function [new_config, new_ctrm, new_norms]  = cicero_km(sp_coords,Theta)

% This code represents the kinematic model created by 'Build_data_frame' as a function.

%%% INPUTS %%%
% sp_coords: a 4 x 1 vector for global position, R3, and rotation, [-pi,pi], in the spatial frame.
% Theta: a vector of N x 1 angles, where N is the number of rotation axes.
%%% Outputs %%%
% new_config: a point cloud from the surface of the kinematic model in the new configuration.
% new_ctrm: a new center of mass estimate for the kinematic model.

% new_norms: a new norm associated with the model point is calculated to reflect the new pose.

%%% Sampled meshes for each segment
I1  = [  0.138108  0.184091 -0.040526  0.015302  0.123625  0.026849 -0.026225  0.093420  0.143072 -0.017730  0.077664  0.060068 -0.045744 -0.029879  0.110946  0.086648 -0.002578  0.018915  0.106468  0.057928  0.173246 -0.023976  0.074910  0.027847  0.096754  0.018497 -0.023957  0.005913  0.059305  0.030690  0.010282  0.079673  0.138311 -0.018389  0.020560  0.115994 -0.039924 -0.031907  0.029587  0.183278  0.075361  0.135575  0.152557  0.041569 -0.031686  0.050541  0.168023  0.122426  0.124941  0.060739  0.132689  0.044254  0.091924  0.092497  0.088652  0.135039 -0.009807  0.097518  0.114249  0.060066 -0.046309 -0.061151  0.010875 -0.050889  0.006590  0.096266  0.106588  0.188963  0.163790 -0.016059  0.109679  0.022696  0.097633  0.041342  0.015955  0.029271 -0.049516 -0.071247  0.042589  0.206707  0.086966  0.039432  0.127517  0.146929  0.045168  0.047747 -0.006206  0.006154  0.010785  0.111852 -0.034651  0.143426  0.120271  0.095019 -0.003459  0.072106  0.091949  0.033733 -0.018621 -0.059293  0.002126  0.009698 -0.015175  0.081302  0.021075  0.085217 -0.000249  0.044733 -0.036013  0.056368  0.156001  0.064267 -0.039084  0.150222 -0.042441  0.021532  0.040505 -0.030228  0.112636 -0.011633  0.145899  0.028503  0.068466 -0.074624  0.145870  0.080291  0.076515 -0.009589 -0.050658  0.139063  0.005411  0.199665  0.061289 -0.027403 -0.023417  0.093670  0.128388 -0.067365  0.015232 -0.019188 -0.009514  0.159301  0.047480  0.127237  0.110978 -0.055470  0.025064  0.009104  0.053898  0.055831  0.161165  0.060037  0.072739  0.011763 -0.026690  0.115076 -0.029566  0.073631  0.035851  0.055529  0.100989  0.185096  0.018454  0.184054 -0.038948 -0.049421  0.115751  0.035768 -0.008017  0.049401 -0.041579 -0.023503  0.025765 -0.013179  0.080163  0.098444  0.006195  0.042579  0.085477 -0.037762  0.087089  0.035696  0.076309  0.037309  0.040598  0.147676  0.039524  0.092841 -0.031625  0.108097  0.139550  0.067964 -0.045730  0.007111  0.032702  0.004377  0.182727  0.004381  0.000337  0.127064 -0.035534  0.094589 -0.005491 -0.076942 -0.009268 -0.026017  0.054991  0.149413  0.046583  0.146291 -0.021445  0.187905 -0.021110  0.133932  0.063615  0.057599  0.099417  0.045856  0.109788 -0.041408  0.063217 -0.030498  0.025696  0.019393  0.105292  0.024815  0.130291 -0.022720  0.078862  0.076649 -0.053207  0.123608  0.105248  0.208579  0.141811 -0.049959  0.018945 -0.047348  0.079601  0.121067  0.199325  0.097929  0.006301  0.030980 -0.035139  0.160607 -0.016569  0.131688  0.049504  0.037166  0.044723  0.208388  0.121806  0.100001  0.193614 -0.041247
         0.042614 -0.195765  0.014780  0.092812 -0.155203 -0.081630  0.066136 -0.222070 -0.204908 -0.143360 -0.085196 -0.155598 -0.167359 -0.110215 -0.131956  0.086808 -0.154109  0.064156 -0.187609 -0.208825 -0.200890  0.052523  0.076944 -0.005445 -0.199487 -0.143230 -0.029421  0.082107  0.087640 -0.219784 -0.171756 -0.067690 -0.201125  0.074481 -0.056441  0.049378 -0.156915 -0.145186 -0.213880 -0.195948 -0.212843 -0.212202 -0.207169  0.083792 -0.177507 -0.046566 -0.205352  0.069519 -0.205421 -0.155551 -0.181524 -0.163956 -0.227906  0.012881 -0.061245  0.024518 -0.024487 -0.227453 -0.222196 -0.184905 -0.072539 -0.068339 -0.217063 -0.096508 -0.205531 -0.228620 -0.159875 -0.202114 -0.200997  0.073088  0.002888 -0.218620 -0.072344 -0.201213  0.001397  0.065177 -0.177153 -0.062318 -0.228829 -0.188779 -0.182455 -0.062373 -0.075018 -0.001566  0.081364 -0.172463 -0.105301 -0.166810  0.000146 -0.181324 -0.179177 -0.205947 -0.193002 -0.220263 -0.160283 -0.059108 -0.225669 -0.188817 -0.135602 -0.170128 -0.210991 -0.064449 -0.187382 -0.202442 -0.198358 -0.078850 -0.051521 -0.158860 -0.043764  0.046544 -0.206217 -0.127216 -0.176560 -0.207694 -0.131903 -0.111795 -0.230294 -0.172964  0.029132 -0.026605 -0.212267 -0.191094  0.083067 -0.104900 -0.211569 -0.151923 -0.196614 -0.073751 -0.047229  0.067603 -0.178088 -0.197129 -0.093759  0.020453 -0.037979  0.093025 -0.006933 -0.036666  0.031851  0.010490 -0.199671 -0.207107 -0.195212 -0.091163  0.033884 -0.010440 -0.029626 -0.196219 -0.203615 -0.041943 -0.008289 -0.228492  0.011790 -0.215395 -0.191236 -0.165254  0.008045 -0.075620 -0.015416 -0.195963 -0.196388 -0.200386 -0.119591 -0.191236  0.002099 -0.076663 -0.207086 -0.202842  0.014871 -0.203377 -0.016487 -0.193806 -0.035569 -0.172935 -0.071365 -0.207739  0.081864 -0.131597 -0.223942 -0.150057 -0.021597 -0.041181 -0.077266  0.002136 -0.175079  0.069861 -0.049835 -0.210998 -0.097616 -0.207315 -0.214059  0.074164 -0.109628  0.028489 -0.068133 -0.091448 -0.197465 -0.115013  0.003086  0.080394 -0.080545  0.084153 -0.006380 -0.122448 -0.152138 -0.134084 -0.131099  0.040910 -0.040861  0.016387  0.016216 -0.194492 -0.125891 -0.215642 -0.220675 -0.150108 -0.043718 -0.094012  0.039807 -0.146262 -0.145878 -0.179107  0.048091  0.090398  0.080579 -0.018706 -0.084335  0.004212  0.047315 -0.178996 -0.078815  0.033542  0.085096 -0.187241 -0.196983 -0.165595 -0.052614 -0.045464 -0.197554  0.098312 -0.195940  0.055785 -0.155175 -0.026064 -0.184391 -0.204160  0.047414 -0.193928  0.064423 -0.227057 -0.194188 -0.187561  0.057809 -0.062607 -0.195508  0.001560
         0.418814  0.289862  0.320755  0.313533  0.438367  0.394650  0.328193  0.292566  0.375767  0.349627  0.430493  0.418602  0.296311  0.348520  0.443048  0.364420  0.354058  0.364638  0.407684  0.321797  0.281949  0.332893  0.377763  0.392603  0.373195  0.383597  0.346693  0.341922  0.309181  0.245374  0.340353  0.431575  0.384937  0.326803  0.390138  0.415654  0.311693  0.329065  0.272466  0.287046  0.206834  0.331795  0.375325  0.322726  0.295220  0.412662  0.340039  0.389817  0.365594  0.419271  0.432909  0.389327  0.260994  0.435892  0.439649  0.439360  0.363849  0.253983  0.270947  0.367756  0.328362  0.305038  0.225885  0.320295  0.260217  0.244954  0.433254  0.357656  0.208868  0.330613  0.441976  0.240080  0.442056  0.328854  0.381266  0.367509  0.255176  0.293006  0.221347  0.352533  0.411751  0.404138  0.455531  0.454793  0.326283  0.375036  0.368779  0.342581  0.377780  0.423123  0.284981  0.370813  0.395270  0.299875  0.342119  0.428301  0.273440  0.340637  0.357978  0.264607  0.236055  0.380707  0.280907  0.356943  0.302956  0.433932  0.370127  0.396828  0.334615  0.405267  0.227274  0.431688  0.287738  0.365051  0.320455  0.390068  0.222062  0.304071  0.431352  0.362487  0.298269  0.333226  0.332789  0.290037  0.252428  0.436535  0.365706  0.363785  0.312292  0.382995  0.328945  0.336967  0.425385  0.331469  0.349470  0.343746  0.446958  0.300676  0.380884  0.341891  0.255986  0.292273  0.344083  0.451782  0.428055  0.310441  0.393985  0.283084  0.334133  0.416721  0.468618  0.255809  0.425843  0.236293  0.252515  0.432541  0.327608  0.428163  0.401447  0.349095  0.381741  0.328448  0.387265  0.260158  0.321633  0.324317  0.354200  0.311860  0.356974  0.331565  0.320881  0.250522  0.395671  0.318938  0.431499  0.346038  0.342285  0.411724  0.285659  0.317677  0.440977  0.401744  0.429364  0.401658  0.363021  0.369449  0.404213  0.331793  0.347639  0.349510  0.315099  0.378676  0.326592  0.374523  0.399164  0.379584  0.304337  0.377200  0.369892  0.365927  0.344228  0.375714  0.365303  0.284186  0.348338  0.345407  0.422296  0.420879  0.409185  0.448859  0.337882  0.301860  0.356932  0.228730  0.288883  0.418666  0.449126  0.415771  0.423587  0.316207  0.425464  0.292849  0.383790  0.320372  0.378315  0.391646  0.453634  0.338049  0.411153  0.403023  0.317284  0.430028  0.371981  0.362136  0.402598  0.294034  0.388628  0.315882  0.366701  0.342121  0.349818  0.407716  0.361674  0.398096  0.256708  0.394903  0.337465  0.401917  0.383052  0.218030  0.343238  0.352932  0.406321  0.445548  0.380120  0.320305
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N1  = [  0.291542  0.695845 -0.544596 -0.059829 -0.168130 -0.631942 -0.468771  0.107589 -0.124940 -0.758502 -0.312832 -0.594941 -0.598175 -0.695730  0.213088 -0.254613 -0.506353 -0.313870 -0.016576 -0.231504  0.570109 -0.525772 -0.226939 -0.701305 -0.127783 -0.591124 -0.789345 -0.525830  0.079610 -0.274500 -0.479165 -0.459180 -0.192579 -0.460650 -0.650056  0.207566 -0.592873 -0.752216 -0.413879  0.654479  0.087265  0.326356  0.004143  0.261121 -0.512840 -0.595439  0.347899  0.271267 -0.010988 -0.594270 -0.262172 -0.481226  0.282926 -0.141918 -0.384050 -0.093326 -0.552246  0.349423  0.353201 -0.412360 -0.906780 -0.836478 -0.380525 -0.959686 -0.411007  0.361354 -0.007818  0.633717  0.725275 -0.611857  0.028017 -0.271630 -0.411251 -0.329764 -0.597683 -0.218154 -0.513678 -0.871708  0.711150  0.786801 -0.226862 -0.583110 -0.148160 -0.388560  0.157983 -0.395673 -0.630095 -0.483568 -0.538139 -0.017301 -0.501686  0.036524 -0.039667  0.133807 -0.504452 -0.409984  0.191498 -0.428428 -0.809745 -0.535136 -0.421621 -0.645869 -0.344852 -0.114593 -0.363677 -0.405361 -0.632844 -0.568927 -0.855416 -0.263642  0.558531 -0.612232 -0.506120  0.213918 -0.910001 -0.602303  0.397877 -0.514468  0.010483 -0.760838  0.483638 -0.452173 -0.283234 -0.764549  0.531138 -0.244187 -0.302648 -0.815172 -0.685902  0.561888 -0.483170  0.886284 -0.413355 -0.666502 -0.751857 -0.308316 -0.120728 -0.689933 -0.586344 -0.813318 -0.434310  0.530581 -0.361517 -0.078292  0.025484 -0.646540 -0.607275 -0.397141 -0.267462 -0.575459 -0.552739 -0.233957 -0.446581 -0.366817 -0.503187 -0.231384 -0.722681 -0.309162 -0.585911 -0.321243 -0.017147  0.386964 -0.612569  0.940246 -0.544380 -0.932007 -0.011757 -0.287788 -0.825458 -0.271959 -0.691328 -0.500000 -0.613754 -0.507994 -0.458690  0.047631  0.020313 -0.716816  0.087719 -0.633424 -0.344332 -0.530172 -0.348627 -0.658985 -0.448609  0.621442 -0.518371  0.041156 -0.644335  0.048018  0.340680 -0.245967 -0.932136 -0.666288 -0.563167 -0.654577  0.585675 -0.570510 -0.631391  0.407585 -0.680777  0.136668 -0.683128 -0.974020 -0.603926 -0.793103 -0.575639  0.162546 -0.558231 -0.099379 -0.793605  0.694257 -0.786239  0.487379 -0.130467 -0.597410 -0.370084 -0.560597  0.046191 -0.677803 -0.633622 -0.452106 -0.383394  0.112791  0.340656 -0.665703 -0.128966 -0.869386 -0.133311 -0.384074 -0.959710  0.029111  0.340611  0.828835 -0.155919 -0.631408 -0.651671 -0.926602 -0.299562  0.405600  0.857752 -0.018769 -0.422994 -0.617384 -0.492732  0.131065 -0.618429 -0.166042 -0.284703 -0.226524 -0.396734  0.909209  0.238646 -0.365962  0.610022 -0.546679
         0.862983 -1.047771  0.001725  1.038606 -0.340562 -0.077333  0.414897 -1.198776 -1.148380 -0.697665  0.030109 -0.441928 -0.820124 -0.120340 -0.285495  0.999337 -0.939150  0.915242 -1.125490 -1.152443 -1.117635  0.104712  0.896410  0.079497 -1.102911 -0.366101  0.164149  0.861603  1.022961 -1.146639 -0.828602 -0.208822 -1.110943  0.741327 -0.059393  0.764654 -0.669681 -0.624552 -1.050679 -1.074509 -1.054503 -1.171630 -1.187019  0.947494 -0.947512  0.022930 -1.183244  0.941090 -1.161078 -0.441881 -0.831879 -0.915238 -1.194576  0.349112 -0.326780  0.591093  0.063029 -1.189381 -1.192014 -0.876061  0.096431 -0.102378 -1.122806 -0.204342 -1.042210 -1.191633 -0.607421 -1.089211 -1.028425  0.604330  0.331206 -1.129194 -0.152619 -1.061633  0.029411  0.915788 -1.000026 -0.197256 -0.972381 -1.002975 -1.125792 -0.042588 -0.364764  0.142951  0.993369 -0.974092 -0.031730 -0.837719 -0.015645 -0.899059 -1.025182 -1.177722 -1.149413 -1.187984 -0.847056 -0.148743 -1.204799 -0.898628 -0.380762 -1.045773 -1.093381  0.036310 -1.114622 -1.129810 -1.121106 -0.084555  0.024882 -0.761320  0.160912  0.636684 -1.119732 -0.248562 -1.022565 -1.199123 -0.374678 -0.137023 -1.155221 -0.884964  0.523957 -0.111440 -1.153498 -0.869968  1.012023 -0.086570 -1.134031 -0.418287 -0.991435 -0.133238  0.185566  0.849113 -0.840689 -0.923492  0.078221  0.034736  0.109946  1.005291  0.246472 -0.037607  0.080449  0.189797 -1.032701 -1.135358 -0.947799 -0.243544  0.624071  0.011903  0.127485 -1.028764 -1.063127  0.048571 -0.072311 -1.182890  0.156914 -1.104250 -1.013795 -0.519466 -0.013094 -0.018041  0.016057 -0.990631 -1.081847 -1.156286 -0.176424 -0.842753  0.012695  0.043914 -1.178527 -1.136830  0.232476 -1.062890  0.053897 -1.016365  0.050696 -0.822083 -0.212496 -1.174777  0.929602 -0.360027 -1.201650 -0.517430  0.182939 -0.033291 -0.058026  0.099717 -0.908149  0.852415 -0.048770 -1.179546 -0.128716 -1.176197 -1.192547  0.902733 -0.315075  0.125778 -0.054854 -0.179325 -1.110108 -0.170764  0.018613  0.936083 -0.058878  0.908268  0.108385 -0.189637 -0.868886 -0.557511 -0.305416  0.929964 -0.013092  0.606184  0.070736 -1.054395 -0.214470 -1.150249 -1.146681 -0.436438 -0.039248  0.081785  0.682550 -0.354285 -0.365469 -1.040332  0.429958  1.014202  0.878500  0.122742 -0.302956  0.110083  0.636331 -1.066422 -0.081519  0.645295  0.883016 -0.966036 -1.103854 -0.784499 -0.055566 -0.059302 -0.992375  0.942616 -0.924763  0.741677 -0.938740  0.063078 -1.030181 -1.160407  0.132323 -1.100800  0.796540 -0.903450 -0.920678 -0.900864  0.812236 -0.320850 -1.104559  0.012156
         0.969679  0.179438  1.184320  0.629492  1.376728  1.146964  1.154340  0.506680  0.570781  0.729106  1.343848  1.117872  0.814691  1.094536  1.425897  0.589879  0.714503  0.770723  0.732092  0.482469  0.236357  1.196303  0.864961  1.071662  0.738446  1.144314  0.960462  0.673035  0.662400  0.464003  0.913934  1.262068  0.635422  0.926570  1.131937  1.108470  0.968441  0.830427  0.593566  0.208938 -0.333043  0.539403  0.508990  0.776395  0.714246  1.172847  0.233400  0.856946  0.626826  1.118541  1.081849  0.788634  0.431484  1.348031  1.279913  1.231093  1.199374  0.359987  0.319482  0.914671  0.809027  0.935679  0.388476  0.723358  0.614592  0.196625  1.320167  0.481158  0.199044  0.932947  1.383007  0.530300  1.299140  0.678076  1.170356  0.831451  0.582947  0.877004  0.233846  0.376532  0.519581  1.186474  1.372074  1.286879  0.720642  0.775997  1.146821  0.899405  1.213502  1.107357  0.542184  0.581112  0.639601  0.548896  0.868758  1.299825  0.450628  0.872215  0.918352  0.347194  0.440566  1.129092  0.458495  0.675710  0.325355  1.305311  1.140832  0.907185  0.870046  1.146434  0.168462  1.158065  0.544942  0.479115  0.754503  1.171217  0.092467  0.812565  1.294320  1.019370  0.302477  0.888276  0.448326  1.013685  0.227245  1.344149  0.839515  0.953274  1.048683  0.841755  0.896614  0.306123  1.288597  1.100461  1.018419  0.422341  1.381691  1.083241  1.178221  0.922586  0.610401  0.269890  0.860160  1.418497  1.230782  1.116752  1.152579  0.659691  0.731583  1.186968  1.165928  0.307694  1.268010  0.494391  0.562913  1.301161  1.048124  1.350202  1.184020  0.825064  0.831191  0.115129  1.160945  0.199328  1.184435  0.778742  0.554311  0.463445  0.890301  0.729014  1.077765  0.560920  1.159591  0.896663  1.261992  0.595546  0.872512  1.020935  0.495617  1.031975  1.319636  1.226202  1.334384  1.112751  0.835551  0.773373  1.234124  0.575195  1.137335  0.589629  0.361014  0.842271  0.741414  1.107373  1.202136  1.126616  0.235656  1.193528  1.144927  0.800788  1.107898  0.940571  1.091690  0.720920  0.712553  0.827372  1.178549  0.878493  1.205067  1.218135  0.970966  0.237240  0.994687  0.188929  0.612680  1.117936  1.332047  1.191213  1.187025  1.058991  1.108250  0.576642  1.212538  0.691672  0.933226  1.100995  1.394374  0.859536  1.190924  0.417545  0.739473  1.215412  0.926892  0.268539  0.700828  0.822120  1.130427  0.792034  0.840510  0.796206  0.537676  1.126002  0.810821  1.154190  0.531021  0.685971  1.131540  0.700147  0.976609 -0.469692  0.869857  0.359924  1.052223  1.291828  0.395311  1.183107
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

I4  = [ -0.122449 -0.099251 -0.051211 -0.084137 -0.124094 -0.117990 -0.109582 -0.041460 -0.119030 -0.110276 -0.049264 -0.070256 -0.117829 -0.032474 -0.120781 -0.117339 -0.070926 -0.134507 -0.108157 -0.104390 -0.135222 -0.022934 -0.116443 -0.105076 -0.118312 -0.081717 -0.116625 -0.009623 -0.118124 -0.065836 -0.069508 -0.092800 -0.101197 -0.122096 -0.114219 -0.086853 -0.004514 -0.108475 -0.032780 -0.090797 -0.048550 -0.099563 -0.126501 -0.076807 -0.072277 -0.111264 -0.119097 -0.116738 -0.097262 -0.096415 -0.107984 -0.088512 -0.111539 -0.103467 -0.107667 -0.064473 -0.111794 -0.109901 -0.071376 -0.125681 -0.113426 -0.111255 -0.101044 -0.124705 -0.115442 -0.098378 -0.099781 -0.131700 -0.015247 -0.019907 -0.115791 -0.042021 -0.139991 -0.079053 -0.030588 -0.089609 -0.106760 -0.118143 -0.114770 -0.100222 -0.075079 -0.115537 -0.110406 -0.116548 -0.100042 -0.060787 -0.108699 -0.102489 -0.069007 -0.047396 -0.099667 -0.118693 -0.111718 -0.083201 -0.093877 -0.115942 -0.116445 -0.090342 -0.112964 -0.118848 -0.058646 -0.083936 -0.097632 -0.055911 -0.034739 -0.042963 -0.065682 -0.117896 -0.089905 -0.033616 -0.122377 -0.069651 -0.108738 -0.110381 -0.128558 -0.106798 -0.081705 -0.111521 -0.134007 -0.016279 -0.098281 -0.067826 -0.102006 -0.111165 -0.109314 -0.100800 -0.044588 -0.083320 -0.058220 -0.104261 -0.085057 -0.141196 -0.100001 -0.112985 -0.121570 -0.114066 -0.066027 -0.116912 -0.100858 -0.070673 -0.055763 -0.100902 -0.118115 -0.130809 -0.126174 -0.113894 -0.105762 -0.110925 -0.114911 -0.104968 -0.056576 -0.087833 -0.114783 -0.062843 -0.051216 -0.115394 -0.108913 -0.068546 -0.121753 -0.111571 -0.123305 -0.106230 -0.083453 -0.110563 -0.113198 -0.093264 -0.115803 -0.132308 -0.026390 -0.079945 -0.106294 -0.114216 -0.133290 -0.117660 -0.114546 -0.079631 -0.058994 -0.111028 -0.100528 -0.037115 -0.119750 -0.096981 -0.118413 -0.077405 -0.068474 -0.084969 -0.127446 -0.107990 -0.087595 -0.083377 -0.111100 -0.083247 -0.104899 -0.068757 -0.068382 -0.066680 -0.102105 -0.119260 -0.118293 -0.108569 -0.109395 -0.117571 -0.082912 -0.072209 -0.117955 -0.030226 -0.134512 -0.121378 -0.110821 -0.137226 -0.117531 -0.045360 -0.113312 -0.141367 -0.115753 -0.076840 -0.054588 -0.115309 -0.029232 -0.134918 -0.128301 -0.136368 -0.082483 -0.104801 -0.090378 -0.118318 -0.102519 -0.114798 -0.087375 -0.141573 -0.079410 -0.083056 -0.113137 -0.101970 -0.090868 -0.063787 -0.031812  0.000744 -0.058436 -0.023279 -0.116822 -0.015431 -0.118502 -0.109532 -0.116595 -0.141968 -0.046285 -0.110118 -0.140514 -0.099569 -0.022836 -0.120801 -0.100125 -0.122044 -0.111329 -0.090950
         0.060741 -0.132632 -0.109141  0.026821  0.059345 -0.008426 -0.059244 -0.126321 -0.013712 -0.105634 -0.109444  0.099713 -0.079675 -0.113162 -0.060444 -0.077822  0.144248 -0.031831  0.098019 -0.123444 -0.025394 -0.140724 -0.025209 -0.101848 -0.017394 -0.142303 -0.020959 -0.138866 -0.074661  0.137761 -0.123199  0.066283  0.014057 -0.052003  0.017219  0.093315 -0.135321  0.040235 -0.128368 -0.097427  0.120502  0.119874 -0.065493 -0.154764  0.133121 -0.045734 -0.003788 -0.060593  0.077621  0.050729  0.100702  0.022137 -0.096408 -0.130559  0.024744 -0.103043 -0.070228  0.065219 -0.118582  0.025686 -0.067743 -0.087603  0.072237  0.058115  0.009645 -0.136120  0.077506 -0.036404 -0.120211 -0.153308  0.001275 -0.128735 -0.020270  0.100845 -0.129448 -0.097889 -0.100290 -0.013956 -0.034588  0.117819  0.125564 -0.029894 -0.046644  0.073437 -0.121695  0.134419 -0.008419  0.056362  0.118715 -0.120236  0.062834  0.042696  0.020930 -0.104085 -0.125214  0.071545 -0.071880  0.082699 -0.063022 -0.050626  0.082485  0.141852  0.001313 -0.113195  0.129875 -0.138065  0.103377  0.002322 -0.109112 -0.124276 -0.035701  0.115467 -0.039527  0.053008 -0.020134  0.101056  0.110675 -0.072780  0.005767 -0.131585  0.047804  0.122846  0.041296 -0.092644  0.094616 -0.125769 -0.108794  0.105853  0.126670  0.073507 -0.100294  0.009231  0.042883 -0.063876  0.019295 -0.081214  0.153507 -0.022217  0.118078  0.131618 -0.154225  0.041305 -0.055990 -0.031490  0.031998 -0.050283 -0.089225 -0.104780 -0.049671  0.044324  0.155195 -0.135748 -0.036570  0.091564  0.141849 -0.068336 -0.069034  0.136466 -0.054338  0.016203 -0.059138  0.044884  0.132551 -0.082885  0.021334  0.121632 -0.074117 -0.049081 -0.118975 -0.101628 -0.109883 -0.046181 -0.042404 -0.032339 -0.078613 -0.111104  0.140195 -0.082515 -0.135386  0.135270  0.003600 -0.103453  0.011346  0.114612 -0.115638  0.138358  0.041966  0.038381 -0.110364  0.098342 -0.078052  0.139089 -0.093116  0.086100  0.133225 -0.126735  0.050297  0.057123 -0.086338  0.038087 -0.062614 -0.063134  0.102752  0.114764 -0.035592 -0.125799  0.035005  0.046690 -0.081328 -0.036866 -0.030398 -0.114815 -0.062974  0.011993 -0.058947  0.145733  0.144461 -0.031498  0.127164  0.030228  0.040430 -0.034805  0.069957 -0.127812 -0.108904 -0.001736  0.045265 -0.077742  0.107511 -0.004833 -0.104201  0.033472 -0.084591  0.019039  0.110914  0.128614 -0.129921 -0.151630  0.107376 -0.132919 -0.055395 -0.133219 -0.022474  0.037524  0.079249 -0.004522 -0.122947 -0.090569 -0.010104  0.093509 -0.118191  0.041876  0.071830  0.062164 -0.089758  0.019753
        -0.001253  0.118661 -0.052259  0.199820 -0.008359  0.111947  0.177280  0.050827  0.140859  0.133649 -0.054028  0.187729 -0.056934 -0.085670  0.017277 -0.036425  0.056873 -0.006166  0.008113  0.141991 -0.003798  0.084252  0.066776  0.076022  0.100477  0.108598  0.071909  0.072457 -0.045088  0.088850  0.063762  0.093383  0.172079  0.019258  0.128923  0.140120  0.042247  0.135518  0.046633 -0.066803  0.198807  0.032058 -0.004835  0.133188  0.080682  0.175073  0.129841  0.034721  0.070763  0.095093  0.029698  0.193325  0.130575  0.135303  0.087731 -0.076435  0.068053  0.052269  0.050821  0.041745  0.048641 -0.058538  0.066161 -0.007814  0.107546  0.149050  0.065787 -0.000491 -0.048087  0.107276  0.088461  0.063261 -0.041160  0.169191  0.049486 -0.064973  0.158482  0.067048  0.079810  0.035298  0.084320  0.071050  0.178042 -0.005506  0.096473  0.107284  0.168901  0.126691  0.178553  0.019036  0.127316  0.047082  0.119969 -0.028605  0.089661  0.031814  0.145425  0.141046  0.104608  0.046061  0.221930  0.009298  0.186219 -0.015105  0.189205  0.083541  0.194822  0.114340  0.028754  0.023130  0.042340  0.121063  0.182645  0.058066  0.021357  0.003206  0.156629  0.050032  0.019933  0.037631  0.102803  0.106191  0.082446 -0.021306  0.000224  0.107399 -0.080315  0.156486  0.183679  0.059024 -0.051376 -0.029040  0.085074  0.099126  0.053890  0.139471  0.006250  0.113990 -0.005220  0.087134  0.123450  0.084512  0.039709  0.005746  0.037523  0.096768  0.048465  0.125213  0.081166  0.118439  0.032997  0.102181  0.084930  0.207122  0.155097  0.130788  0.167984  0.084706  0.018648  0.085822  0.010028  0.123172  0.059634  0.075580  0.138479  0.050430  0.144637 -0.011197 -0.034829 -0.052745  0.147869  0.095292 -0.009433  0.132013  0.141776  0.009953  0.123940  0.096825  0.134977  0.172141  0.063301  0.009604  0.063917  0.089453  0.022566  0.033680  0.027570  0.141453  0.030243  0.133265  0.073416  0.037899 -0.035749  0.198156  0.140198  0.070117  0.114783  0.037004 -0.016778  0.138487  0.175058  0.139330  0.085699  0.125954  0.134631  0.027142  0.009908  0.038947  0.076522 -0.019410  0.140803 -0.024953  0.094690 -0.033248  0.081301  0.025719  0.126364  0.163178  0.201475 -0.013114  0.026531 -0.044524  0.179340  0.134603  0.029639  0.116250  0.112606  0.145049  0.074074 -0.026178 -0.035599  0.198007 -0.053820  0.167824  0.064899  0.108622  0.054761  0.104930  0.204141  0.058561  0.146060  0.046184  0.146980  0.134928 -0.017170 -0.031988  0.038380  0.099957 -0.018337  0.057354 -0.047590  0.043050  0.068222  0.004315  0.149699  0.189664
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N4  = [ -1.015105 -0.907821 -0.326520 -0.948104 -0.991120 -1.114675 -1.095006 -0.341368 -1.118756 -1.094065 -0.324574 -0.941295 -0.979776 -0.295548 -1.057668 -0.939894 -0.540940 -1.075399 -1.061060 -1.037486 -1.077416 -0.150801 -1.103261 -1.031530 -1.114226 -0.482909 -1.109073 -0.188214 -1.002855 -0.843987 -0.324629 -1.046021 -0.971156 -1.060124 -1.057490 -1.041442 -0.240807 -1.060132 -0.326510 -0.372634 -0.649776 -0.969741 -1.065595 -0.308933 -0.875347 -1.087077 -1.118897 -1.062683 -0.965816 -1.066738 -1.048150 -0.965244 -1.095329 -1.011033 -1.013393 -0.309681 -1.101189 -0.979502 -0.333906 -1.009456 -1.052123 -0.677621 -0.969600 -0.991730 -1.080664 -1.031853 -0.968332 -1.063466 -0.257291 -0.107798 -1.095779 -0.331513 -1.113319 -0.947899 -0.324318 -0.375825 -1.071890 -1.078050 -1.111488 -0.962038 -0.861292 -1.102354 -1.086219 -1.081041 -0.848401 -0.846964 -0.986246 -1.002954 -0.939595 -0.289704 -1.000132 -0.992359 -1.010750 -0.344837 -0.700237 -1.034039 -1.101684 -1.041812 -1.110475 -1.068391 -0.948937 -0.696828 -0.975917 -0.324109 -0.221333 -0.181753 -0.934844 -1.107916 -0.576515 -0.309160 -1.092786 -0.907257 -1.052551 -0.979783 -1.077860 -1.050742 -0.960286 -1.072196 -1.093666 -0.278651 -1.054173 -0.892539 -0.950598 -0.745150 -1.047815 -0.879396 -0.366994 -0.961901 -0.289461 -0.972833 -0.350443 -1.126565 -0.981971 -1.109922 -1.007177 -1.094218 -0.495113 -1.110929 -1.002454 -0.848824 -0.167025 -0.982872 -1.075567 -1.062312 -1.022610 -1.110279 -1.019276 -1.096023 -1.105762 -1.019953 -0.473947 -0.565059 -1.114031 -0.921812 -0.193821 -1.094102 -1.079985 -0.846698 -1.059781 -1.037055 -1.056413 -1.031565 -0.938251 -1.088730 -1.090154 -0.945923 -1.090066 -1.067800 -0.287008 -0.345330 -1.042428 -1.112303 -1.066125 -1.115592 -1.094698 -0.378328 -0.838869 -1.099837 -0.946714 -0.020794 -1.036432 -0.639539 -1.005850 -0.910787 -0.325172 -0.777038 -1.032915 -1.040856 -0.470761 -0.960560 -1.098737 -0.703344 -0.668931 -0.938484 -0.817094 -0.180598 -1.005828 -1.033094 -0.860813 -1.060226 -1.099113 -1.110810 -0.954412 -0.895708 -1.115888 -0.323797 -1.088162 -1.016605 -1.088988 -1.101648 -1.113466 -0.323652 -1.101839 -1.127043 -1.097967 -0.581443 -0.695322 -1.056988 -0.077884 -1.107885 -1.033770 -1.086421 -0.952569 -1.012367 -0.576988 -1.115002 -1.017504 -1.070233 -0.955783 -1.134617 -0.341045 -0.947023 -0.941615 -0.971946 -0.957513 -0.969357 -0.302543  0.162486 -0.809908 -0.253566 -1.095117 -0.262241 -1.116112 -1.061189 -1.031977 -1.141048 -0.302444 -1.091901 -1.123926 -0.967273 -0.287231 -0.991389 -0.968681 -1.014700 -1.060182 -0.963107
         0.508564 -0.676223 -1.057997  0.283938  0.538589  0.008543 -0.161936 -1.064417 -0.033116 -0.238716 -1.058300  0.338145 -0.538758 -1.076973 -0.266015 -0.606269  1.004846 -0.228814  0.385406 -0.401536 -0.216925 -1.054649 -0.167909 -0.440173 -0.104698 -0.983495 -0.100694 -1.090624 -0.525113  0.691005 -0.999161  0.329020  0.249115 -0.260148  0.348823  0.375836 -1.098136  0.344385 -1.072852 -1.051435  0.874261  0.599184 -0.323494 -0.975335  0.648657 -0.045485 -0.016086 -0.368072  0.316594  0.265840  0.400264  0.279941 -0.229490 -0.541956  0.444239 -1.067033 -0.215462  0.305048 -1.066843  0.239399 -0.405645 -0.909682  0.311247  0.537359  0.239722 -0.427048  0.316478 -0.243911 -1.085652 -1.013813  0.172787 -1.049702 -0.211171  0.355184 -1.073932 -1.054345 -0.238474 -0.145021 -0.113230  0.556352  0.584909 -0.172594 -0.046395  0.335554 -0.726881  0.655077  0.210395  0.451480  0.448741 -1.085386  0.457952  0.278783  0.434483 -1.061408 -0.845551  0.420713 -0.243009  0.375154 -0.133454 -0.274292  0.381374  0.930979  0.241054 -1.066204  1.071651 -1.020322  0.342574  0.115299 -0.981497 -1.077012 -0.203507  0.645317  0.105967  0.291998 -0.220597  0.430702  0.405689 -0.349931 -0.133379 -1.083762  0.278711  0.566494  0.399020 -0.813629  0.439867 -0.699052 -1.055308  0.400867  0.896089  0.312526 -1.056179  0.126567  0.361053 -0.128054  0.221932 -0.271132  1.052404 -0.131411  0.476299  0.684862 -1.073832  0.359475 -0.334173 -0.238363  0.247296 -0.133738 -0.485716 -0.273335  0.059088  0.293173  1.057917 -0.932360 -0.075019  0.348930  1.099013 -0.209725 -0.254069  0.689710 -0.262483  0.391772 -0.265514  0.386904  0.601548 -0.273125  0.232496  0.493907 -0.293072 -0.271289 -1.076648 -1.057513 -0.403395 -0.105537 -0.248060  0.024734 -0.268532 -1.049991  0.746052 -0.222133 -0.660515  1.040889  0.052537 -0.943421  0.185510  0.440298 -1.079167  0.829160  0.306999  0.294407 -1.033231  0.490188 -0.219513  0.916466 -0.914667  0.321776  0.795045 -1.002288  0.374358  0.318176 -0.709898  0.342236 -0.200788 -0.165092  0.343245  0.561679  0.021481 -1.070596  0.326323  0.300710 -0.271568 -0.234941 -0.115380 -1.066884 -0.134673  0.108855 -0.241782  1.001760  0.909160 -0.000049  1.080086  0.261149  0.305463 -0.310732  0.304963 -0.539209 -0.981289  0.015233  0.294115 -0.340835  0.356987 -0.026084 -1.061524  0.290589 -0.614008  0.254099  0.379468  0.537781 -1.081173 -0.916362  0.568977 -1.089183 -0.093719 -1.091944 -0.091558  0.341674  0.324082 -0.017502 -1.079069 -0.254200 -0.102125  0.336368 -1.075738  0.285496  0.310840  0.509987 -0.307312  0.254822
        -0.052442 -0.106555 -0.206780  0.632777  0.127990  0.032376  0.312901 -0.122469  0.153925  0.253842 -0.208550  0.617196  0.158220 -0.042535  0.300089 -0.246537  0.252981  0.269371 -0.088765  0.370018  0.271131 -0.300964  0.143116 -0.088965  0.123584 -0.253950  0.165136 -0.177063  0.074673  0.386174 -0.345632  0.242847  0.605574  0.296349  0.112262  0.045564 -0.088723  0.178441 -0.100580 -0.168961  0.464089  0.146307  0.222185 -0.389096  0.379515  0.393680  0.114082  0.137897  0.504936  0.205553  0.192027  0.599376  0.250769  0.219428  0.148441 -0.179377  0.069997  0.483867 -0.127722  0.458001  0.116987 -0.000103  0.500310  0.128536 -0.016595  0.358775  0.499965  0.297423 -0.144726 -0.394528 -0.012572 -0.197534 -0.168399  0.593948 -0.097728 -0.122176  0.380811  0.314837  0.098987  0.290174  0.497688  0.147389  0.396650 -0.037858 -0.175020  0.440212  0.595553 -0.055090  0.543464 -0.079820 -0.054464  0.472489 -0.023955 -0.151401 -0.247150  0.219376  0.149690  0.045262  0.107773  0.265926  0.565509  0.049830  0.599910 -0.155971  0.468919 -0.366302  0.627652  0.030097 -0.017673 -0.104817  0.215970 -0.011890  0.479373  0.490529  0.263513  0.020587  0.532211  0.067104  0.264257 -0.118961 -0.078726  0.456940  0.472223 -0.301025  0.004324 -0.147813 -0.093194  0.532067  0.779097  0.493136 -0.177292  0.094571  0.432776  0.143833  0.471786  0.082609  0.094962  0.111578  0.237273  0.384458 -0.253303  0.432214  0.116508  0.304924  0.424885  0.080878  0.139506  0.090974  0.161080 -0.199170  0.137376 -0.268850  0.089876  0.649767  0.407093 -0.018003  0.318922  0.382030  0.295739  0.135076  0.304507 -0.040468  0.281811 -0.008069  0.169588  0.417012  0.091065  0.263538 -0.157061 -0.178660  0.341528  0.112617  0.286412  0.161561  0.084914 -0.161139 -0.033325  0.044257  0.044367  0.595921  0.459911  0.000349  0.490675  0.536000 -0.053058  0.243044  0.359056  0.394854 -0.008486 -0.144237  0.005880  0.143560 -0.118952  0.631782  0.102448 -0.399383 -0.164984  0.348066 -0.261396  0.181409  0.212003  0.083821  0.513076 -0.223497  0.164179 -0.118372  0.085313  0.405066 -0.007127  0.155681  0.110915 -0.151912  0.227629  0.104808  0.038562  0.137947  0.057841  0.498219  0.500760 -0.016577  0.358016 -0.190349  0.612610  0.218728 -0.016788  0.036679 -0.205003  0.278938  0.502594  0.089627 -0.158394  0.630965  0.128779  0.601286  0.485381  0.220533 -0.092967 -0.518788  0.675537 -0.121792  0.349703 -0.094993  0.146541  0.177851  0.302411  0.008891 -0.103794  0.003383  0.137973  0.491070 -0.162477  0.470514  0.502371 -0.046874  0.378495  0.618715
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

I5  = [ -0.131199 -0.142919 -0.133290 -0.117079 -0.131348 -0.133031 -0.115074 -0.122784 -0.146328 -0.138787 -0.147220 -0.079543 -0.162195 -0.132151 -0.096650 -0.109391 -0.149252 -0.098281 -0.110523 -0.145439 -0.162064 -0.152639 -0.132622 -0.094339 -0.172233 -0.118434 -0.150558 -0.118327 -0.129623 -0.127474 -0.140420 -0.141544 -0.153730 -0.154364 -0.117539 -0.100364 -0.127652 -0.147751 -0.107199 -0.137107 -0.080811 -0.155451 -0.091868 -0.104123 -0.153439 -0.125913 -0.120092 -0.162749 -0.146749 -0.141275 -0.124619 -0.139002 -0.109855 -0.147198 -0.171543 -0.136207 -0.163938 -0.150350 -0.136656 -0.154716 -0.123621 -0.137619 -0.132528 -0.144338 -0.112247 -0.156408 -0.114900 -0.150587 -0.143792 -0.159610 -0.097342 -0.124869 -0.127931 -0.119381 -0.137312 -0.118439 -0.143983 -0.124537 -0.150965 -0.101676 -0.132830 -0.132799 -0.144125 -0.090097 -0.153813 -0.115223 -0.131747 -0.142731 -0.145111 -0.146574 -0.162579 -0.139769 -0.075812 -0.078098 -0.145328 -0.155028 -0.104175 -0.120381 -0.137960 -0.132382 -0.147023 -0.160939 -0.152070 -0.162026 -0.148080 -0.153429 -0.138260 -0.139614 -0.131510 -0.150008 -0.140239 -0.109421 -0.136660 -0.157324 -0.133127 -0.091390 -0.171788 -0.145323 -0.117834 -0.144749 -0.136838 -0.101657 -0.110330 -0.094684 -0.138527 -0.070150 -0.152465 -0.107325 -0.131852 -0.128813 -0.126794 -0.127788 -0.165839 -0.120623 -0.135548 -0.097080 -0.142232 -0.163525 -0.129175 -0.158304 -0.162172 -0.131169 -0.136159 -0.078910 -0.159203 -0.151100 -0.147218 -0.115126 -0.166419 -0.135500 -0.129583 -0.139555 -0.141330 -0.135077 -0.158508 -0.106947 -0.126723 -0.128904 -0.136185 -0.171114 -0.104970 -0.146206 -0.113976 -0.141023 -0.121690 -0.122652 -0.166003 -0.165582 -0.151147 -0.142776 -0.108720 -0.145579 -0.158523 -0.132822 -0.121705 -0.100595 -0.109950 -0.145184 -0.148710 -0.167413 -0.133183 -0.164483 -0.151820 -0.158204 -0.145470 -0.171895 -0.152861 -0.170834 -0.123292 -0.120706 -0.130821 -0.096644 -0.121775 -0.145444 -0.148670 -0.101265 -0.144883 -0.138267 -0.128021 -0.152743 -0.119778 -0.137947 -0.098436 -0.136065 -0.107705 -0.148943 -0.106240 -0.140028 -0.147776 -0.158564 -0.168644 -0.135477 -0.137320 -0.138950 -0.137070 -0.136146 -0.159447 -0.152641 -0.167307 -0.132549 -0.134484 -0.140440 -0.148662 -0.132179 -0.149165 -0.164179 -0.143357 -0.133470 -0.106909 -0.140840 -0.169543 -0.109837 -0.116480 -0.123862 -0.144970 -0.135618 -0.170875 -0.167568 -0.139836 -0.164045 -0.140747 -0.097018 -0.134082 -0.132688 -0.103862 -0.132256 -0.128452 -0.103294 -0.113460 -0.119778 -0.159430 -0.141446 -0.147948 -0.100371 -0.117126 -0.138657
        -0.049116 -0.003055  0.063667  0.124151  0.093326 -0.044781  0.110240 -0.053920  0.028675 -0.026242  0.052341  0.153628  0.001452 -0.042264 -0.050420  0.142262 -0.001240 -0.058733  0.124724  0.011595  0.078585 -0.021782 -0.038385 -0.083918  0.047421 -0.033920  0.119281 -0.053168  0.109788 -0.038467 -0.016791  0.066859  0.104994 -0.002745  0.142207  0.148237 -0.058874  0.103147  0.128973 -0.028517 -0.065923  0.102203  0.146748  0.134754  0.099430  0.083839 -0.048651  0.016078 -0.031790  0.115296  0.132544  0.050790  0.123411 -0.012940  0.035259 -0.038120  0.023272  0.113309  0.079825  0.015659  0.088150  0.084136  0.066330  0.035106 -0.039423 -0.007402 -0.045227  0.120410  0.013961  0.091043 -0.033207  0.125459 -0.043737  0.095886 -0.032115  0.130022  0.017529  0.110617  0.100521 -0.083692 -0.044853 -0.042777  0.028854  0.156676  0.045251  0.108942  0.082139  0.002608  0.058238  0.032901  0.036533  0.103667 -0.060872 -0.090318  0.107841 -0.014934  0.134460  0.108672  0.053139 -0.049278  0.000876 -0.025682  0.019282  0.075086  0.025891  0.077660  0.130956  0.078485  0.148515  0.084847 -0.039460 -0.080643  0.147227  0.002193  0.152472 -0.049764  0.028110  0.119109  0.114628 -0.012881 -0.044682  0.149436 -0.080721  0.146795 -0.031706 -0.079362  0.083486 -0.082149 -0.052052  0.153038 -0.060199 -0.037117  0.035607  0.139927  0.143730  0.144785 -0.039195  0.020646  0.155454  0.093986  0.070977  0.088073 -0.037298 -0.064891  0.081454 -0.011653  0.024087 -0.040141  0.012916  0.074430 -0.051757 -0.032975 -0.012989 -0.045100  0.014270  0.129520  0.120930 -0.040848  0.112727  0.028238 -0.083442  0.124075  0.122775  0.135260 -0.042129  0.092356  0.022109  0.006979  0.007058 -0.021696 -0.034288  0.129521  0.070246 -0.041305  0.138561 -0.048216  0.123268  0.018947 -0.015068  0.028207 -0.041814  0.074337  0.039966  0.052626 -0.032521  0.052000  0.014905  0.030244 -0.066338 -0.039098  0.154378  0.142831 -0.044398 -0.033516 -0.014226 -0.083609  0.009048 -0.027911  0.078181  0.044123  0.116603 -0.023610  0.142378  0.058966  0.147092 -0.024265  0.132630  0.129542  0.080868  0.038628  0.067957 -0.039043 -0.029332 -0.039324 -0.025475 -0.046821  0.042926  0.092632  0.026104 -0.044944  0.118455 -0.029743  0.104885 -0.045980  0.057841  0.003115  0.007805  0.152420 -0.074754 -0.034045  0.051768  0.123138  0.130843 -0.064560 -0.019746  0.111294  0.053843  0.067541  0.112918  0.041254 -0.022977 -0.069601  0.071077  0.087878  0.137426 -0.046726  0.156100  0.150018  0.136531  0.152002  0.063932 -0.036926  0.083589 -0.032680  0.156344 -0.037499
        -0.135392 -0.089821 -0.076282 -0.096640 -0.105308 -0.117315 -0.076161 -0.177492 -0.110290 -0.125911 -0.115644 -0.060974 -0.187727 -0.202436 -0.215421 -0.111217 -0.147172 -0.198798 -0.080632 -0.118093 -0.161668 -0.212795 -0.226950 -0.141719 -0.196630 -0.248711 -0.164841 -0.185658 -0.111595 -0.229455 -0.099748 -0.110941 -0.183863 -0.167532 -0.132311 -0.110229 -0.136713 -0.143925 -0.069385 -0.110785 -0.199817 -0.179168 -0.056853 -0.071357 -0.153845 -0.076120 -0.194487 -0.177438 -0.190571 -0.137626 -0.124470 -0.072353 -0.070571 -0.154088 -0.192052 -0.107130 -0.175553 -0.184930 -0.108482 -0.148109 -0.074208 -0.112824 -0.072390 -0.102818 -0.223707 -0.176934 -0.207022 -0.167601 -0.095786 -0.175149 -0.252841 -0.114259 -0.202522 -0.073823 -0.136586 -0.105601 -0.102217 -0.101876 -0.203401 -0.133367 -0.136589 -0.198219 -0.098891 -0.127696 -0.127677 -0.071707 -0.098744 -0.109184 -0.113743 -0.110805 -0.158029 -0.128080 -0.215628 -0.136283 -0.141807 -0.204471 -0.054080 -0.091369 -0.074668 -0.171826 -0.132947 -0.232396 -0.134853 -0.204149 -0.118015 -0.140697 -0.142787 -0.113606 -0.156872 -0.137915 -0.188720 -0.129290 -0.177074 -0.172299 -0.167778 -0.221821 -0.207445 -0.149559 -0.090521 -0.142808 -0.177622 -0.119471 -0.123039 -0.084628 -0.142719 -0.173474 -0.142076 -0.126374 -0.143333 -0.163686 -0.134178 -0.233520 -0.170744 -0.133466 -0.187994 -0.083705 -0.181787 -0.176345 -0.187849 -0.178967 -0.156553 -0.101789 -0.111232 -0.203701 -0.155633 -0.164869 -0.115781 -0.219084 -0.191784 -0.102831 -0.118963 -0.147605 -0.123343 -0.181467 -0.166068 -0.070172 -0.114251 -0.220649 -0.126124 -0.223453 -0.126859 -0.156890 -0.088537 -0.152247 -0.211344 -0.079850 -0.182316 -0.197443 -0.143198 -0.147353 -0.246611 -0.171239 -0.147388 -0.214633 -0.133044 -0.215095 -0.070757 -0.109371 -0.160566 -0.182046 -0.202590 -0.196414 -0.123245 -0.141132 -0.194025 -0.192087 -0.141170 -0.192622 -0.137953 -0.225569 -0.169285 -0.053815 -0.205017 -0.216878 -0.159788 -0.134306 -0.118201 -0.127938 -0.074415 -0.125274 -0.095761 -0.106200 -0.077340 -0.086126 -0.124356 -0.168655 -0.079589 -0.144570 -0.131234 -0.143513 -0.191356 -0.114767 -0.108252 -0.193244 -0.112360 -0.163656 -0.144292 -0.147847 -0.183178 -0.120730 -0.126796 -0.147435 -0.207509 -0.120182 -0.122166 -0.197044 -0.104918 -0.177045 -0.151487 -0.235577 -0.172078 -0.067188 -0.102848 -0.142188 -0.153003 -0.124178 -0.202401 -0.198141 -0.133420 -0.159688 -0.137793 -0.175160 -0.096688 -0.104773 -0.083955 -0.181915 -0.188754 -0.126258 -0.106412 -0.162585 -0.146535 -0.209595 -0.133098 -0.253563 -0.172615 -0.148828
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N5  = [ -1.062666 -1.139083 -1.049463 -0.898473 -0.998167 -1.060207 -1.079049 -0.632835 -1.114442 -1.097562 -1.034975 -0.424009 -1.093796 -0.463024 -0.550591 -0.643813 -1.084060 -0.560190 -0.977520 -1.099921 -1.095203 -1.064584 -0.382300 -0.432008 -1.168104 -0.130322 -1.069879 -0.565249 -0.990332 -0.211378 -1.125502 -1.024824 -1.081825 -1.071291 -0.674349 -0.615118 -1.034146 -1.012916 -1.010116 -1.131138 -0.409409 -1.083546 -0.706679 -0.932260 -1.056949 -1.037275 -0.468133 -1.079870 -0.950518 -1.011059 -0.833654 -1.076243 -1.030297 -1.073821 -1.153495 -1.110913 -1.086856 -1.072641 -1.006409 -1.094670 -1.020170 -1.002283 -1.062178 -1.124211 -0.161294 -1.077577 -0.352628 -1.069908 -1.142811 -1.107091 -0.358744 -0.938674 -0.401095 -1.026936 -1.068932 -0.874537 -1.137931 -0.994740 -1.062048 -0.545594 -1.062464 -0.541051 -1.123999 -0.503901 -1.091053 -1.079198 -1.016434 -1.120898 -1.037826 -1.114688 -1.105069 -1.006321 -0.391635 -0.030089 -1.016430 -1.058879 -0.907322 -0.966882 -1.075201 -0.730462 -1.084783 -0.668593 -1.086344 -1.014359 -1.091486 -1.019926 -0.823379 -1.004278 -0.227615 -1.017943 -0.827917 -0.705446 -1.015909 -1.073702 -0.727503 -0.544538 -1.168623 -1.035593 -0.963388 -1.080621 -0.809308 -0.588507 -0.679234 -0.798922 -1.072153 -0.282567 -1.022346 -0.703351 -1.031590 -0.318878 -0.995155 -0.211692 -1.104116 -0.760489 -0.995336 -0.801318 -0.883140 -1.080647 -0.941551 -1.088128 -1.067297 -1.015856 -1.093055 -0.370428 -1.065463 -1.068120 -1.103578 -0.164173 -1.099317 -1.021748 -1.025104 -1.060974 -1.089213 -0.676299 -1.084746 -1.009864 -0.934375 -0.140583 -0.998111 -1.162453 -0.535806 -1.042653 -0.997900 -1.042871 -0.254438 -1.019201 -1.090667 -1.105454 -1.089101 -1.071808 -0.101033 -1.028100 -1.045990 -0.342330 -0.761570 -0.554536 -1.030392 -1.117138 -1.065602 -1.097235 -0.464055 -1.016732 -1.069375 -1.094733 -0.969085 -1.166248 -1.091900 -1.116331 -0.952608 -0.087302 -0.567652 -0.808590 -0.254523 -0.685528 -1.065563 -0.438934 -1.099365 -1.097041 -1.039382 -1.089983 -0.979223 -1.090826 -0.753177 -1.070205 -0.668838 -1.064405 -0.973809 -0.970471 -1.014912 -1.099222 -1.059173 -1.092372 -1.117330 -0.826628 -1.131101 -0.863211 -1.097541 -1.034271 -1.097128 -1.049162 -0.966762 -1.061859 -1.086676 -1.048792 -1.036920 -1.085079 -1.137572 -0.843248 -0.579454 -0.413283 -1.122792 -1.030279 -0.872577 -0.953178 -1.065794 -0.997543 -1.153098 -1.068948 -0.998372 -1.110236 -1.082402 -0.480547 -1.042130 -1.017376 -0.898139 -0.673477 -0.940828 -0.587651 -0.788680 -0.090128 -1.066432 -0.788462 -1.015884 -0.176206 -0.073141 -1.056694
        -0.374898 -0.085751  0.464427  0.585845  0.344946 -0.407925  0.370716 -0.850899 -0.030582 -0.292012  0.237861  1.092190 -0.284797 -0.975078 -0.821074  0.933161 -0.299027 -0.857880  0.573644 -0.187821  0.343143 -0.372956 -0.957146 -0.978072  0.131925 -1.009751  0.508357 -0.887961  0.383174 -0.994314 -0.152202  0.297064  0.445447 -0.246398  0.949881  0.988783 -0.460218  0.357505  0.558661  0.007306 -0.937690  0.442656  0.935421  0.693474  0.323489  0.491801 -0.910443 -0.217723 -0.615121  0.377753  0.747472  0.399132  0.514210 -0.282401 -0.066497 -0.249681 -0.203016  0.451339  0.325843 -0.260740  0.498043  0.334686  0.433226  0.059944 -1.015964 -0.276286 -0.925596  0.509486 -0.025356  0.407488 -0.937524  0.565471 -0.968023  0.505713 -0.379774  0.663573 -0.075433  0.383421  0.474486 -0.960995 -0.362968 -0.941780  0.053692  1.059571  0.007239  0.369418  0.340522 -0.184530  0.253900 -0.026357 -0.196216  0.348036 -0.916335 -1.052647  0.384782 -0.441170  0.729820  0.415018  0.401482 -0.833621 -0.244193 -0.647185 -0.196708  0.540219 -0.100478  0.323475  0.651341  0.329035  0.998245  0.327911 -0.760685 -0.883517  0.607985 -0.237379  0.933713 -0.822297 -0.049467  0.374599  0.429047 -0.307124 -0.781086  0.998172 -0.902862  0.837892 -0.341941 -1.008523  0.329526 -0.885023 -0.444752  1.058543 -0.549853 -0.992964 -0.198871  0.866013  0.600734  0.835882 -0.705139 -0.213156  0.688815  0.440588  0.289244  0.346456 -0.321843 -0.944462  0.347154 -0.252192 -0.143316 -1.016682 -0.238768  0.331149 -0.481790 -0.294660 -0.211720 -0.859913 -0.250013  0.559208  0.581701 -1.011753  0.365911 -0.014329 -0.971316  0.458102  0.496422  0.503459 -0.979430  0.502248 -0.212007 -0.306012 -0.263227 -0.307370 -1.006788  0.582615  0.292046 -1.015921  0.864648 -0.818869  0.514068 -0.120106 -0.258902 -0.182147 -0.974628  0.550448  0.005058  0.042138 -0.599604  0.128826 -0.230588 -0.161226 -0.622816 -1.016367  1.046810  0.844984 -0.981699 -0.860806 -0.258060 -0.977763 -0.190367 -0.293680  0.486143  0.006110  0.410791 -0.208523  0.889748  0.411050  0.952906 -0.302040  0.623151  0.498220  0.323883 -0.107481  0.502309 -0.323588 -0.113658 -0.760549  0.010348 -0.724561 -0.023986  0.330005 -0.184250 -0.437050  0.423957 -0.291428  0.443946 -0.438086  0.243362 -0.386635 -0.098061  0.856846 -0.893255 -0.995311  0.054433  0.513938  0.664394 -0.621039 -0.272816  0.364477  0.224947  0.440154  0.373704 -0.085731 -0.336476 -0.921452  0.338934  0.346260  0.705064 -0.861539  0.689461  1.013677  0.755073  1.061520  0.205220 -0.796117  0.326653 -0.994063  1.074439 -0.326214
         0.026581 -0.118425 -0.071988  0.323196  0.325172 -0.209351 -0.022272 -0.501023  0.133110 -0.025323  0.305631 -0.039892  0.036285 -0.345201 -0.662669  0.186900  0.046365 -0.583511  0.135672  0.103714  0.081767 -0.000585 -0.532792 -0.435774 -0.229811 -0.466915 -0.105945 -0.507188  0.317868 -0.511086 -0.205948  0.297499 -0.334631  0.148502  0.061661  0.058623 -0.005596  0.288267 -0.079866 -0.007738 -0.563197 -0.329936 -0.054934 -0.026405  0.211487 -0.021465 -0.563515  0.145400 -0.307531  0.280217  0.220687 -0.087756 -0.062668  0.108135 -0.032628 -0.179175  0.135920 -0.372322  0.319309  0.052119  0.093685  0.322584 -0.106132  0.095251 -0.433377  0.104399 -0.617431 -0.108705 -0.116158 -0.128861 -0.590302  0.265358 -0.469126  0.017751 -0.030667  0.273397 -0.043696  0.308398 -0.376832 -0.315788  0.049379 -0.356723  0.099178 -0.011303  0.218930 -0.017818  0.289284 -0.018803  0.292183  0.132595  0.081846  0.307090 -0.626041 -0.403896  0.263761 -0.167383 -0.031720  0.344049 -0.090071 -0.336467  0.113120  0.364280  0.148835 -0.443269  0.188607  0.293767  0.366929  0.321802  0.361514  0.295223 -0.271993 -0.141411 -0.298002  0.148411  0.022956 -0.666625 -0.224798  0.227463  0.340964  0.051006 -0.251736  0.086986 -0.143846  0.077958  0.036436 -0.476027  0.285440 -0.138495  0.047083  0.215702 -0.055513 -0.515151  0.083534  0.118270 -0.415836  0.078880 -0.268822  0.146493 -0.423583 -0.302633  0.208287  0.286239 -0.169414 -0.579697  0.173149  0.153274  0.123703 -0.428754  0.065813  0.282733 -0.233479  0.139638  0.125707 -0.389216  0.102701 -0.080653  0.253699 -0.459825  0.313173 -0.099214 -0.288286  0.134331  0.192648  0.073804 -0.533594  0.088043  0.117994 -0.060778  0.074031  0.087784 -0.479387 -0.045290  0.256601 -0.135705  0.118691 -0.662343 -0.062855  0.080282  0.155430  0.119919 -0.345354 -0.413185  0.272829  0.209301 -0.202611 -0.265293  0.099537  0.070769 -0.188615 -0.434927 -0.056392 -0.043118 -0.527266 -0.371473  0.156208 -0.428361  0.103606 -0.027350 -0.019760  0.221333  0.322337 -0.346676  0.035590 -0.027655  0.064837  0.122500  0.002340  0.273093  0.303530  0.162777 -0.326621 -0.172949 -0.288447 -0.276517 -0.009313 -0.273402  0.195566  0.260052  0.118787 -0.198663  0.335784  0.139807 -0.279390 -0.198115  0.299109 -0.203257 -0.123039 -0.177026 -0.478225 -0.277299  0.130098 -0.059285  0.276150 -0.192849  0.143711  0.315120 -0.279609 -0.418760  0.308063  0.137965 -0.015308 -0.531890  0.225339  0.283255  0.132633 -0.389664 -0.424488  0.013353  0.295438  0.252021  0.250182 -0.138887  0.300040 -0.518123  0.221297  0.122928
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

I7  = [ -0.261487 -0.185487 -0.301586 -0.242174 -0.076907 -0.217593 -0.188216 -0.235915 -0.271617 -0.312598 -0.203308 -0.193926 -0.133039 -0.225071 -0.109464 -0.248359 -0.234685 -0.221773 -0.307690 -0.242131 -0.171427 -0.093739 -0.176340 -0.198519 -0.259068 -0.259602 -0.315064 -0.238767 -0.270918 -0.260989 -0.217597 -0.230804 -0.212213 -0.302592 -0.076258 -0.104403 -0.186364 -0.203296 -0.301887 -0.226863 -0.256930 -0.128938 -0.197224 -0.233155 -0.146985 -0.293850 -0.296292 -0.296279 -0.209587 -0.222754 -0.235804 -0.213684 -0.194019 -0.197473 -0.250916 -0.214512 -0.117409 -0.217163 -0.277538 -0.131016 -0.259865 -0.124732 -0.275446 -0.252446 -0.219744 -0.046049 -0.286215 -0.201235 -0.154476 -0.302361 -0.152251 -0.311242 -0.026260 -0.067714 -0.217684 -0.100125 -0.213549 -0.112497 -0.120992 -0.298845 -0.282830 -0.194116 -0.229150 -0.254225 -0.286210 -0.099545 -0.239778 -0.171921 -0.155437 -0.094426 -0.161687 -0.189899 -0.009147 -0.007823 -0.201805 -0.198022 -0.151257 -0.190215 -0.032618 -0.219404 -0.296063 -0.136318 -0.254223 -0.215813 -0.172435 -0.253616 -0.163460 -0.086229 -0.056420 -0.221085 -0.205139 -0.258597 -0.106373 -0.071073 -0.246546 -0.212265 -0.189548 -0.220212 -0.269592 -0.190672 -0.223998 -0.088031 -0.045037 -0.305877 -0.290553 -0.225898 -0.163135 -0.091095 -0.041610 -0.295421 -0.153915 -0.070656 -0.209418 -0.094024 -0.167425 -0.273574 -0.254430 -0.185359 -0.072569 -0.191468 -0.194390 -0.184973 -0.034435 -0.245650 -0.267043 -0.017876 -0.120839 -0.297198 -0.021413 -0.276078 -0.187510 -0.205749 -0.270289 -0.266672 -0.302525 -0.132246 -0.202573 -0.177365 -0.233127 -0.163497 -0.219084 -0.185036 -0.225002 -0.251162 -0.222429 -0.276678 -0.162466 -0.207427 -0.238008 -0.294828 -0.180778 -0.351021 -0.110371 -0.088256 -0.166563 -0.290584 -0.243459 -0.025602 -0.178382 -0.194519 -0.203065 -0.240075 -0.238443 -0.344011 -0.230715 -0.046777 -0.255359 -0.241983 -0.262106 -0.294206 -0.253619 -0.178461 -0.287720 -0.198898 -0.231966 -0.093489 -0.345520 -0.061672 -0.243245 -0.300155 -0.232205 -0.299931 -0.122826 -0.241940 -0.268491 -0.256532 -0.071038 -0.282166 -0.343054 -0.163616 -0.251414 -0.185352 -0.204095 -0.134742 -0.209643 -0.200495 -0.157601 -0.107702 -0.307272 -0.160284 -0.141733 -0.226481 -0.078433 -0.152725 -0.337627 -0.062979 -0.216893 -0.316211 -0.157405 -0.202738 -0.242117 -0.240780 -0.185649 -0.193940 -0.305615 -0.215873 -0.217692 -0.189121 -0.210582 -0.153027 -0.239751 -0.109766 -0.173278 -0.099773 -0.195432 -0.204630 -0.179444 -0.097331 -0.055830 -0.259511 -0.162943 -0.205789 -0.319602 -0.106145 -0.251231 -0.015496 -0.082757 -0.238483 -0.196685 -0.265934 -0.308137 -0.280036 -0.188815 -0.256445 -0.311737 -0.183498 -0.144389 -0.096529 -0.164993 -0.179382 -0.291687 -0.223032 -0.216154 -0.118942 -0.251709 -0.327803 -0.103974 -0.277261 -0.169068 -0.169825 -0.147606 -0.122001 -0.097059 -0.304559 -0.148631 -0.301162 -0.118477 -0.184400 -0.216186 -0.282062 -0.333472 -0.203376 -0.264156 -0.038496 -0.318971 -0.187247 -0.317171 -0.158737 -0.066394 -0.069885 -0.215728 -0.099055 -0.268609 -0.013230 -0.243548 -0.210169 -0.153979 -0.196176 -0.196728 -0.215859 -0.143108 -0.317219 -0.125946 -0.268860 -0.315154 -0.249133 -0.288775 -0.237408 -0.216715 -0.313259 -0.311534 -0.327198 -0.260274 -0.195175 -0.240621 -0.211965 -0.191754 -0.018269 -0.282531 -0.140861 -0.157330 -0.212533 -0.126258 -0.142643 -0.234461 -0.250888 -0.197935 -0.248455 -0.145265 -0.239733 -0.325825 -0.223862 -0.134576 -0.295711 -0.044889 -0.198150 -0.109515 -0.091687 -0.078223 -0.146042 -0.076324 -0.220481 -0.239212 -0.241552 -0.129403 -0.022336 -0.058116 -0.194616 -0.235636 -0.203157 -0.273843 -0.203224 -0.213900 -0.027095 -0.204287 -0.242790 -0.135100 -0.206624 -0.333007 -0.156080 -0.061271 -0.251723 -0.146525 -0.230903 -0.232150 -0.247477 -0.229278 -0.225158 -0.237688 -0.225962 -0.152729 -0.112905 -0.206476 -0.276306 -0.120151 -0.052587 -0.221721 -0.194912 -0.221370 -0.164544 -0.083363 -0.037772 -0.266678 -0.060465 -0.112442 -0.216340 -0.238989 -0.323655 -0.082934 -0.042235 -0.227704 -0.228057 -0.054100 -0.044739 -0.269906 -0.319328 -0.270797 -0.271869 -0.150728 -0.172291 -0.276701 -0.253273 -0.304262 -0.065720 -0.285460 -0.271229 -0.051136 -0.158484 -0.173722 -0.269875 -0.035356 -0.245247 -0.088505 -0.279186 -0.041034 -0.133830 -0.195244 -0.203695 -0.221430 -0.139425 -0.317304 -0.025461 -0.096094 -0.084109 -0.217008 -0.226782 -0.046388 -0.199286 -0.289607 -0.251877 -0.215531 -0.009728 -0.244853 -0.286235 -0.056848 -0.240922 -0.212147 -0.184810 -0.033940 -0.234499 -0.196983 -0.049485 -0.259674 -0.215451 -0.236853 -0.237503 -0.192815 -0.235495 -0.193377 -0.259413 -0.006468 -0.112615 -0.301014 -0.246750 -0.273149 -0.140324 -0.204783 -0.141123 -0.056628 -0.183328 -0.206021 -0.177009 -0.028504 -0.089643 -0.244055 -0.202684 -0.203040 -0.246107 -0.311254 -0.112312 -0.201903 -0.258247 -0.178042 -0.047349 -0.015763 -0.082797 -0.329869 -0.251877 -0.228523 -0.019931 -0.146958 -0.315787 -0.228342 -0.235046 -0.186904 -0.231120 -0.066718 -0.231212 -0.348661 -0.186709 -0.135535 -0.212271 -0.258081 -0.222250 -0.221693 -0.330891 -0.331177 -0.183080 -0.211059 -0.107772 -0.205434 -0.024747
         0.039899  0.171045  0.179061  0.105468  0.202038  0.027602  0.010543  0.183440  0.182260  0.012864  0.166677 -0.002230  0.172153  0.054059  0.203896  0.140974  0.051292  0.033962  0.146063  0.150936 -0.002203  0.101557  0.096968  0.159125  0.114458  0.163862  0.101559  0.164676  0.050140  0.166064  0.137519  0.042260  0.001324  0.172068  0.110442  0.203973  0.171087  0.152616  0.009351  0.010905  0.148064  0.024265  0.011014  0.025270  0.065439  0.180040  0.033436  0.076811  0.177621 -0.002609 -0.007490  0.089491 -0.003017  0.010464  0.070136  0.122784  0.165779  0.007327  0.118630 -0.012379  0.184041  0.123546  0.158462  0.007340  0.171065  0.140312  0.005220  0.005480  0.110071  0.068729  0.079829  0.132285  0.155939  0.162982 -0.001756  0.019173  0.053817  0.007735  0.011905  0.056897  0.156770  0.042686  0.122599  0.028538  0.094947  0.061557  0.079252  0.166171  0.045479  0.183819  0.033718  0.168407  0.122038  0.139367  0.029954  0.036402  0.014904  0.166872  0.145827 -0.007829  0.153169  0.196383  0.116218  0.150876  0.171996  0.006096  0.180150  0.203174  0.046574  0.089602  0.044458  0.093298  0.126140  0.005130  0.013371  0.006731 -0.001053  0.001960  0.140387 -0.001610  0.039323  0.130817  0.092066  0.011722  0.016370  0.042449  0.016511  0.190979  0.060054  0.013167  0.054226  0.174889  0.114860  0.165599  0.096130  0.096521  0.124511  0.171723  0.119384  0.050521  0.042516  0.021264  0.076894  0.175812  0.006500  0.152741  0.004981  0.177441  0.164801  0.045457  0.115102  0.084431  0.149206  0.127509  0.144092  0.192029  0.094191  0.167902  0.007546  0.115004  0.130817  0.171543  0.167092  0.037159  0.030023  0.091563  0.148631 -0.004028 -0.007323  0.015153  0.166366  0.059690  0.208306  0.165865  0.005347  0.004556  0.159195  0.117561  0.158616  0.078621  0.153185  0.101367  0.169923  0.065443  0.168984  0.198118  0.181566 -0.003279  0.183456  0.027664  0.040395  0.178004  0.181894  0.066937 -0.003072  0.190476  0.059728  0.171240 -0.001889  0.031525  0.183542  0.098355  0.140802  0.179351  0.002246  0.014690  0.159761  0.030743  0.076375  0.174467  0.039675 -0.000167  0.120449 -0.017359  0.144176  0.177464  0.190374  0.208621  0.127489  0.001675  0.143743  0.185028  0.078148  0.110153  0.125376  0.044786  0.033407  0.083719  0.106538  0.001637  0.099177  0.136532  0.042866  0.107476  0.176888  0.107883  0.044285 -0.000443  0.022668  0.022029  0.072969  0.204462  0.099193  0.003118  0.015207  0.178628  0.012233  0.008619  0.118896  0.024705  0.170805  0.043925  0.095188  0.207336  0.140773  0.109374  0.185376  0.181180  0.044714  0.186548  0.012705  0.049138  0.122577  0.032666  0.045238  0.129615  0.196630  0.002773  0.107503  0.093478  0.057603  0.031601  0.000255  0.143789  0.089103  0.162009  0.149283  0.020912  0.113547  0.040823 -0.016106  0.012531  0.164624  0.005835  0.103048  0.110560  0.136026  0.022898  0.019741  0.020215  0.126855  0.145989  0.108202  0.082026  0.076027  0.128200  0.059768  0.099840  0.120255  0.076739  0.116876  0.192296  0.104956  0.152769  0.121858 -0.005177  0.179840  0.161105  0.165073  0.101723  0.181924  0.144042  0.203808  0.044130  0.013327  0.116130  0.169672  0.019715  0.133656  0.006801  0.004283  0.163850  0.119618  0.098250  0.099034  0.124768 -0.002922  0.163995  0.003357 -0.011146  0.145861  0.009156  0.014134  0.192987  0.021876  0.027003 -0.000618  0.175189  0.028420  0.179272  0.158549  0.067581  0.185952  0.010913  0.182109 -0.003982 -0.006929  0.154203  0.201669  0.190762  0.152828  0.121855  0.097214  0.150723  0.168806  0.164481  0.197660  0.059176  0.020929  0.034574  0.038649  0.154498  0.005429  0.180027 -0.001681  0.130789  0.045830  0.116628  0.141426  0.025285  0.153858  0.153776  0.179013 -0.007375  0.169914  0.173235  0.109654  0.136464  0.170766  0.093674  0.191390  0.124298 -0.006441  0.175523  0.193756  0.202164  0.064586 -0.001188  0.025395  0.049273  0.020083  0.182344  0.096986  0.072011  0.109248  0.137762  0.013461  0.034473  0.101480  0.143850  0.179823  0.009447  0.153098  0.173237  0.063704  0.137872  0.163044  0.042240  0.167482  0.027524  0.044453  0.179981  0.169793  0.190238  0.175944  0.136431  0.203304  0.005968  0.091539  0.064899  0.070685  0.026151  0.206323  0.025793  0.066718  0.133691  0.006111  0.082844  0.020470  0.071206  0.072619  0.124664  0.064219  0.097299  0.185374  0.165723  0.070847  0.177030  0.007061  0.175805  0.085584  0.145186  0.011657  0.166428  0.068850  0.162347  0.181144  0.107446  0.100551  0.180867 -0.002428  0.060095  0.068163  0.012992 -0.003514  0.031617 -0.002677  0.094040  0.066182  0.042712  0.128327  0.204120  0.007491  0.107465  0.056601  0.155539  0.069093  0.190685  0.164720  0.171280  0.029434  0.005992  0.150723  0.171230  0.080879  0.035982  0.158278  0.022478  0.008044 -0.005143 -0.004176  0.001425  0.119288  0.077131  0.153769  0.114778  0.156533  0.101614  0.040345  0.169130  0.186621  0.103639  0.131230  0.004414  0.155870  0.018077  0.028428  0.186133  0.064054  0.022861 -0.015342  0.133768  0.036811  0.090214  0.053477  0.111127  0.098534  0.034227  0.125810  0.023440  0.020286  0.167254
        -0.457410 -0.308855 -0.415412 -0.307143 -0.375218 -0.302863 -0.386975 -0.390570 -0.421385 -0.368049 -0.398217 -0.357403 -0.394281 -0.435514 -0.336419 -0.319811 -0.298522 -0.300714 -0.345152 -0.319060 -0.331561 -0.443734 -0.408736 -0.289324 -0.463569 -0.338568 -0.333777 -0.327641 -0.467306 -0.345897 -0.430323 -0.445169 -0.319940 -0.376708 -0.463900 -0.338593 -0.313816 -0.288585 -0.383162 -0.327230 -0.446644 -0.389548 -0.296155 -0.314445 -0.405396 -0.411226 -0.324657 -0.317607 -0.395096 -0.340252 -0.406624 -0.426156 -0.351814 -0.297302 -0.305682 -0.286500 -0.408932 -0.422848 -0.461899 -0.338335 -0.421935 -0.416794 -0.349337 -0.371366 -0.339732 -0.475771 -0.397226 -0.309712 -0.391059 -0.319672 -0.404867 -0.338583 -0.475990 -0.444893 -0.331731 -0.402531 -0.418584 -0.387770 -0.385851 -0.316206 -0.350315 -0.403269 -0.441179 -0.325986 -0.319482 -0.428370 -0.455772 -0.360447 -0.389855 -0.406910 -0.386116 -0.383298 -0.470331 -0.464681 -0.290401 -0.404202 -0.373620 -0.324724 -0.476976 -0.379756 -0.349195 -0.330791 -0.319170 -0.420187 -0.262193 -0.377074 -0.291829 -0.349967 -0.423101 -0.292412 -0.410731 -0.315422 -0.427138 -0.391869 -0.349008 -0.415595 -0.354910 -0.329568 -0.334520 -0.354067 -0.298996 -0.440049 -0.456955 -0.372838 -0.356157 -0.440453 -0.377694 -0.404467 -0.423062 -0.360470 -0.395505 -0.429897 -0.270320 -0.417181 -0.402341 -0.319913 -0.455299 -0.298303 -0.463818 -0.403398 -0.403408 -0.391268 -0.436989 -0.348222 -0.386416 -0.477743 -0.375698 -0.390770 -0.462975 -0.465200 -0.414537 -0.280061 -0.446098 -0.457474 -0.343682 -0.385195 -0.269058 -0.353578 -0.341199 -0.391485 -0.294468 -0.310861 -0.331266 -0.308480 -0.303686 -0.317569 -0.376513 -0.327532 -0.402173 -0.356225 -0.355353 -0.323743 -0.368079 -0.421313 -0.358355 -0.400139 -0.435648 -0.479124 -0.377598 -0.412886 -0.405524 -0.448856 -0.334789 -0.322464 -0.421975 -0.419109 -0.392191 -0.390092 -0.396589 -0.337017 -0.306122 -0.329901 -0.402101 -0.411787 -0.365914 -0.404295 -0.323356 -0.443372 -0.387127 -0.330091 -0.392597 -0.324096 -0.412658 -0.358557 -0.408237 -0.357185 -0.443249 -0.324895 -0.325773 -0.360453 -0.454528 -0.348996 -0.423405 -0.320509 -0.291641 -0.375118 -0.339466 -0.362272 -0.336340 -0.347421 -0.394599 -0.368405 -0.438156 -0.391264 -0.349552 -0.424308 -0.426924 -0.329010 -0.392476 -0.392000 -0.306257 -0.314256 -0.398272 -0.418945 -0.399260 -0.431303 -0.424065 -0.302212 -0.416522 -0.379323 -0.456326 -0.394164 -0.405463 -0.381978 -0.289775 -0.385218 -0.378048 -0.392285 -0.475392 -0.335284 -0.362898 -0.410982 -0.334119 -0.353271 -0.448326 -0.472636 -0.411840 -0.411514 -0.405379 -0.417745 -0.355194 -0.468225 -0.412676 -0.318602 -0.320692 -0.403459 -0.359545 -0.380643 -0.396201 -0.411520 -0.312874 -0.302938 -0.413580 -0.413670 -0.467302 -0.370414 -0.419409 -0.350436 -0.396228 -0.391110 -0.319917 -0.385467 -0.416288 -0.393286 -0.397543 -0.328926 -0.416701 -0.391446 -0.427617 -0.444292 -0.349187 -0.410390 -0.466060 -0.443567 -0.327276 -0.409093 -0.322812 -0.397925 -0.468732 -0.437149 -0.432566 -0.402460 -0.322888 -0.460906 -0.450429 -0.390368 -0.265228 -0.310106 -0.337532 -0.430151 -0.377287 -0.347184 -0.379377 -0.307699 -0.366650 -0.455820 -0.436021 -0.327706 -0.431203 -0.388048 -0.398537 -0.373210 -0.323955 -0.418418 -0.450158 -0.271720 -0.340048 -0.457222 -0.408526 -0.337375 -0.380977 -0.417606 -0.382203 -0.325731 -0.320770 -0.327372 -0.318920 -0.351158 -0.383255 -0.356063 -0.365879 -0.428885 -0.385290 -0.369130 -0.436940 -0.356725 -0.350153 -0.425310 -0.382981 -0.319682 -0.441607 -0.295849 -0.448447 -0.439140 -0.399767 -0.465448 -0.391160 -0.407245 -0.439206 -0.288662 -0.459558 -0.304674 -0.417498 -0.427336 -0.319839 -0.314142 -0.405918 -0.425413 -0.355454 -0.381441 -0.462200 -0.441712 -0.374388 -0.399560 -0.334333 -0.429111 -0.440485 -0.436195 -0.335973 -0.295905 -0.338306 -0.423302 -0.367467 -0.375004 -0.395126 -0.403124 -0.426017 -0.365215 -0.434217 -0.393258 -0.406927 -0.434652 -0.319267 -0.432729 -0.427481 -0.294657 -0.339992 -0.329619 -0.456583 -0.475599 -0.402885 -0.428980 -0.467612 -0.460008 -0.304830 -0.346000 -0.439383 -0.461864 -0.375205 -0.386109 -0.309930 -0.386735 -0.371165 -0.421377 -0.376326 -0.334153 -0.414091 -0.359542 -0.406999 -0.305126 -0.429893 -0.445325 -0.368656 -0.340241 -0.426894 -0.408881 -0.299814 -0.277572 -0.432868 -0.412938 -0.325973 -0.480864 -0.430192 -0.451218 -0.393045 -0.328625 -0.430768 -0.379112 -0.390501 -0.362161 -0.288697 -0.457702 -0.350555 -0.437850 -0.430047 -0.432709 -0.369065 -0.414183 -0.467296 -0.408292 -0.366686 -0.424220 -0.306514 -0.424488 -0.382616 -0.309009 -0.349999 -0.300870 -0.408446 -0.305914 -0.467045 -0.394493 -0.388052 -0.311394 -0.472614 -0.392625 -0.280240 -0.302199 -0.457460 -0.333914 -0.407827 -0.366320 -0.476673 -0.416052 -0.461215 -0.407014 -0.274944 -0.331497 -0.384101 -0.360191 -0.367085 -0.412748 -0.402737 -0.436153 -0.471480 -0.454371 -0.365249 -0.464456 -0.442845 -0.449398 -0.289785 -0.334709 -0.439761 -0.349806 -0.390553 -0.435228 -0.416427 -0.379539 -0.322334 -0.393294 -0.327500 -0.280353 -0.454546 -0.432306 -0.428515 -0.342692 -0.337609 -0.394437 -0.266178 -0.403270 -0.299182 -0.464873
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];
N7  = [ -0.022419 -0.825145 -0.313781 -0.824344  0.230283 -0.644476  0.385209 -0.452473 -0.499567 -0.463056  0.324706  0.151226 -0.757832  0.670352 -0.010334 -0.775894 -0.507430 -0.543980 -0.411834 -0.660767 -0.424044 -0.731778  0.488331 -1.034053 -0.090558 -0.996688 -0.796924 -0.338065  0.039227 -0.843212  0.425914  0.348431 -0.545145 -0.605573 -0.713867 -0.008770 -0.837159 -1.027045 -0.274893 -0.898036 -0.175422 -0.684543 -0.987990 -0.670298 -0.615176 -0.524456 -0.482645 -0.766964  0.337470 -0.752765 -0.367447  0.340356  0.151133 -0.988240 -0.477375 -1.126460 -0.525221  0.236596 -0.125481 -0.071794 -0.372131 -0.621080 -0.568269 -0.640815 -0.013643 -0.372109 -0.320935 -0.600034 -0.030805 -0.736490 -0.537786 -0.589560 -0.199947 -0.741321 -0.717831 -0.260804  0.472139 -0.431327 -0.737650 -0.737279 -0.461866  0.326126  0.315430 -0.374285 -0.421335 -0.237627  0.631079 -0.640008 -0.214518 -0.387996 -0.019399  0.463387  0.748022  0.930064 -0.955377  0.305017  0.103111 -0.855773 -0.003004 -0.392370 -0.372201 -0.525699 -0.871296  0.436164 -0.570627 -0.587224 -0.494029  0.160892  0.193521 -0.730920  0.322322 -0.577698 -0.654683 -0.229907 -0.694330  0.486651  0.155604 -0.868955 -0.825287  0.154480 -0.579546 -0.697044 -0.093273 -0.446836 -0.098295  0.548882 -0.022796 -0.301017  0.097529 -0.113379 -0.538241 -0.655485 -1.177118 -0.560788  0.299259 -0.373894  0.016885 -0.801891 -0.730080  0.309342  0.325852  0.425585 -0.083171 -0.509105 -0.435296  0.242840 -0.470546 -0.596971  0.640408 -0.164583  0.359785 -1.017336 -0.305002 -0.141822 -0.406669 -0.842700 -1.116061 -0.599584 -0.844231  0.243491 -0.881567 -0.835831 -0.175154 -0.504332 -0.589626 -0.313421 -0.386457 -0.327005 -0.369650 -0.094245 -0.182605 -0.422685 -0.161615 -0.638286 -0.151166 -0.304019  0.166480  0.037002  0.496917  0.166306  0.358195  0.606721 -0.255010 -0.227427  0.241745  0.112999 -0.187789 -0.545574 -0.194535 -0.173681 -0.462021 -0.906328 -0.595475  0.329548 -0.682110 -0.252389 -0.417183 -0.585758 -0.621349 -0.206375 -0.448763 -0.725472 -0.594176 -0.482650 -0.401317 -0.626394 -0.778924 -0.459060 -0.208253 -0.755358  0.064260  0.081899  0.422941 -0.010730 -0.948181  0.243012 -0.400351 -0.166091 -0.483079 -0.322660 -0.827963 -0.321496 -0.178103 -0.639184 -0.443584  0.048968  0.683094 -0.528446 -0.033734  0.531165 -0.909152 -0.757414  0.257280  0.241049 -0.372978  0.325571  0.642785 -0.863472  0.685722 -0.003096  0.555428 -0.098971  0.410559 -0.125608 -1.109902  0.297465  0.209347 -0.186989 -0.524896 -0.466675 -0.712804  0.321671 -0.723141 -0.124056 -0.048161  0.421405 -0.551784  0.049836  0.330644 -0.261584 -0.300867 -0.158182  0.344270 -0.417419 -0.658426  0.545514 -0.506984 -0.122364  0.351740  0.354310 -0.700128 -0.590229  0.277733 -0.590293  0.266697 -0.352138 -0.602054 -0.245087  0.463845  0.113008 -0.299515 -0.738659 -0.430581 -0.267649 -0.857583 -0.701074 -0.593930  0.426159  0.642296 -0.224415 -0.601852  0.388752 -0.111773 -0.153661 -0.363596  0.452308 -0.444236  0.120437 -0.609565 -0.068142  0.342636 -0.257955 -0.455876  0.895946  0.247430  0.150347 -0.450639 -0.848475 -0.174219  0.341045 -0.865425 -0.859784 -0.579523 -0.530571 -0.465612  0.302862 -0.200621 -0.760396  0.411771 -0.277570 -0.259445 -0.351534 -0.724097  0.157268  0.606176 -1.205297  0.094688  0.748855 -0.330879 -0.308199 -0.618117  0.637830 -0.676951 -0.528643 -0.767142 -0.549657 -0.137666 -0.630209 -0.402890 -0.480442 -0.635308  0.467165 -0.845030 -0.184723 -0.033076  0.166714  0.001511 -0.681491  0.155778 -0.538678 -0.803877 -0.961219  0.607584  0.163952 -0.802390  0.474628  0.207851  0.302967  0.039276 -0.950116 -0.079923 -0.886738  0.485017  0.600642 -0.177157 -0.754417 -0.746813  0.347170 -0.599739 -0.006150 -0.695222  0.113224 -0.864080 -0.230990 -0.182303  0.085777  0.344018  0.282543 -0.254255 -0.700540 -0.440603 -0.661215  0.120499 -0.284462 -0.617646  0.120583  0.469305  0.235129  0.461932  0.068586 -0.280631  0.147091 -0.481930  0.091694 -0.700707 -0.901332 -0.813034 -0.463523 -0.961439 -0.348486  0.174357 -0.078622 -0.495556 -0.308586 -0.280275 -0.845478 -0.268073 -0.077949 -0.840348  0.170367 -0.530421 -0.329001 -0.625232 -0.424149 -0.363254 -0.702086  0.138002 -0.143087  0.410116 -0.280244 -0.030619 -0.085611  0.188846 -0.378759  0.058807 -0.709631 -0.956609 -1.015282  0.208029 -0.791261 -0.556007  0.055458 -0.191285 -0.460506  0.123900 -0.176935 -0.064146  0.306191 -0.318632 -0.645940 -0.725367  0.917820 -0.692637 -0.229967  0.095311  0.169018  0.123639  0.436480 -0.035553  0.091488  0.233058  0.185771 -0.279958  0.508640 -0.555551 -0.599028  0.091266 -0.762169  0.304206 -0.496957  0.805282 -0.101819 -0.274020 -0.883387  0.048980 -0.832222 -0.913010 -0.456489 -0.686803 -0.886725  0.464958  0.078783 -0.154915 -0.622970  0.425281  0.319109 -1.040562 -0.531042 -0.231318 -0.053609  0.228138 -0.370543  0.539949 -0.136860  0.578860 -0.847557 -0.525848  0.245745  0.350712  0.541076 -0.500792 -0.797647  0.303008 -0.831258  0.500243 -0.074632 -0.101692 -0.514995 -0.430721  0.423849 -0.131298 -1.169325 -0.028638  0.361800  0.603753 -0.362771 -0.306656  0.295104 -1.204391 -0.440686 -0.776845  0.472217
        -0.473627  0.939695  1.178815  0.292335  1.146247 -0.436096 -0.670421  1.130957  1.079493 -0.974177  0.596682 -0.931904  0.555308  0.235221  1.157525  0.356975 -0.144483 -0.432912  0.663005  0.525640 -0.918813 -0.106789  0.213725  0.681578  0.433942  0.758442  0.314778  0.946361 -0.459672  0.924260  0.506091 -0.165660 -0.632582  1.090712  0.400305  1.171473  0.925317  0.715343 -0.941804 -0.564748  0.553788 -0.521777 -0.413113 -0.672880 -0.237929  1.153029 -0.829197  0.228932  0.756524 -0.771790 -0.998133 -0.081472 -0.932692 -0.413664  0.351624  0.206875  0.374817 -0.593964  0.576991 -0.988540  0.964732  0.296224  0.750335 -0.867193  1.023772  0.446790 -0.971460 -0.842269  0.460308  0.209560 -0.040563  0.492358  0.483344  0.660403 -0.783756 -0.647898 -0.017885 -0.829245 -0.613610  0.146570  0.716345 -0.144155  0.121269 -0.821860  0.419357 -0.359822  0.242958  0.761450 -0.422718  0.522693 -0.349256  0.824418  0.024608  0.474845 -0.355931 -0.175410 -0.640098  0.913161  0.509597 -0.992741  0.693665  1.110591  0.248385  0.523732  1.071063 -0.887176  1.113168  1.153479 -0.200110  0.224934 -0.156334  0.402256  0.356549 -0.888810 -0.789648 -0.529159 -0.930727 -0.623954  0.394199 -0.931285 -0.329296  0.525916 -0.692944 -0.974781 -0.895321  0.044504 -0.623263  0.699943 -0.319121 -0.912965 -0.435201  0.697851 -0.109505  0.732191  0.388134  0.525726  0.472289  0.951925  0.355898 -0.140454 -0.144324 -0.336496 -0.717534  1.093544 -0.907397  0.720237 -0.785599  1.116007  0.874857 -0.560472  0.329619 -0.036513  0.596294  0.546333  0.661035  0.475120 -0.172326  0.956759 -0.661004  0.438608  0.329653  0.925773  0.979564 -0.708863 -0.462945  0.524741  0.673520 -0.992661 -0.997967 -0.843146  1.149768 -0.179740  1.206393  0.684016 -0.943300 -0.982453  0.598081 -0.235146  0.778889 -0.193243  0.556115  0.243080  1.046602  0.007697  0.771446  0.835520  1.134983 -0.930024  1.136872 -0.811944 -0.586703  0.846176  1.130525 -0.119734 -0.878051  0.589872 -0.179702  0.876613 -0.890361 -0.725830  1.131058  0.343953  0.476770  1.116870 -0.987539 -0.838671  0.565671 -0.838780  0.394330  0.635515 -0.352831 -0.958065  0.271877 -0.980483  0.761071  1.056122  1.138059  1.205775  0.427947 -0.915438  0.413443  1.155336 -0.506121  0.280096  0.547382 -0.256501  0.207707  0.416035  0.456775 -0.528414  0.177778  0.321898 -0.187216  0.161608  1.149929 -0.032567  0.166388 -0.723605  0.085883 -0.452130  0.127680  1.121828  0.219948 -0.908503 -0.246859  1.038891 -0.617736 -0.819903  0.229550 -0.893009  0.589864 -0.156866  0.378834  1.195396  0.489987 -0.372726  0.719344  1.120446 -0.147026  1.126158 -0.938406 -0.525957  0.438222 -0.824312 -0.273752  0.547410  1.127683 -0.908849  0.528469  0.014708  0.042798 -0.461366 -0.721064  0.479758  0.189567  0.899383  0.509304 -0.876268  0.461934 -0.324134 -0.925307 -0.612984  0.795674 -0.964378  0.556701  0.396017  0.409238 -0.334862 -0.032264 -0.718652  0.514872  0.617014  0.468492 -0.715519  0.379289  0.525974  0.251170  0.716127  0.222590 -0.553574  0.062407  0.591692  0.446160  0.546226  0.267750 -0.909196  1.118816  0.912656  1.148661 -0.057040  0.510960  0.572526  1.072431 -0.526468 -0.973714  0.344742  0.772344 -0.691639  0.403992 -0.962118 -0.982958  0.901224  0.318415 -0.015812  0.240747  0.105134 -0.959389  0.738655 -0.994940 -0.952892  0.515558 -0.160043 -0.576197  1.107803 -0.714057 -0.810640 -0.918956  1.081559 -0.541696  1.116791  0.872993 -0.025401  0.469044 -0.963504  1.024894 -0.930958 -0.966739  0.526069  1.173734  1.103243  0.523671  0.162364  0.238927  0.576463  0.425748  0.890588  1.108430 -0.155865 -0.527322 -0.400499 -0.541011  0.872291 -0.530461  0.909168 -0.792136  0.319972 -0.545181  0.105524  0.573116 -0.448873  0.497845  0.619446  0.419933 -1.007359  0.982386  0.747135  0.026684  0.432569  1.047445  0.243114  1.132914  0.354706 -0.950907  1.070088  0.471639  1.094803 -0.028396 -0.896997 -0.066345 -0.321981 -0.568248  1.025480  0.464510 -0.443886  0.305813  0.546538 -0.710710 -0.531028 -0.151048  0.466909  1.034814 -0.640496  0.478302  1.058960  0.381559  0.505925  0.624780 -0.537420  0.618910 -0.356304 -0.484906  1.142087  1.037797  0.876084  1.077347  0.434576  1.176427 -0.942679  0.212294  0.382753 -0.645470 -0.572797  1.165579 -0.908208 -0.475021  0.427536 -0.577251 -0.038099 -0.306254 -0.018609  0.320598  0.002262 -0.349152 -0.554625  1.095153  0.978195 -0.620666  1.027456 -0.965063  1.076402  0.220915  0.487717 -0.791361  0.668860 -0.447047  0.601233  1.059300  0.265879 -0.574432  1.105237 -0.898237 -0.227602  0.390439 -0.350603 -0.942981 -0.718438 -0.959060  0.169799 -0.148860 -0.577610  0.121210  1.121486 -0.943664  0.255039 -0.413699  0.382386  0.024205  1.127711  0.651018  0.857522 -0.080102 -0.926231  0.304171  0.606733  0.073524 -0.168286  0.665443 -0.774169 -0.930011 -0.945995 -0.899984 -0.944161  0.435728 -0.679682  0.908022  0.278240  0.791899  0.363301 -0.167576  0.930275  1.111829  0.316858  0.273781 -0.724076  0.544760 -0.560371 -0.420935  1.144809 -0.035218 -0.334899 -0.979468  0.416838 -0.442446 -0.065979  0.179113  0.495197  0.531494 -0.231761  0.106177 -0.493020 -0.431781  0.893361
        -1.281507 -0.304959 -0.433905  0.484159 -0.493971  0.473510 -0.842468 -0.625763 -0.799554 -0.312263 -1.130539 -0.486147 -1.074594 -0.842204 -0.052228  0.501804  0.643434  0.522822  0.504509  0.508189 -0.641417 -1.185015 -1.146692 -0.459401 -1.396058 -0.017352  0.516134  0.288077 -1.269740 -0.052376 -1.101179 -1.233367  0.378143 -0.123144 -1.177646 -0.104505 -0.226624 -0.357701 -0.075630  0.139834 -1.356998 -1.016559  0.145212  0.252558 -1.235314 -0.421828  0.145594  0.551481 -0.999746  0.016746 -0.442622 -1.240902 -0.480559  0.144065  0.626778  0.115095 -1.297747 -1.080535 -1.337560 -0.547146 -1.036685 -1.267571  0.401623 -0.080915  0.140282 -1.370062 -0.185350  0.039975 -1.319519  0.570102 -1.319672  0.551859 -1.404774 -0.991543  0.040197 -1.129991 -1.142940 -0.832531 -0.863830  0.578073  0.458895 -1.236599 -1.279886  0.186273  0.616733 -1.324681 -0.919248 -1.013544 -1.271502 -1.300767 -1.298851 -0.761274 -1.116243 -0.553128  0.241785 -1.242109 -1.085146 -0.334000 -1.407994 -0.385417  0.488700 -0.218515  0.456557 -1.080418 -0.080196 -0.075793 -0.149695 -0.160621 -1.359411  0.557149 -1.236242  0.580524 -1.231046 -0.810968  0.044249 -0.889237 -0.483654  0.103287  0.457176 -0.482811  0.559902 -1.127799 -1.074557 -0.289514  0.006963 -1.072680 -1.133336 -1.239266 -1.337866 -0.030104 -1.178292 -1.049966 -0.155346 -1.096228 -1.237170  0.577706 -1.352761 -0.404007 -1.179178 -1.247624 -1.236738 -1.097827 -1.042389 -0.050968 -0.016978 -1.258752 -0.878380 -0.219804 -0.703417 -1.252866 -1.223518  0.291514 -1.339914 -1.356917  0.505979 -1.029489  0.038365 -0.800162  0.082585 -1.245676  0.427737 -0.223669  0.249599  0.307439  0.485079  0.582990 -1.197682 -0.236404 -0.438171  0.116098 -0.536781  0.644522 -0.402674 -1.076284 -0.674317 -0.240036 -1.235228 -1.412762 -0.776636 -1.305016 -1.128458 -0.961548  0.146002  0.669036 -1.065265 -1.172893 -0.098199 -0.168785 -0.102597  0.192635  0.444422 -0.484025 -0.328715 -1.239978 -0.187638 -1.307198  0.644909 -0.920639 -0.127022  0.316144 -0.627791  0.546878 -1.228105 -0.107324 -0.460026  0.010207 -1.021292  0.136230  0.612701 -1.021721 -1.318409 -0.453919 -1.187535 -0.559282 -0.019608 -0.198312 -0.132181 -0.314579  0.601113 -0.711478 -1.070136 -0.145973 -1.243572 -1.248280  0.550828 -1.371247 -0.826477  0.589969 -1.320937 -0.816774  0.434612  0.521644 -1.264803 -1.317753 -0.178688 -1.260226 -0.918706 -0.152922 -0.855432 -1.246902 -1.060229 -0.792062 -1.208303 -0.792196  0.018551 -0.473803 -1.050343 -0.945017 -1.351596  0.003660 -1.085423 -1.236492  0.535766 -0.200248 -1.363100 -1.232042 -1.115325 -0.597661 -1.233122 -0.759965 -0.046431 -1.277185 -1.197653  0.170966  0.561381 -0.945665 -0.318727 -0.790861 -1.141705 -1.253522  0.599790  0.485827 -0.899147 -1.229117 -1.316514  0.304632 -1.208269  0.090057 -1.087638 -1.278134 -0.707572 -0.863446 -1.116672 -0.153858 -0.937530  0.542042 -1.252942 -1.098005 -0.937816 -1.115674  0.532524 -1.064240 -1.386370 -1.035732  0.624585 -1.066927  0.650440 -1.134303 -1.302094 -1.213488 -1.260372 -1.305363  0.598259 -0.597254 -1.309298 -0.620103 -0.091110 -0.211726 -0.158510 -1.245413 -0.985558  0.375329 -0.578779  0.470714 -0.310864 -1.257717 -1.229126  0.141824 -1.160534 -0.143257 -0.248064  0.301835  0.539381 -1.347274 -0.962851 -0.158116 -0.395921 -0.742330 -0.441158 -0.629116 -1.187823 -0.915858 -0.972327 -0.206930  0.097148  0.129893  0.072262 -0.170169 -1.163382 -0.104831  0.261648 -1.145709 -1.029583 -0.173701 -0.975060 -0.443851 -0.607910 -1.142142 -0.401208 -0.204727 -1.018791  0.374723 -0.961140 -1.248035 -1.093359 -0.940628 -0.075313 -1.247583 -1.229045  0.214095 -1.251005 -0.172075 -0.891140 -0.699917  0.292080  0.523979 -0.931763 -1.257992  0.506229 -1.249021 -1.154860 -1.247916 -1.027896 -0.393825  0.246531 -1.177162 -1.255622 -1.245245  0.144817  0.571529 -0.163201 -1.227210 -0.400202  0.071860 -1.216880  0.013060 -1.142841 -0.477426 -1.158566 -1.292047 -1.191116 -0.939575  0.585494 -1.275758 -1.211896  0.308409  0.042172  0.483182 -0.862116 -1.371055 -0.730509 -1.174126 -1.303889 -0.841950  0.643253  0.420619 -1.326396 -1.253311 -0.941454 -1.243583  0.499641 -0.124785  0.007712 -1.054737  0.049609  0.517593 -0.545468 -0.675504 -1.209839  0.642957 -1.127819 -1.230040 -0.314765  0.002873 -1.261490 -1.171842 -0.016950  0.294004 -1.274781 -1.165961  0.612924 -1.470040 -1.335766 -1.109489 -0.629866  0.252240 -1.152913 -0.524950 -0.157834 -0.178751  0.560864 -0.607129  0.042702 -1.300634 -1.273077 -1.232290 -0.028344 -1.181580 -1.205128 -0.606466 -0.478896 -1.352598  0.639914 -1.010570 -0.256787  0.244811 -0.418040  0.545815 -1.248784  0.441597 -1.051006 -0.792390 -0.080520  0.445518 -1.294230 -1.078057  0.424316 -0.152109 -1.062764 -0.519131 -1.141168 -0.622310 -1.456711 -1.141240 -1.204137 -1.235269 -0.478270  0.201575 -0.046962 -0.693885 -0.479295 -0.718128 -1.022700 -1.083627 -0.749916 -1.077606  0.381679 -1.291433 -1.231043 -0.774865 -0.152702  0.515202 -1.274834 -0.012412 -1.004225 -1.235796 -1.309091 -0.359317  0.669337 -1.099853 -0.592913 -0.217753 -1.301699 -1.228854 -0.978837  0.580061  0.563470 -1.231450 -0.152574 -1.192217  0.385744 -0.940052
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000];

%%% Ordered transformation matrices
%Root Node
% Global rotation operator
w1a = [-0.912693 -0.242616 0.328830]';
q1a = [0.0, 0.0, 0.0]';
t1b = twist_matrix_fast(w1a,q1a,sp_coords(4));

% Global translation operator
t1a = twist_matrix_fast(sp_coords(1:3),0,0);

w1c = [0.694923 0.400725 -0.597078]';
q1c = [0.169369 -0.120422 0.403550]';
t1c = twist_matrix_fast(w1c,q1c,Theta(1));

w1d = [-0.701444 0.194972 -0.685538]';
q1d = [0.169369 -0.120422 0.403550]';
t1d = twist_matrix_fast(w1d,q1d,Theta(2));

w1e = [-0.158299 0.895212 0.416577]';
q1e = [0.169369 -0.120422 0.403550]';
t1e = twist_matrix_fast(w1e,q1e,Theta(3));

w4a = [-0.046038 0.947452 0.316569]';
q4a = [-0.040882 -0.061981 0.198067]';
t4a = twist_matrix_fast(w4a,q4a,Theta(4));

w4b = [-0.101153 0.310854 -0.945060]';
q4b = [-0.040882 -0.061981 0.198067]';
t4b = twist_matrix_fast(w4b,q4b,Theta(5));

w4c = [0.993805 0.075530 -0.081527]';
q4c = [-0.040882 -0.061981 0.198067]';
t4c = twist_matrix_fast(w4c,q4c,Theta(6));

w5a = [-0.188680 0.926698 0.325010]';
q5a = [-0.071158 0.031062 -0.084801]';
t5a = twist_matrix_fast(w5a,q5a,Theta(7));

w5b = [-0.303941 0.259598 -0.916640]';
q5b = [-0.071158 0.031062 -0.084801]';
t5b = twist_matrix_fast(w5b,q5b,Theta(8));

w5c = [0.933820 0.271735 -0.232680]';
q5c = [-0.071158 0.031062 -0.084801]';
t5c = twist_matrix_fast(w5c,q5c,Theta(9));

w6a = [-0.108259 0.946515 0.303956]';
q6a = [-0.126571 0.078390 -0.251917]';
t6a = twist_matrix_fast(w6a,q6a,Theta(10));

w6b = [-0.747570 0.124034 -0.652499]';
q6b = [-0.126571 0.078390 -0.251917]';
t6b = twist_matrix_fast(w6b,q6b,Theta(11));

w6c = [0.655301 0.297867 -0.694158]';
q6c = [-0.126571 0.078390 -0.251917]';
t6c = twist_matrix_fast(w6c,q6c,Theta(12));

w7a = [-0.032446 0.964371 0.262556]';
q7a = [-0.182555 0.087679 -0.300782]';
t7a = twist_matrix_fast(w7a,q7a,Theta(13));

w7b = [0.665775 0.216782 -0.713967]';
q7b = [-0.182555 0.087679 -0.300782]';
t7b = twist_matrix_fast(w7b,q7b,Theta(14));

w7c = [0.745447 -0.151638 0.649088]';
q7c = [-0.182555 0.087679 -0.300782]';
t7c = twist_matrix_fast(w7c,q7c,Theta(15));

%%% Construct kinematic chains of transformations
% Generate new_config and new_norms
U1 = t1a*t1b*t1c*t1d*t1e*I1;
V1 = t1a*t1b*t1c*t1d*t1e*N1;
V1 = V1-U1;

U4 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*I4;
V4 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*N4;
V4 = V4-U4;

U5 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*I5;
V5 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*N5;
V5 = V5-U5;

U7 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*I7;
V7 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*N7;
V7 = V7-U7;

%%% Construct complete update
new_config = [U1(1:3,:) U4(1:3,:) U5(1:3,:) U7(1:3,:)];
new_norms  = [V1(1:3,:) V4(1:3,:) V5(1:3,:) V7(1:3,:)];

% Update center of mass estimate
new_ctrm = mean(new_config,2);

%%% Twist matrix function
function [twist] = twist_matrix_fast(w,q,theta)
% Overview:
% This code generates an exponential map matrix for rotation and translation
% using the Rodrigues' formula for the matrix exponential, from "A Mathematical 
% Introduction to Robotic Manipulation" by Murray, Li, and Sastry (1994) p. 28. 
% The equation for the exponential map for twists is from Ibid. 42.
%
% This code has very little error checking to increase speed.
%
% [twist] = twist_matrix_fast(w,q,theta)
% INPUTS %
% w: a 3d vector pointing: 1) in the direction of translation or 2) 
%      along the axis of rotation relative to the origin.
% q: a 3d point along the axis of rotation, providing the offset
% theta: the amount of rotation, in radians
%
% OUTPUTS %
% twist: the resulting matrix for left multiplication
%
% I treat 2 cases: 1) pure translation and 2) pure rotation
if numel(q) < 3 && (q == 0 || theta == 0)
    
    % we want column vectors
    if size(w,1)<size(w,2)
        w = w';
    end
    
    % 1) pure translation
	% pure translation in absolute frame
	twist = [eye(3) w;zeros(1,3) 1];
else
    % 2) pure rotation twist
    % correct for case where w is the origin
    if sum(w) == 0
        w = q;
        W = 0;
    else
        W = 1;
    end
    
    % Generate cross product operator so(3)
    w_hat = [0   -w(3) w(2);
             w(3) 0   -w(1);
            -w(2) w(1) 0];
    
    v = -w_hat*q;
    % Generate rotation matrix using the Rodrigues' equation pg. 28
    Id3x3  = eye(3);
    w_hat2 = w*w'-W*Id3x3;
    R      = Id3x3+w_hat*sin(theta)+w_hat2*(1-cos(theta));
    
    % Generate relative frame twist, pg. 42
    twist  = [R (Id3x3-R)*w_hat*v+w*w'*v*theta;
              zeros(1,3) 1];
end
