176 5.1216 5.1255 5.1294 5.1333 5.1373 5.1412 5.1451 5.1490 5.1529 5.1569 5.1608 5.1647 5.1686 5.1725 5.1765 5.1804 5.1843 5.1882 5.1922 5.1961 5.2000 5.2039 5.2078 5.2118 5.2157 5.2196 5.2235 5.2275 5.2314 5.2353 5.2392 5.2431 5.2471 5.2510 5.2549 5.2588 5.2627 5.2667 5.2706 5.2745 5.2784 5.2824 5.2863 5.2902 5.2941 5.2980 5.3020 5.3059 5.3098 5.3137 5.3176 5.3216 5.3255 5.3294 5.3333 5.3373 5.3412 5.3451 5.3490 5.3529 5.3569 5.3608 5.3647 5.3686 5.3725 5.3765 5.3804 5.3843 5.3882 5.3922 5.3961 5.4000 5.4039 5.4078 5.4118 5.4157 5.4196 5.4235 5.4275 5.4314 5.4353 5.4392 5.4431 5.4471 5.4510 5.4549 5.4588 5.4627 5.4667 5.4706 5.4745 5.4784 5.4824 5.4863 5.4902 5.4941 5.4980 5.5020 5.5059 5.5098 5.5137 5.5176 5.5216 5.5255 5.5294 5.5333 5.5373 5.5412 5.5451 5.5490 5.5529 5.5569 5.5608 5.5647 5.5686 5.5725 5.5765 5.5804 5.5843 5.5882 5.5922 5.5961 5.6000 5.6039 5.6078 5.6118 5.6157 5.6196 5.6235 5.6275 5.6314 5.6353 5.6392 5.6431 5.6471 5.6510 5.6549 5.6588 5.6627 5.6667 5.6706 5.6745 5.6784 5.6824 5.6863 5.6902 5.6941 5.6980 5.7020 5.7059 5.7098 5.7137 5.7176 5.7216 5.7255 5.7294 5.7333 5.7373 5.7412 5.7451 5.7490 5.7529 5.7569 5.7608 5.7647 5.7686 5.7725 5.7765 5.7804 5.7843 5.7882 5.7922 5.7961 5.8000 5.8039 5.8078 5.8118 5.8157 5.8196 5.8235 5.8275 5.8314 5.8353 5.8392 5.8431 5.8471 5.8510 5.8549 5.8588 5.8627 5.8667 5.8706 5.8745 5.8784 5.8824 5.8863 5.8902 5.8941 5.8980 5.9020 5.9059 5.9098 5.9137 5.9176 5.9216 5.9255 5.9294 5.9333 5.9373 5.9412 5.9451 5.9490 5.9529 5.9569 5.9608 5.9647 5.9686 5.9725 5.9765 5.9804 5.9843 5.9882 5.9922 5.9961 6.0000 6.0039 6.0078 6.0118 6.0157 6.0196 6.0235 6.0275 6.0314 6.0353 6.0392 6.0431 6.0471 6.0510 6.0549 6.0588 6.0627 6.0667 6.0706 6.0745 6.0784 6.0824 6.0863 6.0902 6.0941 6.0980 6.1020 6.1059 6.1098 6.1137 6.1176 6.1216 6.1255 6.1294 6.1333 6.1373 6.1412 6.1451 6.1490 6.1529 6.1569 6.1608 6.1647 6.1686 6.1725 6.1765 6.1804 6.1843 6.1882 6.1922 6.1961 6.2000 6.2039 6.2078 6.2118 6.2157 6.2196 6.2235 6.2275 6.2314 6.2353 6.2392 6.2431 6.2471 6.2510 6.2549 6.2588 6.2627 6.2667 6.2706 6.2745 6.2784 6.2824 6.2863 6.2902 6.2941 6.2980 6.3020 6.3059 6.3098 6.3137 6.3176 6.3216 6.3255 6.3294 6.3333 6.3373 6.3412 6.3451 6.3490 6.3529 6.3569 6.3608 6.3647 6.3686 6.3725 6.3765 6.3804 6.3843 6.3882 6.3922 6.3961 6.4000 6.4039 6.4078 6.4118 6.4157 6.4196 6.4235 6.4275 6.4314 6.4353 6.4392 6.4431 6.4471 6.4510 6.4549 6.4588 6.4627 6.4667 6.4706 6.4745 6.4784 6.4824 6.4863 6.4902 6.4941 6.4980 6.5020 6.5059 6.5098 6.5137 6.5176 6.5216 6.5255 6.5294 6.5333 6.5373 6.5412 6.5451 6.5490 6.5529 6.5569 6.5608 6.5647 6.5686 6.5725 6.5765 6.5804 6.5843 6.5882 6.5922 6.5961 6.6000 6.6039 6.6078 6.6118 6.6157 6.6196 6.6235 6.6275 6.6314 6.6353 6.6392 6.6431 6.6471 6.6510 6.6549 6.6588 6.6627 6.6667 6.6706 6.6745 6.6784 6.6824 6.6863 6.6902 6.6941 6.6980 6.7020 6.7059 6.7098 6.7137 6.7176 6.7216 6.7255 6.7294 6.7333 6.7373 6.7412 6.7451 6.7490 6.7529 6.7569 6.7608 6.7647 6.7686 6.7725 6.7765 6.7804 6.7843 6.7882 6.7922 6.7961 6.8000 6.8039 6.8078 6.8118 6.8157 6.8196 6.8235 6.8275 6.8314 6.8353 6.8392 6.8431 6.8471 6.8510 6.8549 6.8588 6.8627 6.8667 6.8706 6.8745 6.8784 6.8824 6.8863 6.8902 6.8941 6.8980 6.9020 6.9059 6.9098 6.9137 6.9176 6.9216 6.9255 6.9294 6.9333 6.9373 6.9412 6.9451 6.9490 6.9529 6.9569 6.9608 6.9647 6.9686 6.9725 6.9765 6.9804 6.9843 6.9882 6.9922 6.9961 7.0000 7.0039 7.0078 7.0118 7.0157 7.0196 7.0235 7.0275 7.0314 7.0353 7.0392 7.0431 7.0471 7.0510 7.0549 7.0588 7.0627 7.0667 7.0706 7.0745 7.0784 7.0824 7.0863 7.0902 7.0941 7.0980 7.1020 7.1059 7.1098 7.1137 7.1176 7.1216 7.1255 7.1294 7.1333 7.1373 7.1412 7.1451 7.1490 7.1529 7.1569 7.1608 7.1647 7.1686 7.1725 7.1765 7.1804 7.1843 7.1882 7.1922 7.1961 7.2000 7.2039 7.2078 7.2118 7.2157 7.2196 7.2235 7.2275 7.2314 7.2353 7.2392 7.2431 7.2471 7.2510 7.2549 7.2588 7.2627 7.2667 7.2706 7.2745 7.2784 7.2824 7.2863 7.2902 7.2941 7.2980 7.3020 7.3059 7.3098 7.3137 7.3176 7.3216 7.3255 7.3294 7.3333 7.3373 7.3412 7.3451 7.3490 7.3529 7.3569 7.3608 7.3647 7.3686 7.3725 7.3765 7.3804 7.3843 7.3882 7.3922 7.3961 7.4000 7.4039 7.4078 7.4118 7.4157 7.4196 7.4235 7.4275 7.4314 7.4353 7.4392 7.4431 7.4471 7.4510 7.4549 7.4588 7.4627 7.4667 7.4706 7.4745 7.4784 7.4824 7.4863 7.4902 7.4941 7.4980 7.5020 7.5059 7.5098 7.5137 7.5176 7.5216 7.5255 7.5294 7.5333 7.5373 7.5412 7.5451 7.5490 7.5529 7.5569 7.5608 7.5647 7.5686 7.5725 7.5765 7.5804 7.5843 7.5882 7.5922 7.5961 7.6000 7.6039 7.6078 7.6118 7.6157 7.6196 7.6235 7.6275 7.6314 7.6353 7.6392 7.6431 7.6471 7.6510 7.6549 7.6588 7.6627 7.6667 7.6706 7.6745 7.6784 7.6824 7.6863 7.6902 7.6941 7.6980 7.7020 7.7059 7.7098 7.7137 7.7176 7.7216 7.7255 7.7294 7.7333 7.7373 7.7412 7.7451 7.7490 7.7529 7.7569 7.7608 7.7647 7.7686 7.7725 7.7765 7.7804 7.7843 7.7882 7.7922 7.7961 7.8000 7.8039 7.8078 7.8118 7.8157 7.8196 7.8235 7.8275 7.8314 7.8353 7.8392 7.8431 7.8471 7.8510 7.8549 7.8588 7.8627 7.8667 7.8706 7.8745 7.8784 7.8824 7.8863 7.8902 7.8941 7.8980 7.9020 7.9059 7.9098 7.9137 7.9176 7.9216 7.9255 7.9294 7.9333 7.9373 7.9412 7.9451 7.9490 7.9529 7.9569 7.9608 7.9647 7.9686 7.9725 7.9765 7.9804 7.9843 7.9882 7.9922 7.9961 8.0000 8.0039 8.0078 8.0118 8.0157 8.0196 8.0235 8.0275 8.0314 8.0353 8.0392 8.0431 8.0471 8.0510 8.0549 8.0588 8.0627 8.0667 8.0706 8.0745 8.0784 8.0824 8.0863 8.0902 8.0941 8.0980 8.1020 8.1059 8.1098 8.1137 8.1176 8.1216 8.1255 8.1294 8.1333 8.1373 8.1412 8.1451 8.1490 8.1529 8.1569 8.1608 8.1647 8.1686 8.1725 8.1765 8.1804 8.1843 8.1882 8.1922 8.1961 8.2000 8.2039 8.2078 8.2118 8.2157 8.2196 8.2235 8.2275 8.2314 8.2353 8.2392 8.2431 8.2471 8.2510 8.2549 8.2588 8.2627 8.2667 8.2706 8.2745 8.2784 8.2824 8.2863 8.2902 8.2941 8.2980 8.3020 8.3059 8.3098 8.3137 8.3176 8.3216 8.3255 8.3294 8.3333 8.3373 8.3412 8.3451 8.3490 8.3529 8.3569 8.3608 8.3647 8.3686 8.3725 8.3765 8.3804 8.3843 8.3882 8.3922 8.3961 8.4000 8.4039 8.4078 8.4118 8.4157 8.4196 8.4235 8.4275 8.4314 8.4353 8.4392 8.4431 8.4471 8.4510 8.4549 8.4588 8.4627 8.4667 8.4706 8.4745 8.4784 8.4824 8.4863 8.4902 8.4941 8.4980 8.5020 8.5059 8.5098 8.5137 8.5176 8.5216 8.5255 8.5294 8.5333 8.5373 8.5412 8.5451 8.5490 8.5529 8.5569 8.5608 8.5647 8.5686 8.5725 8.5765 8.5804 8.5843 8.5882 8.5922 8.5961 8.6000 8.6039 8.6078 8.6118 8.6157 8.6196 8.6235 8.6275 8.6314 8.6353 8.6392 8.6431 8.6471 8.6510 8.6549 8.6588 8.6627 8.6667 8.6706 8.6745 8.6784 8.6824 8.6863 8.6902 8.6941 8.6980 8.7020 8.7059 8.7098 8.7137 8.7176 8.7216 8.7255 8.7294 8.7333 8.7373 8.7412 8.7451 8.7490 8.7529 8.7569 8.7608 8.7647 8.7686 8.7725 8.7765 8.7804 8.7843 8.7882 8.7922 8.7961 8.8000 8.8039 8.8078 8.8118 8.8157 8.8196 8.8235 8.8275 8.8314 8.8353 8.8392 8.8431 8.8471 8.8510 8.8549 8.8588 8.8627 8.8667 8.8706 8.8745 8.8784 8.8824 8.8863 8.8902 8.8941 8.8980 8.9020 8.9059 8.9098 8.9137 8.9176 8.9216 8.9255 8.9294 8.9333 8.9373 8.9412 8.9451 8.9490 8.9529 8.9569 8.9608 8.9647 8.9686 8.9725 8.9765 8.9804 8.9843 8.9882 8.9922 8.9961 9.0000 9.0039 9.0078 9.0118 9.0157 9.0196 9.0235 9.0275 9.0314 9.0353 9.0392 9.0431 9.0471 9.0510 9.0549 9.0588 9.0627 9.0667 9.0706 9.0745 9.0784 9.0824 9.0863 9.0902 9.0941 9.0980 9.1020 9.1059 9.1098 9.1137 9.1176 9.1216 9.1255 9.1294 9.1333 9.1373 9.1412 9.1451 9.1490 9.1529 9.1569 9.1608 9.1647 9.1686 9.1725 9.1765 9.1804 9.1843 9.1882 9.1922 9.1961 9.2000 9.2039 9.2078 9.2118 9.2157 9.2196 9.2235 9.2275 9.2314 9.2353 9.2392 9.2431 9.2471 9.2510 9.2549 9.2588 9.2627 9.2667 9.2706 9.2745 9.2784 9.2824 9.2863 9.2902 9.2941 9.2980 9.3020 9.3059 9.3098 9.3137 9.3176 9.3216 9.3255 9.3294 9.3333 9.3373 9.3412 9.3451 9.3490 9.3529 9.3569 9.3608 9.3647 9.3686 9.3725 9.3765 9.3804 9.3843 9.3882 9.3922 9.3961 9.4000 9.4039 9.4078 9.4118 9.4157 9.4196 9.4235 9.4275 9.4314 9.4353 9.4392 9.4431 9.4471 9.4510 9.4549 9.4588 9.4627 9.4667 9.4706 9.4745 9.4784 9.4824 9.4863 9.4902 9.4941 9.4980 9.5020 9.5059 9.5098 9.5137 9.5176 9.5216 9.5255 9.5294 9.5333 9.5373 9.5412 9.5451 9.5490 9.5529 9.5569 9.5608 9.5647 9.5686 9.5725 9.5765 9.5804 9.5843 9.5882 9.5922 9.5961 9.6000 9.6039 9.6078 9.6118 9.6157 9.6196 9.6235 9.6275 9.6314 9.6353 9.6392 9.6431 9.6471 9.6510 9.6549 9.6588 9.6627 9.6667 9.6706 9.6745 9.6784 9.6824 9.6863 9.6902 9.6941 9.6980 9.7020 9.7059 9.7098 9.7137 9.7176 9.7216 9.7255 9.7294 9.7333 9.7373 9.7412 9.7451 9.7490 9.7529 9.7569 9.7608 9.7647 9.7686 9.7725 9.7765 9.7804 9.7843 9.7882 9.7922 9.7961 9.8000 9.8039 9.8078 9.8118 9.8157 9.8196 9.8235 9.8275 9.8314 9.8353 9.8392 9.8431 9.8471 9.8510 9.8549 9.8588 9.8627 9.8667 9.8706 9.8745 9.8784 9.8824 9.8863 9.8902 9.8941 9.8980 9.9020 9.9059 9.9098 9.9137 9.9176 9.9216 9.9255 9.9294 9.9333 9.9373 9.9412 9.9451 9.9490 9.9529 9.9569 9.9608 9.9647 9.9686 9.9725 9.9765 9.9804 9.9843 9.9882 9.9922 9.9961 10.0000 10.0039 10.0078 10.0118 10.0157 10.0196 10.0235 10.0275 10.0314 10.0353 10.0392 10.0431 10.0471 10.0510 10.0549 10.0588 10.0627 10.0667 10.0706 10.0745 10.0784 10.0824 10.0863 10.0902 10.0941 10.0980 10.1020 10.1059 10.1098 10.1137 10.1176 10.1216 10.1255 10.1294 10.1333 10.1373 10.1412 10.1451 10.1490 10.1529 10.1569 10.1608 10.1647 10.1686 10.1725 10.1765 10.1804 10.1843 10.1882 10.1922 10.1961 10.2000 10.2039 10.2078 10.2118 10.2157 10.2196 10.2235 10.2275 10.2314 10.2353 10.2392 10.2431 10.2471 10.2510 10.2549 10.2588 10.2627 10.2667 10.2706 10.2745 10.2784 10.2824 10.2863 10.2902 10.2941 10.2980 10.3020 10.3059 10.3098 10.3137 10.3176 10.3216 10.3255 10.3294 10.3333 10.3373 10.3412 10.3451 10.3490 10.3529 10.3569 10.3608 10.3647 10.3686 10.3725 10.3765 10.3804 10.3843 10.3882 10.3922 10.3961 10.4000 10.4039 10.4078 10.4118 10.4157 10.4196 10.4235 10.4275 10.4314 10.4353 10.4392 10.4431 10.4471 10.4510 10.4549 10.4588 10.4627 10.4667 10.4706 10.4745 10.4784 10.4824 10.4863 10.4902 10.4941 10.4980 10.5020 10.5059 10.5098 10.5137 10.5176 10.5216 10.5255 10.5294 10.5333 10.5373 10.5412 10.5451 10.5490 10.5529 10.5569 10.5608 10.5647 10.5686 10.5725 10.5765 10.5804 10.5843 10.5882 10.5922 10.5961 10.6000 10.6039 10.6078 10.6118 10.6157 10.6196 10.6235 10.6275 10.6314 10.6353 10.6392 10.6431 10.6471 10.6510 10.6549 10.6588 10.6627 10.6667 10.6706 10.6745 10.6784 10.6824 10.6863 10.6902 10.6941 10.6980 10.7020 10.7059 10.7098 10.7137 10.7176 10.7216 10.7255 10.7294 10.7333 10.7373 10.7412 10.7451 10.7490 10.7529 10.7569 10.7608 10.7647 10.7686 10.7725 10.7765 10.7804 10.7843 10.7882 10.7922 10.7961 10.8000 10.8039 10.8078 10.8118 10.8157 10.8196 10.8235 10.8275 10.8314 10.8353 10.8392 10.8431 10.8471 10.8510 10.8549 10.8588 10.8627 10.8667 10.8706 10.8745 10.8784 10.8824 10.8863 10.8902 10.8941 10.8980 10.9020 10.9059 10.9098 10.9137 10.9176 10.9216 10.9255 10.9294 10.9333 10.9373 10.9412 10.9451 10.9490 10.9529 10.9569 10.9608 10.9647 10.9686 10.9725 10.9765 10.9804 10.9843 10.9882 10.9922 10.9961 11.0000 11.0039 11.0078 11.0118 11.0157 11.0196 11.0235 11.0275 11.0314 11.0353 11.0392 11.0431 11.0471 11.0510 11.0549 11.0588 11.0627 11.0667 11.0706 11.0745 11.0784 11.0824 11.0863 11.0902 11.0941 11.0980 11.1020 11.1059 11.1098 11.1137 11.1176 11.1216 11.1255 11.1294 11.1333 11.1373 11.1412 11.1451 11.1490 11.1529 11.1569 11.1608 11.1647 11.1686 11.1725 11.1765 11.1804 11.1843 11.1882 11.1922 11.1961 11.2000 11.2039 11.2078 11.2118 11.2157 11.2196 11.2235 11.2275 11.2314 11.2353 11.2392 11.2431 11.2471 11.2510 11.2549 11.2588 11.2627 11.2667 11.2706 11.2745 11.2784 11.2824 11.2863 11.2902 11.2941 11.2980 11.3020 11.3059 11.3098 11.3137 11.3176 11.3216 11.3255 11.3294 11.3333 11.3373 11.3412 11.3451 11.3490 11.3529 11.3569 11.3608 11.3647 11.3686 11.3725 11.3765 11.3804 11.3843 11.3882 11.3922 11.3961 11.4000 11.4039 11.4078 11.4118 11.4157 11.4196 11.4235 11.4275 11.4314 11.4353 11.4392 11.4431 11.4471 11.4510 11.4549 11.4588 11.4627 11.4667 11.4706 11.4745 11.4784 11.4824 11.4863 11.4902 11.4941 11.4980 11.5020 11.5059 11.5098 11.5137 11.5176 11.5216 11.5255 11.5294 11.5333 11.5373 11.5412 11.5451 11.5490 11.5529 11.5569 11.5608 11.5647 11.5686 11.5725 11.5765 11.5804 11.5843 11.5882 11.5922 11.5961 11.6000 11.6039 11.6078 11.6118 11.6157 11.6196 11.6235 11.6275 11.6314 11.6353 11.6392 11.6431 11.6471 11.6510 11.6549 11.6588 11.6627 11.6667 11.6706 11.6745 11.6784 11.6824 11.6863 11.6902 11.6941 11.6980 11.7020 11.7059 11.7098 11.7137 11.7176 11.7216 11.7255 11.7294 11.7333 11.7373 11.7412 11.7451 11.7490 11.7529 11.7569 11.7608 11.7647 11.7686 11.7725 11.7765 11.7804 11.7843 11.7882 11.7922 11.7961 11.8000 11.8039 11.8078 11.8118 11.8157 11.8196 11.8235 11.8275 11.8314 11.8353 11.8392 11.8431 11.8471 11.8510 11.8549 11.8588 11.8627 11.8667 11.8706 11.8745 11.8784 11.8824 11.8863 11.8902 11.8941 11.8980 11.9020 11.9059 11.9098 11.9137 11.9176 11.9216 11.9255 11.9294 11.9333 11.9373 11.9412 11.9451 11.9490 11.9529 11.9569 11.9608 11.9647 11.9686 11.9725 11.9765 11.9804 11.9843 11.9882 11.9922 11.9961 12.0000 12.0039 12.0078 12.0118 12.0157 12.0196 12.0235 12.0275 12.0314 12.0353 12.0392 12.0431 12.0471 12.0510 12.0549 12.0588 12.0627 12.0667 12.0706 12.0745 12.0784 12.0824 12.0863 12.0902 12.0941 12.0980 12.1020 12.1059 12.1098 12.1137 12.1176 12.1216 12.1255 12.1294 12.1333 12.1373 12.1412 12.1451 12.1490 12.1529 12.1569 12.1608 12.1647 12.1686 12.1725 12.1765 12.1804 12.1843 12.1882 12.1922 12.1961 12.2000 12.2039 12.2078 12.2118 12.2157 12.2196 12.2235 12.2275 12.2314 12.2353 12.2392 12.2431 12.2471 12.2510 12.2549 12.2588 12.2627 12.2667 12.2706 12.2745 12.2784 12.2824 12.2863 12.2902 12.2941 12.2980 12.3020 12.3059 12.3098 12.3137 12.3176 12.3216 12.3255 12.3294 12.3333 12.3373 12.3412 12.3451 12.3490 12.3529 12.3569 12.3608 12.3647 12.3686 12.3725 12.3765 12.3804 12.3843 12.3882 12.3922 12.3961 12.4000 12.4039 12.4078 12.4118 12.4157 12.4196 12.4235 12.4275 12.4314 12.4353 12.4392 12.4431 12.4471 12.4510 12.4549 12.4588 12.4627 12.4667 12.4706 12.4745 12.4784 12.4824 12.4863 12.4902 12.4941 12.4980 12.5020 12.5059 12.5098 12.5137 12.5176 12.5216 12.5255 12.5294 12.5333 12.5373 12.5412 12.5451 12.5490 12.5529 12.5569 12.5608 12.5647 12.5686 12.5725 12.5765 12.5804 12.5843 12.5882 12.5922 12.5961 12.6000 12.6039 12.6078 12.6118 12.6157 12.6196 12.6235 12.6275 12.6314 12.6353 12.6392 12.6431 12.6471 12.6510 12.6549 12.6588 12.6627 12.6667 12.6706 12.6745 12.6784 12.6824 12.6863 12.6902 12.6941 12.6980 12.7020 12.7059 12.7098 12.7137 12.7176 12.7216 12.7255 12.7294 12.7333 12.7373 12.7412 12.7451 12.7490 12.7529 12.7569 12.7608 12.7647 12.7686 12.7725 12.7765 12.7804 12.7843 12.7882 12.7922 12.7961 12.8000 12.8039 12.8078 12.8118 12.8157 12.8196 12.8235 12.8275 12.8314 12.8353 12.8392 12.8431 12.8471 12.8510 12.8549 12.8588 12.8627 12.8667 12.8706 12.8745 12.8784 12.8824 12.8863 12.8902 12.8941 12.8980 12.9020 12.9059 12.9098 12.9137 12.9176 12.9216 12.9255 12.9294 12.9333 12.9373 12.9412 12.9451 12.9490 12.9529 12.9569 12.9608 12.9647 12.9686 12.9725 12.9765 12.9804 12.9843 12.9882 12.9922 12.9961 13.0000 13.0039 13.0078 13.0118 13.0157 13.0196 13.0235 13.0275 13.0314 13.0353 13.0392 13.0431 13.0471 13.0510 13.0549 13.0588 13.0627 13.0667 13.0706 13.0745 13.0784 13.0824 13.0863 13.0902 13.0941 13.0980 13.1020 13.1059 13.1098 13.1137 13.1176 13.1216 13.1255 13.1294 13.1333 13.1373 13.1412 13.1451 13.1490 13.1529 13.1569 13.1608 13.1647 13.1686 13.1725 13.1765 13.1804 13.1843 13.1882 13.1922 13.1961 13.2000 13.2039 13.2078 13.2118 13.2157 13.2196 13.2235 13.2275 13.2314 13.2353 13.2392 13.2431 13.2471 13.2510 13.2549 13.2588 13.2627 13.2667 13.2706 13.2745 13.2784 13.2824 13.2863 13.2902 13.2941 13.2980 13.3020 13.3059 13.3098 13.3137 13.3176 13.3216 13.3255 13.3294 13.3333 13.3373 13.3412 13.3451 13.3490 13.3529 13.3569 13.3608 13.3647 13.3686 13.3725 13.3765 13.3804 13.3843 13.3882 13.3922 13.3961 13.4000 13.4039 13.4078 13.4118 13.4157 13.4196 13.4235 13.4275 13.4314 13.4353 13.4392 13.4431 13.4471 13.4510 13.4549 13.4588 13.4627 13.4667 13.4706 13.4745 13.4784 13.4824 13.4863 13.4902 13.4941 13.4980 13.5020 13.5059 13.5098 13.5137 13.5176 13.5216 13.5255 13.5294 13.5333 13.5373 13.5412 13.5451 13.5490 13.5529 13.5569 13.5608 13.5647 13.5686 13.5725 13.5765 13.5804 13.5843 13.5882 13.5922 13.5961 13.6000 13.6039 13.6078 13.6118 13.6157 13.6196 13.6235 13.6275 13.6314 13.6353 13.6392 13.6431 13.6471 13.6510 13.6549 13.6588 13.6627 13.6667 13.6706 13.6745 13.6784 13.6824 13.6863 13.6902 13.6941 13.6980 13.7020 13.7059 13.7098 13.7137 13.7176 13.7216 13.7255 13.7294 13.7333 13.7373 13.7412 13.7451 13.7490 13.7529 13.7569 13.7608 13.7647 13.7686 13.7725 13.7765 13.7804 13.7843 13.7882 13.7922 13.7961 13.8000 13.8039 13.8078 13.8118 13.8157 13.8196 13.8235 13.8275 13.8314 13.8353 13.8392 13.8431 13.8471 13.8510 13.8549 13.8588 13.8627 13.8667 13.8706 13.8745 13.8784 13.8824 13.8863 13.8902 13.8941 13.8980 13.9020 13.9059 13.9098 13.9137 13.9176 13.9216 13.9255 13.9294 13.9333 13.9373 13.9412 13.9451 13.9490 13.9529 13.9569 13.9608 13.9647 13.9686 13.9725 13.9765 13.9804 13.9843 13.9882 13.9922 13.9961 14.0000 14.0039 14.0078 14.0118 14.0157 14.0196 14.0235 14.0275 14.0314 14.0353 14.0392 14.0431 14.0471 14.0510 14.0549 14.0588 14.0627 14.0667 14.0706 14.0745 14.0784 14.0824 14.0863 14.0902 14.0941 14.0980 14.1020 14.1059 14.1098 14.1137 14.1176 14.1216 14.1255 14.1294 14.1333 14.1373 14.1412 14.1451 14.1490 14.1529 14.1569 14.1608 14.1647 14.1686 14.1725 14.1765 14.1804 14.1843 14.1882 14.1922 14.1961 14.2000 14.2039 14.2078 14.2118 14.2157 14.2196 14.2235 14.2275 14.2314 14.2353 14.2392 14.2431 14.2471 14.2510 14.2549 14.2588 14.2627 14.2667 14.2706 14.2745 14.2784 14.2824 14.2863 14.2902 14.2941 14.2980 14.3020 14.3059 14.3098 14.3137 14.3176 14.3216 14.3255 14.3294 14.3333 14.3373 14.3412 14.3451 14.3490 14.3529 14.3569 14.3608 14.3647 14.3686 14.3725 14.3765 14.3804 14.3843 14.3882 14.3922 14.3961 14.4000 14.4039 14.4078 14.4118 14.4157 14.4196 14.4235 14.4275 14.4314 14.4353 14.4392 14.4431 14.4471 14.4510 14.4549 14.4588 14.4627 14.4667 14.4706 14.4745 14.4784 14.4824 14.4863 14.4902 14.4941 14.4980 14.5020 14.5059 14.5098 14.5137 14.5176 14.5216 14.5255 14.5294 14.5333 14.5373 14.5412 14.5451 14.5490 14.5529 14.5569 14.5608 14.5647 14.5686 14.5725 14.5765 14.5804 14.5843 14.5882 14.5922 14.5961 14.6000 14.6039 14.6078 14.6118 14.6157 14.6196 14.6235 14.6275 14.6314 14.6353 14.6392 14.6431 14.6471 14.6510 14.6549 14.6588 14.6627 14.6667 14.6706 14.6745 14.6784 14.6824 14.6863 14.6902 14.6941 14.6980 14.7020 14.7059 14.7098 14.7137 14.7176 14.7216 14.7255 14.7294 14.7333 14.7373 14.7412 14.7451 14.7490 14.7529 14.7569 14.7608 14.7647 14.7686 14.7725 14.7765 14.7804 14.7843 14.7882 14.7922 14.7961 14.8000 14.8039 14.8078 14.8118 14.8157 14.8196 14.8235 14.8275 14.8314 14.8353 14.8392 14.8431 14.8471 14.8510 14.8549 14.8588 14.8627 14.8667 14.8706 14.8745 14.8784 14.8824 14.8863 14.8902 14.8941 14.8980 14.9020 14.9059 14.9098 14.9137 14.9176 14.9216 14.9255 14.9294 14.9333 14.9373 14.9412 14.9451 14.9490 14.9529 14.9569 14.9608 14.9647 14.9686 14.9725 14.9765 14.9804 14.9843 14.9882 14.9922 14.9961 15.0000 15.0039 15.0078 15.0118 15.0157 15.0196 15.0235 15.0275 15.0314 15.0353 15.0392 15.0431 15.0471 15.0510 15.0549 15.0588 15.0627 15.0667 15.0706 15.0745 15.0784 15.0824 15.0863 15.0902 15.0941 15.0980 15.1020 15.1059 15.1098 15.1137 15.1176 15.1216 15.1255 15.1294 15.1333 15.1373 15.1412 15.1451 15.1490 15.1529 15.1569 15.1608 15.1647 15.1686 15.1725 15.1765 15.1804 15.1843 15.1882 15.1922 15.1961 15.2000 15.2039 15.2078 15.2118 15.2157 15.2196 15.2235 15.2275 15.2314 15.2353 15.2392 15.2431 15.2471 15.2510 15.2549 15.2588 15.2627 15.2667 15.2706 15.2745 15.2784 15.2824 15.2863 15.2902 15.2941 15.2980 15.3020 15.3059 15.3098 15.3137 15.3176 15.3216 15.3255 15.3294 15.3333 15.3373 15.3412 15.3451 15.3490 15.3529 15.3569 15.3608 15.3647 15.3686 15.3725 15.3765 15.3804 15.3843 15.3882 15.3922 15.3961 15.4000 15.4039 15.4078 15.4118 15.4157 15.4196 15.4235 15.4275 15.4314 15.4353 15.4392 15.4431 15.4471 15.4510 15.4549 15.4588 15.4627 15.4667 15.4706 15.4745 15.4784 15.4824 15.4863 15.4902 15.4941 15.4980 15.5020 15.5059 15.5098 15.5137 15.5176 15.5216 15.5255 15.5294 15.5333 15.5373 15.5412 15.5451 15.5490 15.5529 15.5569 15.5608 15.5647 15.5686 15.5725 15.5765 15.5804 15.5843 15.5882 15.5922 15.5961 15.6000 15.6039 15.6078 15.6118 15.6157 15.6196 15.6235 15.6275 15.6314 15.6353 15.6392 15.6431 15.6471 15.6510 15.6549 15.6588 15.6627 15.6667 15.6706 15.6745 15.6784 15.6824 15.6863 15.6902 15.6941 15.6980 15.7020 15.7059 15.7098 15.7137 15.7176 15.7216 15.7255 15.7294 15.7333 15.7373 15.7412 15.7451 15.7490 15.7529 15.7569 15.7608 15.7647 15.7686 15.7725 15.7765 15.7804 15.7843 15.7882 15.7922 15.7961 15.8000 15.8039 15.8078 15.8118 15.8157 15.8196 15.8235 15.8275 15.8314 15.8353 15.8392 15.8431 15.8471 15.8510 15.8549 15.8588 15.8627 15.8667 15.8706 15.8745 15.8784 15.8824 15.8863 15.8902 15.8941 15.8980 15.9020 15.9059 15.9098 15.9137 15.9176 15.9216 15.9255 15.9294 15.9333 15.9373 15.9412 15.9451 15.9490 15.9529 15.9569 15.9608 15.9647 15.9686 15.9725 15.9765 15.9804 15.9843 15.9882 15.9922 15.9961 16.0000 16.0039 16.0078 16.0118 16.0157 16.0196 16.0235 16.0275 16.0314 16.0353 16.0392 16.0431 16.0471 16.0510 16.0549 16.0588 16.0627 16.0667 16.0706 16.0745 16.0784 16.0824 16.0863 16.0902 16.0941 16.0980 16.1020 16.1059 16.1098 16.1137 16.1176 16.1216 16.1255 16.1294 16.1333 16.1373 16.1412 16.1451 16.1490 16.1529 16.1569 16.1608 16.1647 16.1686 16.1725 16.1765 16.1804 16.1843 16.1882 16.1922 16.1961 16.2000 16.2039 16.2078 16.2118 16.2157 16.2196 16.2235 16.2275 16.2314 16.2353 16.2392 16.2431 16.2471 16.2510 16.2549 16.2588 16.2627 16.2667 16.2706 16.2745 16.2784 16.2824 16.2863 16.2902 16.2941 16.2980 16.3020 16.3059 16.3098 16.3137 16.3176 16.3216 16.3255 16.3294 16.3333 16.3373 16.3412 16.3451 16.3490 16.3529 16.3569 16.3608 16.3647 16.3686 16.3725 16.3765 16.3804 16.3843 16.3882 16.3922 16.3961 16.4000 16.4039 16.4078 16.4118 16.4157 16.4196 16.4235 16.4275 16.4314 16.4353 16.4392 16.4431 16.4471 16.4510 16.4549 16.4588 16.4627 16.4667 16.4706 16.4745 16.4784 16.4824 16.4863 16.4902 16.4941 16.4980 16.5020 16.5059 16.5098 16.5137 16.5176 16.5216 16.5255 16.5294 16.5333 16.5373 16.5412 16.5451 16.5490 16.5529 16.5569 16.5608 16.5647 16.5686 16.5725 16.5765 16.5804 16.5843 16.5882 16.5922 16.5961 16.6000 16.6039 16.6078 16.6118 16.6157 16.6196 16.6235 16.6275 16.6314 16.6353 16.6392 16.6431 16.6471 16.6510 16.6549 16.6588 16.6627 16.6667 16.6706 16.6745 16.6784 16.6824 16.6863 16.6902 16.6941 16.6980 16.7020 16.7059 16.7098 16.7137 16.7176 16.7216 16.7255 16.7294 16.7333 16.7373 16.7412 16.7451 16.7490 16.7529 16.7569 16.7608 16.7647 16.7686 16.7725 16.7765 16.7804 16.7843 16.7882 16.7922 16.7961 16.8000 16.8039 16.8078 16.8118 16.8157 16.8196 16.8235 16.8275 16.8314 16.8353 16.8392 16.8431 16.8471 16.8510 16.8549 16.8588 16.8627 16.8667 16.8706 16.8745 16.8784 16.8824 16.8863 16.8902 16.8941 16.8980 16.9020 16.9059 16.9098 16.9137 16.9176 16.9216 16.9255 16.9294 16.9333 16.9373 16.9412 16.9451 16.9490 16.9529 16.9569 16.9608 16.9647 16.9686 16.9725 16.9765 16.9804 16.9843 16.9882 16.9922 16.9961 17.0000 17.0039 17.0078 17.0118 17.0157 17.0196 17.0235 17.0275 17.0314 17.0353 17.0392 17.0431 17.0471 17.0510 17.0549 17.0588 17.0627 17.0667 17.0706 17.0745 17.0784 17.0824 17.0863 17.0902 17.0941 17.0980 17.1020 17.1059 17.1098 17.1137 17.1176 17.1216 17.1255 17.1294 17.1333 17.1373 17.1412 17.1451 17.1490 17.1529 17.1569 17.1608 17.1647 17.1686 17.1725 17.1765 17.1804 17.1843 17.1882 17.1922 17.1961 17.2000 17.2039 17.2078 17.2118 17.2157 17.2196 17.2235 17.2275 17.2314 17.2353 17.2392 17.2431 17.2471 17.2510 17.2549 17.2588 17.2627 17.2667 17.2706 17.2745 17.2784 17.2824 17.2863 17.2902 17.2941 17.2980 17.3020 17.3059 17.3098 17.3137 17.3176 17.3216 17.3255 17.3294 17.3333 17.3373 17.3412 17.3451 17.3490 17.3529 17.3569 17.3608 17.3647 17.3686 17.3725 17.3765 17.3804 17.3843 17.3882 17.3922 17.3961 17.4000 17.4039 17.4078 17.4118 17.4157 17.4196 17.4235 17.4275 17.4314 17.4353 17.4392 17.4431 17.4471 17.4510 17.4549 17.4588 17.4627 17.4667 17.4706 17.4745 17.4784 17.4824 17.4863 17.4902 17.4941 17.4980 17.5020 17.5059 17.5098 17.5137 17.5176 17.5216 17.5255 17.5294 17.5333 17.5373 17.5412 17.5451 17.5490 17.5529 17.5569 17.5608 17.5647 17.5686 17.5725 17.5765 17.5804 17.5843 17.5882 17.5922 17.5961 17.6000 17.6039 17.6078 17.6118 17.6157 17.6196 17.6235 17.6275 17.6314 17.6353 17.6392 17.6431 17.6471 17.6510 17.6549 17.6588 17.6627 17.6667 17.6706 17.6745 17.6784 17.6824 17.6863 17.6902 17.6941 17.6980 17.7020 17.7059 17.7098 17.7137 17.7176 17.7216 17.7255 17.7294 17.7333 17.7373 17.7412 17.7451 17.7490 17.7529 17.7569 17.7608 17.7647 17.7686 17.7725 17.7765 17.7804 17.7843 17.7882 17.7922 17.7961 17.8000 17.8039 17.8078 17.8118 17.8157 17.8196 17.8235 17.8275 17.8314 17.8353 17.8392 17.8431 17.8471 17.8510 17.8549 17.8588 17.8627 17.8667 17.8706 17.8745 17.8784 17.8824 17.8863 17.8902 17.8941 17.8980 17.9020 17.9059 17.9098 17.9137 17.9176 17.9216 17.9255 17.9294 17.9333 17.9373 17.9412 17.9451 17.9490 17.9529 17.9569 17.9608 17.9647 17.9686 17.9725 17.9765 17.9804 17.9843 17.9882 17.9922 17.9961 18.0000 18.0039 18.0078 18.0118 18.0157 18.0196 18.0235 18.0275 18.0314 18.0353 18.0392 18.0431 18.0471 18.0510 18.0549 18.0588 18.0627 18.0667 18.0706 18.0745 18.0784 18.0824 18.0863 18.0902 18.0941 18.0980 18.1020 18.1059 18.1098 18.1137 18.1176 18.1216 18.1255 18.1294 18.1333 18.1373 18.1412 18.1451 18.1490 18.1529 18.1569 18.1608 18.1647 18.1686 18.1725 18.1765 18.1804 18.1843 18.1882 18.1922 18.1961 18.2000 18.2039 18.2078 18.2118 18.2157 18.2196 18.2235 18.2275 18.2314 18.2353 18.2392 18.2431 18.2471 18.2510 18.2549 18.2588 18.2627 18.2667 18.2706 18.2745 18.2784 18.2824 18.2863 18.2902 18.2941 18.2980 18.3020 18.3059 18.3098 18.3137 18.3176 18.3216 18.3255 18.3294 18.3333 18.3373 18.3412 18.3451 18.3490 18.3529 18.3569 18.3608 18.3647 18.3686 18.3725 18.3765 18.3804 18.3843 18.3882 18.3922 18.3961 18.4000 18.4039 18.4078 18.4118 18.4157 18.4196 18.4235 18.4275 18.4314 18.4353 18.4392 18.4431 18.4471 18.4510 18.4549 18.4588 18.4627 18.4667 18.4706 18.4745 18.4784 18.4824 18.4863 18.4902 18.4941 18.4980 18.5020 18.5059 18.5098 18.5137 18.5176 18.5216 18.5255 18.5294 18.5333 18.5373 18.5412 18.5451 18.5490 18.5529 18.5569 18.5608 18.5647 18.5686 18.5725 18.5765 18.5804 18.5843 18.5882 18.5922 18.5961 18.6000 18.6039 18.6078 18.6118 18.6157 18.6196 18.6235 18.6275 18.6314 18.6353 18.6392 18.6431 18.6471 18.6510 18.6549 18.6588 18.6627 18.6667 18.6706 18.6745 18.6784 18.6824 18.6863 18.6902 18.6941 18.6980 18.7020 18.7059 18.7098 18.7137 18.7176 18.7216 18.7255 18.7294 18.7333 18.7373 18.7412 18.7451 18.7490 18.7529 18.7569 18.7608 18.7647 18.7686 18.7725 18.7765 18.7804 18.7843 18.7882 18.7922 18.7961 18.8000 18.8039 18.8078 18.8118 18.8157 18.8196 18.8235 18.8275 18.8314 18.8353 18.8392 18.8431 18.8471 18.8510 18.8549 18.8588 18.8627 18.8667 18.8706 18.8745 18.8784 18.8824 18.8863 18.8902 18.8941 18.8980 18.9020 18.9059 18.9098 18.9137 18.9176 18.9216 18.9255 18.9294 18.9333 18.9373 18.9412 18.9451 18.9490 18.9529 18.9569 18.9608 18.9647 18.9686 18.9725 18.9765 18.9804 18.9843 18.9882 18.9922 18.9961 19.0000 19.0039 19.0078 19.0118 19.0157 19.0196 19.0235 19.0275 19.0314 19.0353 19.0392 19.0431 19.0471 19.0510 19.0549 19.0588 19.0627 19.0667 19.0706 19.0745 19.0784 19.0824 19.0863 19.0902 19.0941 19.0980 19.1020 19.1059 19.1098 19.1137 19.1176 19.1216 19.1255 19.1294 19.1333 19.1373 19.1412 19.1451 19.1490 19.1529 19.1569 19.1608 19.1647 19.1686 19.1725 19.1765 19.1804 19.1843 19.1882 19.1922 19.1961 19.2000 19.2039 19.2078 19.2118 19.2157 19.2196 19.2235 19.2275 19.2314 19.2353 19.2392 19.2431 19.2471 19.2510 19.2549 19.2588 19.2627 19.2667 19.2706 19.2745 19.2784 19.2824 19.2863 19.2902 19.2941 19.2980 19.3020 19.3059 19.3098 19.3137 19.3176 19.3216 19.3255 19.3294 19.3333 19.3373 19.3412 19.3451 19.3490 19.3529 19.3569 19.3608 19.3647 19.3686 19.3725 19.3765 19.3804 19.3843 19.3882 19.3922 19.3961 19.4000 19.4039 19.4078 19.4118 19.4157 19.4196 19.4235 19.4275 19.4314 19.4353 19.4392 19.4431 19.4471 19.4510 19.4549 19.4588 19.4627 19.4667 19.4706 19.4745 19.4784 19.4824 19.4863 19.4902 19.4941 19.4980 19.5020 19.5059 19.5098 19.5137 19.5176 19.5216 19.5255 19.5294 19.5333 19.5373 19.5412 19.5451 19.5490 19.5529 19.5569 19.5608 19.5647 19.5686 19.5725 19.5765 19.5804 19.5843 19.5882 19.5922 19.5961 19.6000 19.6039 19.6078 19.6118 19.6157 19.6196 19.6235 19.6275 19.6314 19.6353 19.6392 19.6431 19.6471 19.6510 19.6549 19.6588 19.6627 19.6667 19.6706 19.6745 19.6784 19.6824 19.6863 19.6902 19.6941 19.6980 19.7020 19.7059 19.7098 19.7137 19.7176 19.7216 19.7255 19.7294 19.7333 19.7373 19.7412 19.7451 19.7490 19.7529 19.7569 19.7608 19.7647 19.7686 19.7725 19.7765 19.7804 19.7843 19.7882 19.7922 19.7961 19.8000 19.8039 19.8078 19.8118 19.8157 19.8196 19.8235 19.8275 19.8314 19.8353 19.8392 19.8431 19.8471 19.8510 19.8549 19.8588 19.8627 19.8667 19.8706 19.8745 19.8784 19.8824 19.8863 19.8902 19.8941 19.8980 19.9020 19.9059 19.9098 19.9137 19.9176 19.9216 19.9255 19.9294 19.9333 19.9373 19.9412 19.9451 19.9490 19.9529 19.9569 19.9608 19.9647 19.9686 19.9725 19.9765 19.9804 19.9843 19.9882 19.9922 19.9961 20.0000
