function [new_config, new_ctrm, new_norms]  = gatsby140_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  = [ -0.055008 -0.028084 -0.070220 -0.012380 -0.054343 -0.059262 -0.090405 -0.034594 -0.037617 -0.036654 -0.003259 -0.017769  0.029138  0.017293 -0.045738 -0.073499 -0.052840 -0.052306 -0.084917 -0.035207 -0.074864 -0.010552  0.030665  0.044385 -0.051022  0.043163 -0.065902 -0.013440  0.018025 -0.035052  0.040741 -0.086609  0.001324 -0.005151  0.006042 -0.039754 -0.047545 -0.052421 -0.024706  0.023779 -0.027956 -0.052111 -0.083853  0.028489 -0.006345  0.011438 -0.041355 -0.042244 -0.051616  0.006076 -0.050326  0.014027 -0.020838 -0.038904 -0.027118 -0.066177 -0.052129  0.033449 -0.006940 -0.023986 -0.073097 -0.085488 -0.008693 -0.083968 -0.004942 -0.072379 -0.055934 -0.041714 -0.026552 -0.054662  0.030746  0.002956 -0.014060 -0.065065  0.007798  0.039164 -0.023678 -0.009723 -0.022970 -0.041762 -0.014427 -0.000458  0.053179  0.036946 -0.019481 -0.029470 -0.010801 -0.025480 -0.036892 -0.031542  0.029276  0.032805 -0.073090 -0.031595 -0.083566 -0.075978  0.033801 -0.028518  0.046235 -0.050698 -0.086458 -0.038299  0.048227 -0.040605  0.007173  0.039803  0.028592 -0.077604 -0.052181 -0.051737 -0.056449  0.013043 -0.081286  0.035268 -0.037327 -0.024276 -0.038390 -0.025604  0.030198 -0.076396 -0.015803 -0.076515  0.016844 -0.029615 -0.066203 -0.041830 -0.068855 -0.060891  0.019057  0.005794 -0.046811 -0.015806 -0.030478 -0.021409 -0.050316 -0.088535  0.009767 -0.003906 -0.054782 -0.056762  0.027514 -0.038287 -0.030502  0.040357 -0.023073 -0.029683 -0.070719 -0.079831 -0.086350 -0.073344 -0.028235  0.002566 -0.073693 -0.023108 -0.048512 -0.086244 -0.017959 -0.024325 -0.079797  0.032543 -0.001297 -0.060939  0.010718  0.026999  0.010825 -0.026668 -0.014376  0.030554  0.029171 -0.012615 -0.009441 -0.007501 -0.032428 -0.047304 -0.060566 -0.054648  0.012456 -0.026960 -0.067587 -0.045883 -0.031064 -0.005071  0.026121 -0.007887  0.012199 -0.077759  0.028970 -0.048964 -0.084606  0.012101 -0.015523 -0.075170  0.009019 -0.083504 -0.021870 -0.044826  0.010347 -0.049432 -0.068343  0.003390  0.025444 -0.075093  0.043154 -0.051620 -0.077299 -0.034830 -0.003806 -0.060777 -0.048823 -0.088038 -0.006800  0.048210 -0.076468  0.003416  0.038839  0.027874  0.017152 -0.038416 -0.047944 -0.006562  0.022738 -0.001985 -0.062790  0.009804  0.010997  0.002019 -0.062946 -0.048907 -0.036501 -0.010981 -0.088564  0.001890  0.042015  0.014213 -0.039797 -0.076029 -0.047287  0.007599 -0.036744  0.043932 -0.061448  0.028465  0.048735  0.007410 -0.061437  0.014648 -0.050929 -0.076906 -0.081680 -0.020142 -0.051765 -0.034880 -0.014096 -0.052914 -0.034405 -0.082221
         0.081653  0.129704  0.095949 -0.066246  0.023394  0.015877  0.011139  0.124936 -0.072727  0.061875  0.126036 -0.004143 -0.070444 -0.077449  0.020741  0.030134 -0.062775  0.101910 -0.000824 -0.010138  0.050052  0.105332 -0.067510  0.137089 -0.061258  0.129911 -0.042921  0.109623  0.092427  0.029711  0.119338  0.046618  0.135579 -0.071783 -0.033592  0.099490 -0.025015  0.032685  0.121549  0.143874  0.088389  0.021338  0.037329  0.101711  0.096473  0.092352 -0.011543  0.048644  0.009605 -0.031886 -0.032602  0.117421  0.119963 -0.082151  0.126498  0.093556  0.087454  0.127593 -0.095095 -0.067392  0.067908 -0.007596  0.133134 -0.002948  0.130166 -0.038517  0.037703  0.030191 -0.091049 -0.010818 -0.025436  0.130500  0.065801  0.044763  0.136603 -0.056933  0.131146 -0.061369  0.049968  0.102129 -0.081908  0.135489  0.146543 -0.090550  0.111954 -0.079451  0.106804 -0.021411 -0.072164  0.122799 -0.064016  0.138175  0.071205  0.042090  0.056650  0.063812 -0.070355  0.128340  0.108644  0.094467  0.039895  0.055332  0.137073  0.122421  0.136595 -0.030211  0.141170 -0.000865 -0.034469  0.114714 -0.009375  0.135427 -0.008527 -0.088567 -0.064847 -0.005389  0.007049  0.025157 -0.066877 -0.009496  0.131447  0.033221  0.126716  0.010926  0.086134  0.117024  0.005735  0.086452  0.138317 -0.092592  0.089055  0.043890  0.113186  0.079131 -0.018039  0.027696  0.113627 -0.070946  0.010188  0.087675  0.102148  0.068339  0.115214  0.135847  0.020415  0.112042 -0.013652  0.014429  0.031297  0.013730 -0.055435  0.134926  0.018681  0.127249  0.095192  0.040700 -0.039913  0.113363 -0.023871 -0.090023  0.106390 -0.037671 -0.091435  0.145113  0.136535  0.118675 -0.003863  0.137828  0.118945  0.067461  0.122806  0.131624  0.013161  0.108834  0.101290 -0.037055 -0.042474  0.127788 -0.018891 -0.026959  0.123895 -0.048909  0.105157 -0.095692  0.140040  0.043832  0.109667 -0.066534  0.059345  0.135963 -0.044560  0.086108  0.138929  0.050272  0.120043  0.105584 -0.077220 -0.027571 -0.029781  0.091115  0.138674  0.060199  0.145423  0.095421  0.078389  0.113108  0.134074  0.071593  0.020314  0.040096  0.112227  0.137360 -0.019163 -0.059253 -0.057090  0.141000  0.110077 -0.083043 -0.001277 -0.078093 -0.082755 -0.028920 -0.021118 -0.061355 -0.091151  0.090165  0.092432  0.117620  0.098740 -0.028106  0.031701  0.004840  0.137340  0.137890  0.062307  0.016592  0.010820 -0.076127 -0.010335  0.143542  0.074173 -0.078726  0.145468  0.136145 -0.046579  0.113050 -0.072021  0.077596  0.035032  0.075330  0.000013  0.067521 -0.064616  0.000684  0.082799  0.061000
        -0.299251 -0.206033 -0.221491 -0.301114 -0.294477 -0.285586 -0.203734 -0.232518 -0.254063 -0.326210 -0.304198 -0.346571 -0.295334 -0.277767 -0.311816 -0.255734 -0.239615 -0.256638 -0.220302 -0.328070 -0.250751 -0.330884 -0.302749 -0.303205 -0.248172 -0.324632 -0.238757 -0.320921 -0.359525 -0.331964 -0.338354 -0.219845 -0.248224 -0.290337 -0.350318 -0.302317 -0.294383 -0.297233 -0.262104 -0.203619 -0.335710 -0.299128 -0.230563 -0.354973 -0.344262 -0.356621 -0.317786 -0.315650 -0.301434 -0.351069 -0.278962 -0.335098 -0.287636 -0.225951 -0.190985 -0.241332 -0.303101 -0.327821 -0.228248 -0.288091 -0.254555 -0.203933 -0.259108 -0.222141 -0.295597 -0.229615 -0.289709 -0.318717 -0.222771 -0.294910 -0.370673 -0.303589 -0.360717 -0.270830 -0.210350 -0.327735 -0.233514 -0.313587 -0.352660 -0.281328 -0.258736 -0.250319 -0.249831 -0.231986 -0.307495 -0.249607 -0.328516 -0.330761 -0.256926 -0.244384 -0.311967 -0.274352 -0.254365 -0.337398 -0.225260 -0.247340 -0.294465 -0.198909 -0.348779 -0.289805 -0.202119 -0.322824 -0.296898 -0.207960 -0.274798 -0.370101 -0.234919 -0.249022 -0.273841 -0.218172 -0.292229 -0.305984 -0.232122 -0.244106 -0.270655 -0.340824 -0.327595 -0.348737 -0.304571 -0.252655 -0.250483 -0.249277 -0.323203 -0.342084 -0.264196 -0.238045 -0.267732 -0.280448 -0.302338 -0.225127 -0.310719 -0.364764 -0.277354 -0.353203 -0.297379 -0.211180 -0.336074 -0.292622 -0.295099 -0.289903 -0.354327 -0.324554 -0.270290 -0.316239 -0.353205 -0.284116 -0.263818 -0.243046 -0.222428 -0.257754 -0.300211 -0.229087 -0.256487 -0.249283 -0.295199 -0.201036 -0.327519 -0.296590 -0.225404 -0.212918 -0.336086 -0.255293 -0.223999 -0.190055 -0.222267 -0.268149 -0.349088 -0.271880 -0.339514 -0.361557 -0.302725 -0.285914 -0.337996 -0.193129 -0.240293 -0.266443 -0.349208 -0.194765 -0.265867 -0.294893 -0.242660 -0.332910 -0.351524 -0.218054 -0.197388 -0.245209 -0.348108 -0.242422 -0.203827 -0.237954 -0.327018 -0.224952 -0.196408 -0.229404 -0.283799 -0.262814 -0.277795 -0.287759 -0.251438 -0.354501 -0.295522 -0.249738 -0.222591 -0.281102 -0.227868 -0.264888 -0.202354 -0.282623 -0.305755 -0.215956 -0.323582 -0.295819 -0.247137 -0.322965 -0.327921 -0.234484 -0.343755 -0.223208 -0.309199 -0.272676 -0.264418 -0.346452 -0.272769 -0.318573 -0.239209 -0.354623 -0.193846 -0.214241 -0.312201 -0.339746 -0.203768 -0.363500 -0.304668 -0.298844 -0.320551 -0.251849 -0.309866 -0.280381 -0.326157 -0.264310 -0.282467 -0.274465 -0.258645 -0.213992 -0.243864 -0.339866 -0.213385 -0.231108 -0.237506 -0.353357 -0.301873 -0.330330 -0.303965 -0.299699 -0.332446 -0.228195
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  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  = [ -0.970544 -0.425935 -0.893207 -0.281580 -0.945823 -0.950746 -1.089724 -0.576890 -0.589151 -0.922950 -0.507012 -0.576177  0.166239 -0.003734 -0.937234 -0.968321 -0.803683 -0.660959 -1.028385 -0.803811 -0.974691 -0.442079  0.225418  0.260157 -0.841077  0.153770 -0.867368 -0.496070 -0.291817 -0.925130  0.205408 -1.056563 -0.057278 -0.078262 -0.527457 -0.554036 -0.796202 -0.943899 -0.649065 -0.308357 -0.596528 -0.943591 -1.035881 -0.197498 -0.366365 -0.277403 -0.874666 -0.932147 -0.942205 -0.527423 -0.799581 -0.400429 -0.647451 -0.614739 -0.598907 -0.845797 -0.900527  0.001137 -0.060599 -0.626572 -1.015165 -0.995091 -0.404971 -1.027436 -0.521632 -0.906229 -0.947430 -0.933213 -0.434700 -0.884108 -0.392943 -0.510474 -0.785676 -0.957120 -0.274576  0.348428 -0.461910 -0.382574 -0.891161 -0.605514 -0.209573 -0.103333  0.201768  0.168095 -0.604299 -0.456816 -0.437654 -0.647727 -0.652029 -0.638487  0.078637 -0.140952 -1.015158 -0.918711 -1.051899 -1.006635  0.170902 -0.488426  0.492374 -0.692202 -1.055938 -0.923937  0.042516 -0.680952 -0.120882 -0.064478 -0.163203 -1.036253 -0.846013 -0.758151 -0.934617 -0.334167 -1.062779  0.202943 -0.740572 -0.619496 -0.918501 -0.855178  0.224951 -1.012431 -0.450873 -0.976780 -0.418998 -0.855459 -0.867139 -0.638848 -0.962958 -0.859564 -0.182027  0.249819 -0.800412 -0.824653 -0.703287 -0.379261 -0.797965 -1.078111 -0.435321 -0.045805 -0.946266 -0.813052 -0.198473 -0.893399 -0.655480  0.286368 -0.815488 -0.743219 -0.930983 -1.014544 -1.069202 -0.973379 -0.815169 -0.060042 -0.969983 -0.591769 -0.646269 -1.079872 -0.708986 -0.692130 -1.043341  0.141587 -0.418091 -0.825866  0.131240 -0.068465 -0.262436 -0.633598 -0.572785 -0.143203 -0.031890 -0.689024 -0.542081 -0.542138 -0.858271 -0.692516 -0.755437 -0.797203 -0.382761 -0.486868 -0.864883 -0.794539 -0.604004 -0.457129 -0.226031  0.145375 -0.350333 -0.983112 -0.111211 -0.753022 -1.076661 -0.143937 -0.657460 -0.963292 -0.353513 -1.027860 -0.692321 -0.678380 -0.021616 -0.782674 -0.842509 -0.316060  0.031647 -0.997197  0.068274 -0.629629 -0.992843 -0.615488 -0.194782 -0.940877 -0.940306 -1.074813 -0.502580  0.042499 -0.989149 -0.110763  0.348103 -0.163088 -0.303709 -0.669497 -0.926644 -0.118388  0.004559 -0.570130 -0.919902 -0.018783  0.120611 -0.352436 -0.725155 -0.700866 -0.595324 -0.607692 -1.072201 -0.496565  0.257787 -0.209157 -0.912002 -0.986973 -0.938744 -0.029981 -0.805348 -0.210623 -0.941548  0.074434 -0.132049 -0.233273 -0.855179 -0.373828 -0.811591 -0.991524 -1.001679 -0.434630 -0.941289 -0.900488 -0.417171 -0.942439 -0.769531 -1.045306
         0.063696  1.034865  0.658871 -0.943837  0.074243  0.066725  0.047631  0.928533 -0.851395  0.024277  0.896240 -0.372844 -0.982881 -1.009776  0.071631  0.079813 -0.668457  0.833719 -0.271730 -0.288702  0.080080  0.794821 -0.989340  1.113467 -0.593183  0.874978 -0.541714  0.880382  0.781412  0.076255  0.955666  0.214859  1.133614 -1.000645 -0.421646  0.934067 -0.535260  0.083548  0.863395  1.080171  0.678867  0.072187  0.121532  0.698942  0.818148  0.750694 -0.347911  0.088293  0.054750 -0.419941 -0.559243  0.824275  0.868604 -0.864628  0.893427  0.669109  0.441003  0.851591 -1.063428 -0.751743  0.114064 -0.393003  1.042462 -0.273855  0.839039 -0.516908  0.088567  0.081078 -0.956267 -0.271653 -0.501922  0.882229  0.355559  0.093848  1.091624 -0.954182  1.011138 -0.837081  0.148760  0.918238 -0.991057  1.130158  1.126944 -1.065874  0.825213 -0.926240  0.847831 -0.428675 -0.783592  0.849647 -0.997852  1.122094  0.117362  0.093292  0.240272  0.117281 -0.982792  0.975658  0.800998  0.842947  0.211814  0.053947  1.049251  0.879236  1.128106 -0.717437  1.122382 -0.000253 -0.481723  0.821466 -0.059704  1.025862 -0.082830 -1.050614 -0.678972 -0.368288  0.018560  0.064093 -0.988707 -0.065342  1.015092  0.081052  0.780555 -0.100268  0.627047  0.856454  0.055100  0.642986  1.101003 -1.056165  0.532599 -0.115727  0.824416  0.642667 -0.498864  0.035932  0.778955 -1.003414  0.061051  0.698689  0.699379 -0.070045  0.878128  1.069316  0.042625  0.790363 -0.206056 -0.038330  0.102179  0.058544 -0.561257  1.132590  0.066327  0.906037  0.879248  0.133811 -0.409580  0.790769 -0.252263 -1.059630  0.768788 -0.524249 -1.082846  1.140423  1.096872  0.897609 -0.372565  1.121748  0.937876  0.397715  0.891542  0.970585 -0.098033  0.743480  0.757838 -0.543849 -0.665261  0.975107 -0.430506 -0.537204  0.890966 -0.692326  0.702857 -1.081445  1.061707  0.094353  0.795804 -0.722627  0.179562  1.123285 -0.491086  0.480043  1.060596  0.093367  0.843173  0.798935 -1.008961 -0.562452 -0.546150  0.730419  1.137980  0.056140  1.140638  0.895752  0.418277  0.902557  1.115612 -0.132443  0.071198  0.076546  0.848739  1.049538 -0.327917 -0.961036 -0.954339  1.120913  0.772979 -0.834418 -0.041186 -1.009501 -1.013256 -0.346432 -0.392545 -0.992074 -1.070083  0.703420  0.696029  0.873631  0.832391 -0.382979  0.141414 -0.315431  1.113718  1.105127 -0.006307  0.048393  0.058548 -1.008435 -0.288899  1.103626 -0.129863 -1.008001  1.121684  1.105482 -0.515652  0.709789 -0.714834  0.440226  0.111820  0.215398  0.022017 -0.044732 -0.883663  0.022687  0.354819  0.283576
        -0.701086 -0.056373 -0.297717 -0.697808 -0.744675 -0.735775 -0.209212 -0.477765 -0.553207 -0.787801 -0.695375 -1.089700 -0.680902 -0.638772 -0.761976 -0.699384 -0.503023 -0.563227 -0.411295 -0.903961 -0.685963 -0.912597 -0.637863 -0.314604 -0.552915 -0.982387 -0.568692 -0.736853 -1.014734 -0.785390 -0.861270 -0.395586 -0.226027 -0.653477 -1.101845 -0.499789 -0.717661 -0.747432 -0.506727 -0.317787 -0.908476 -0.749326 -0.524761 -1.124547 -0.935507 -1.051716 -0.756478 -0.770072 -0.753997 -1.102596 -0.680543 -0.908321 -0.504185 -0.462899  0.100354 -0.488174 -0.697086 -1.016866 -0.472073 -0.698644 -0.586785 -0.359127 -0.385937 -0.413134 -0.775735 -0.504999 -0.739873 -0.768873 -0.513998 -0.788858 -1.141028 -0.717464 -0.926975 -0.720084 -0.300907 -0.642854 -0.416728 -0.822756 -0.838956 -0.408410 -0.626658 -0.243185 -0.120466 -0.409592 -0.693824 -0.566345 -0.846855 -0.999300 -0.596745 -0.565801 -0.666248 -0.315708 -0.586595 -0.796096 -0.394419 -0.609306 -0.680032  0.066676 -0.915882 -0.457881 -0.027323 -0.787200 -0.706651 -0.076859 -0.252237 -1.089022 -0.213971 -0.533612 -0.685902 -0.179694 -0.767925 -0.600212 -0.408616 -0.459397 -0.628842 -1.057774 -0.802223 -0.905776 -0.639685 -0.600102 -0.423352 -0.681985 -0.941698 -0.894911 -0.520936 -0.549191 -0.712865 -0.509339 -0.483449 -0.115684 -0.795854 -0.930705 -0.481019 -1.097763 -0.755450 -0.354959 -0.935437 -0.651436 -0.745286 -0.523755 -1.123901 -0.824187 -0.435717 -0.577225 -0.962783 -0.459463 -0.735969 -0.594513 -0.392657 -0.691262 -0.653594 -0.201759 -0.697388 -0.514072 -0.462365 -0.137510 -0.948669 -0.605063 -0.364759  0.006106 -0.958591 -0.677346 -0.173212 -0.205704 -0.277768 -0.425943 -1.092216 -0.313236 -0.910149 -1.019892 -0.656759 -0.387443 -0.890824  0.232224 -0.533719 -0.704361 -1.024441  0.070820 -0.707333 -0.718171 -0.531351 -0.950694 -1.112559 -0.148759 -0.335593 -0.666852 -1.061947 -0.514167 -0.240900 -0.267073 -0.950342 -0.461710 -0.334613 -0.555495 -0.449866 -0.606140 -0.639509 -0.707591 -0.617538 -1.053959 -0.258816 -0.636658 -0.317013 -0.440397 -0.442936 -0.463901 -0.212941 -0.711335 -0.755943 -0.373904 -0.783749 -0.705572 -0.514876 -0.739798 -0.643039 -0.177003 -1.020223 -0.416013 -0.784901 -0.619051 -0.630255 -1.105660 -0.629700 -0.683190 -0.411482 -1.060512  0.250170 -0.155961 -0.698816 -1.059469 -0.060863 -1.169086 -0.316067 -0.419499 -0.804855 -0.663152 -0.760451 -0.640089 -0.902048 -0.380243 -0.711179 -0.640981 -0.378311 -0.263571 -0.631089 -1.041997 -0.122915 -0.409918 -0.621829 -1.252568 -0.758230 -0.818307 -0.712245 -0.756056 -0.953409 -0.379615
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  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  = [ -0.032992 -0.034131 -0.056423 -0.068027 -0.029770  0.010338 -0.053507 -0.063328 -0.027428 -0.033445 -0.027429 -0.052602 -0.014848 -0.035424 -0.035914  0.002031 -0.076536 -0.040865 -0.083044 -0.028588 -0.009677 -0.018824 -0.035372 -0.071261 -0.051937  0.016226 -0.026294 -0.063740 -0.056298 -0.057178 -0.029675 -0.050336 -0.042511 -0.065729 -0.055148 -0.040551 -0.056760 -0.031190 -0.036779 -0.072201 -0.072737 -0.024415  0.007919  0.002009 -0.040206 -0.055370 -0.023302 -0.036213 -0.027978 -0.047350 -0.080704 -0.050491 -0.037688 -0.019470 -0.041003 -0.028251 -0.021658 -0.016963 -0.040640 -0.050899 -0.035798 -0.008175 -0.024100 -0.028986 -0.056859 -0.004525 -0.071523 -0.000307 -0.000817 -0.008886 -0.058249 -0.048446 -0.038646 -0.053441 -0.060174 -0.063140 -0.011267 -0.056434 -0.052713 -0.031644 -0.057559 -0.050343 -0.015505 -0.039292 -0.037738 -0.075792 -0.052366 -0.043716 -0.041880 -0.051695 -0.022098 -0.016010 -0.039188 -0.067118 -0.050286 -0.028440 -0.035839 -0.024676  0.010219 -0.055845 -0.047288 -0.000081 -0.008249 -0.027660 -0.058297  0.004236 -0.023930 -0.079598 -0.003401 -0.016090 -0.074334 -0.083665 -0.046118 -0.055381 -0.048989 -0.072251 -0.080152  0.010667 -0.057965 -0.009079 -0.040875 -0.013310 -0.063066 -0.050377 -0.057636 -0.076651 -0.043771 -0.045088 -0.004510 -0.058531 -0.073206 -0.034198 -0.057543 -0.031613 -0.076508 -0.046856 -0.079659  0.001357 -0.018139 -0.004863 -0.038762 -0.058311 -0.068152 -0.062810 -0.054040 -0.000242  0.010158 -0.078127 -0.007059 -0.029191  0.015507 -0.035172 -0.049272 -0.056217 -0.074636 -0.039755 -0.047855 -0.045871 -0.040879 -0.011992 -0.064905 -0.074696 -0.004748 -0.082374 -0.042072 -0.016467 -0.020366 -0.075664 -0.007866 -0.042479  0.009083 -0.010992 -0.031427 -0.067244 -0.049657 -0.047721 -0.051508 -0.067389 -0.058205 -0.053950 -0.047783 -0.070224  0.005892  0.011140  0.011701 -0.042387 -0.019571 -0.030330 -0.014653 -0.012724 -0.056170 -0.047733 -0.028349 -0.036211 -0.036695 -0.023726 -0.009289 -0.045964 -0.003514 -0.012447  0.001003 -0.029545 -0.043149 -0.022892 -0.051482 -0.027655  0.000944 -0.026488 -0.002167 -0.013071 -0.009555  0.007312 -0.052877 -0.024034 -0.037397 -0.004755 -0.041731 -0.063070 -0.037507 -0.077349 -0.074129 -0.049101 -0.010619 -0.004150 -0.057556 -0.052997 -0.063411 -0.012278 -0.043798 -0.039560 -0.037490  0.012436 -0.055386 -0.048044 -0.039325 -0.045801 -0.057672 -0.053024 -0.054925 -0.060460 -0.056516 -0.047407  0.001814 -0.003882 -0.007696 -0.022977 -0.035397 -0.046604 -0.063542 -0.027301 -0.039761 -0.015976 -0.054167 -0.027549 -0.005945 -0.044424
        -0.070556 -0.072102  0.018985  0.004715 -0.078103  0.082976 -0.000422  0.049775 -0.073509  0.044656  0.097536 -0.009519 -0.064826 -0.060450 -0.068994 -0.095485 -0.009438 -0.061289 -0.001457  0.046168 -0.078057  0.093932  0.092688 -0.023681 -0.026719 -0.094635  0.080118  0.039099  0.008488 -0.025060 -0.078213  0.034717  0.080772 -0.030746 -0.048459  0.034827  0.058330  0.092238  0.039555 -0.023957 -0.003692 -0.081531  0.101193 -0.095670 -0.043770 -0.048242  0.102539 -0.034267 -0.080007 -0.059181 -0.008230  0.060492 -0.068211  0.086154 -0.060726  0.087942 -0.056566 -0.088936  0.084560  0.011073 -0.053753  0.092065 -0.086248  0.087936 -0.040095 -0.087396  0.001724 -0.095103  0.078300 -0.090439  0.008781  0.005125  0.061106  0.070649  0.037664 -0.034925 -0.079315 -0.030667 -0.028553 -0.075366  0.042087 -0.048667  0.100504 -0.040475  0.083743 -0.010179 -0.046761 -0.060004 -0.034031 -0.006889  0.086065  0.111754  0.034326 -0.019387  0.059560  0.047006 -0.050028  0.104098 -0.092324 -0.004221 -0.053338 -0.095216  0.090216 -0.055098 -0.008110 -0.093849  0.089661  0.025946 -0.079967  0.065919 -0.011776  0.002903 -0.056082 -0.002730 -0.013511  0.050419  0.012443  0.086194  0.030240  0.102736 -0.053200  0.059687 -0.033920  0.028046  0.008207  0.009652  0.052758 -0.060992 -0.092847 -0.038772  0.016423 -0.048305 -0.038603  0.086311  0.003755  0.076877  0.016973  0.108282 -0.086010 -0.092827  0.039516  0.029495 -0.028932 -0.013291 -0.050211  0.105463 -0.095807  0.033367  0.074185  0.099294  0.085532  0.095267  0.080986  0.016855  0.010444 -0.065207 -0.052998  0.032268  0.075079 -0.090140 -0.031304  0.002531 -0.092931  0.004489  0.064477  0.086237 -0.058356 -0.009836 -0.092011 -0.002555 -0.094949 -0.093192 -0.043153  0.023547  0.025085  0.059730  0.064275 -0.023622  0.009928  0.072629  0.009215 -0.023807 -0.095028  0.086730  0.087007 -0.057983  0.073469 -0.073904 -0.087975  0.074790  0.004175 -0.030727  0.099748  0.074466  0.068984  0.082714 -0.071765 -0.023240  0.100378  0.063031 -0.095360  0.092665 -0.010616 -0.083777  0.074707  0.089882 -0.089341 -0.056095  0.099671 -0.089014  0.066744  0.079203  0.004529  0.049935  0.038289  0.098791  0.021341  0.060470 -0.049937 -0.012407  0.023929 -0.051954 -0.094633  0.098531  0.033617  0.004912  0.011360 -0.068529  0.005940 -0.064715  0.037883 -0.093608 -0.033586  0.069207  0.059192  0.017521  0.059416  0.078172  0.073705 -0.037991  0.023886 -0.043237 -0.094815  0.088566  0.068000 -0.086150  0.060686  0.032207  0.036509  0.050002  0.090586  0.096426  0.053040 -0.057906 -0.075417 -0.056310
        -0.153498 -0.119006 -0.071454 -0.098322 -0.125002 -0.020332 -0.046490 -0.123704 -0.062317 -0.035805 -0.130621 -0.042018 -0.029571 -0.059650 -0.139587 -0.104876 -0.105755 -0.146123 -0.134919 -0.016481 -0.043739 -0.106308 -0.137211 -0.108363 -0.058274 -0.067251 -0.084739 -0.117243 -0.071369 -0.069100 -0.075863 -0.062033 -0.126146 -0.099324 -0.090092 -0.040942 -0.120693 -0.127242 -0.033403 -0.124827 -0.100451 -0.068645 -0.056165 -0.099585 -0.052061 -0.093771 -0.134299 -0.024613 -0.131921 -0.094683 -0.125856 -0.104977 -0.076515 -0.084981 -0.155271 -0.113869 -0.030592 -0.129758 -0.129045 -0.048865 -0.055147 -0.069528 -0.083684 -0.115264 -0.155711 -0.057303 -0.101260 -0.106579 -0.036447 -0.176711 -0.086769 -0.038295 -0.070846 -0.129410 -0.111886 -0.122165 -0.049647 -0.068106 -0.060302 -0.075166 -0.108575 -0.153239 -0.111832 -0.045568 -0.123328 -0.103316 -0.074301 -0.075858 -0.040618 -0.040477 -0.093144 -0.143687 -0.032570 -0.091315 -0.099792 -0.019735 -0.052081 -0.146787 -0.072626 -0.067377 -0.144831 -0.079677 -0.066014 -0.043737 -0.077270 -0.137697 -0.108743 -0.132719 -0.030533 -0.042662 -0.100450 -0.150297 -0.118876 -0.053320 -0.036151 -0.137567 -0.125386 -0.029249 -0.102018 -0.105291 -0.060189 -0.010462 -0.115520 -0.058275 -0.084031 -0.113760 -0.067757 -0.081688 -0.133730 -0.159487 -0.111931 -0.047107 -0.078236 -0.117214 -0.110378 -0.127544 -0.126682 -0.095832 -0.159391 -0.133064 -0.042472 -0.102302 -0.125997 -0.083326 -0.089244 -0.092528 -0.046217 -0.133210 -0.041010 -0.143577 -0.013357 -0.153287 -0.144059 -0.068554 -0.110291 -0.107487 -0.142006 -0.050667 -0.114701 -0.182878 -0.140406 -0.106217 -0.130594 -0.127246 -0.082790 -0.075039 -0.030873 -0.103035 -0.123758 -0.018860 -0.051582 -0.066653 -0.028953 -0.110103 -0.054707 -0.086304 -0.116803 -0.093833 -0.087452 -0.133669 -0.038437 -0.144296 -0.115827 -0.029570 -0.028909 -0.068671 -0.058817 -0.068958 -0.062718 -0.050461 -0.068465 -0.051463 -0.142410 -0.100599 -0.081085 -0.085836 -0.029158 -0.035027 -0.083410 -0.024853 -0.083941 -0.124345 -0.020539 -0.164943 -0.132443 -0.116105 -0.041627 -0.042742 -0.076445 -0.164774 -0.029610 -0.015567 -0.048313 -0.012679 -0.032291 -0.080760 -0.016634 -0.132459 -0.054164 -0.113632 -0.118224 -0.111652 -0.082416 -0.077782 -0.102478 -0.048791 -0.096609 -0.030435 -0.027353 -0.112843 -0.030579 -0.064835 -0.066712 -0.117510 -0.069178 -0.039067 -0.123834 -0.145769 -0.138502 -0.120241 -0.073830 -0.060349 -0.112615 -0.056049 -0.026587 -0.101020 -0.065279 -0.052133 -0.115275 -0.029994 -0.151592 -0.105983 -0.099213 -0.048463 -0.027793 -0.156200
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  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  = [ -0.806960 -0.806689 -1.055392 -0.826706 -0.751515 -0.601159 -0.990137 -0.791316 -0.725088 -0.792408 -0.714389 -0.982569 -0.772760 -0.685691 -0.811913 -0.082867 -1.032455 -0.823143 -1.065570 -0.743095 -0.756198 -0.709269 -0.645454 -0.879936 -0.966705 -0.328534 -0.703776 -0.771352 -1.056081 -0.971048 -0.778328 -0.925443 -0.725294 -0.895794 -0.936580 -0.917913 -0.871638 -0.706053 -0.937122 -0.866477 -0.882755 -0.756634 -0.555646 -0.053347 -0.742310 -0.894102 -0.704204 -0.830778 -0.757418 -0.822162 -1.027131 -0.809154 -0.800766 -0.645333 -0.825291 -0.703198 -0.779764 -0.480820 -0.699362 -0.947958 -0.667675 -0.616588 -0.684230 -0.703933 -0.860915 -0.236441 -0.826174 -0.119556 -0.688225 -0.098310 -0.967803 -0.980245 -0.720719 -0.772455 -0.831918 -0.834983 -0.681433 -0.986356 -0.967481 -0.790425 -1.013441 -0.833591 -0.665405 -0.811983 -0.687575 -1.031711 -0.872678 -0.814749 -0.848489 -0.891902 -0.668113 -0.685650 -0.939531 -0.912848 -0.834934 -0.731799 -0.716789 -0.713026 -0.092555 -1.054679 -0.836286  0.094894 -0.644485 -0.782008 -0.967106 -0.010919 -0.705815 -0.974449 -0.759560 -0.669561 -0.981011 -1.061063 -0.844326 -1.048099 -0.892127 -0.827940 -0.988791 -0.641737 -0.995134 -0.654557 -0.753616 -0.664855 -0.847684 -0.955327 -0.967190 -1.012371 -0.742491 -0.816867 -0.230554 -0.862587 -0.784299 -0.790440 -0.961716 -0.709718 -0.972976 -0.730873 -0.988298 -0.671050 -0.488617 -0.230907 -0.880924 -0.995480 -0.850759 -0.935497 -0.907202 -0.658516 -0.490839 -0.987463 -0.685112 -0.677579 -0.579954 -0.746098 -0.732257 -1.055186 -0.860363 -0.832636 -0.836854 -0.863485 -0.700251 -0.088157 -0.838525 -0.899160 -0.230792 -1.040710 -0.702532 -0.733722 -0.778389 -0.928191 -0.232501 -1.034310 -0.412020 -0.395789 -0.795883 -0.737339 -0.977827 -0.772565 -0.827168 -0.888023 -0.967759 -0.786243 -0.959912 -0.850244 -0.052862 -0.565646 -0.565085 -0.799082 -0.686214 -0.782248 -0.443367 -0.674840 -1.055547 -0.925209 -0.697050 -0.728249 -0.710182 -0.666381 -0.767240 -0.892194 -0.637074 -0.700755  0.095979 -0.704388 -1.005611 -0.647219 -0.741880 -0.702602 -0.692831 -0.780836 -0.632403 -0.338900 -0.701434 -0.656109 -0.923049 -0.714855 -0.905147 -0.607325 -1.032077 -0.772253 -0.718457 -1.040629 -0.794431 -0.840172 -0.239894 -0.606720 -1.038398 -0.923170 -0.799489 -0.770217 -0.974332 -0.835746 -0.905241 -0.332324 -0.925717 -0.747765 -0.713175 -0.934361 -0.849026 -0.721070 -0.743454 -0.832303 -1.045124 -0.749331 -0.117434 -0.675844 -0.698314 -0.599601 -0.705254 -0.864218 -0.759563 -0.728416 -0.667160 -0.658043 -0.936952 -0.731595 -0.763923 -0.822743
        -0.702698 -0.703362  0.022036  0.349539 -0.767186  0.842381  0.113111  0.443229 -0.619261  0.680910  0.795913 -0.033059 -0.655479 -0.524537 -0.683793 -1.090075 -0.009355 -0.679703 -0.176045  0.728002 -0.688435  0.728677  0.860712 -0.611679 -0.158399 -1.018469  0.790084  0.419834 -0.009511 -0.046694 -0.690672  0.303746  0.701434 -0.569078 -0.512698  0.415197  0.501852  0.755384  0.459194 -0.626113  0.241057 -0.652065  0.804265 -1.093900 -0.515912 -0.590511  0.815020 -0.575938 -0.761201 -0.680275 -0.319478  0.686941 -0.654803  0.846803 -0.681023  0.724000 -0.647002 -0.974769  0.735805  0.270490 -0.516108  0.821921 -0.825739  0.723994 -0.622378 -0.954832  0.288418 -1.084388  0.725937 -1.086400  0.233110  0.141815  0.656147  0.648250  0.385260 -0.667393 -0.679290 -0.188053 -0.160234 -0.663844  0.227654 -0.670348  0.738730 -0.594901  0.723131 -0.010096 -0.553131 -0.626173 -0.549245  0.071864  0.822978  0.825737  0.453965 -0.174382  0.672220  0.745275 -0.526097  0.796650 -1.086252 -0.046032 -0.660849 -1.089008  0.754799 -0.638839  0.158771 -1.093450  0.730475  0.267334 -0.674743  0.741763 -0.080807 -0.207229 -0.654560 -0.013496 -0.122647  0.551380  0.235903  0.781845  0.236121  0.757551 -0.549576  0.790713 -0.653112  0.239482  0.232537  0.175818  0.601106 -0.640228 -1.066401 -0.621054  0.389962 -0.613681 -0.394162  0.721033  0.202491  0.701633  0.240433  0.776396 -0.959425 -1.066381  0.505823  0.235376 -0.647389  0.054347 -0.536326  0.831215 -0.959735  0.287704  0.703454  0.843554  0.868081  0.784773  0.787956  0.019906  0.309362 -0.651389 -0.660508  0.416046  0.723016 -1.084498 -0.653315  0.267768 -1.066484  0.038675  0.765457  0.719881 -0.648935  0.114504 -1.066359  0.013916 -0.995677 -0.948304 -0.624445  0.455198  0.212152  0.685145  0.603243 -0.291506  0.234258  0.662958  0.212511 -0.640686 -1.088125  0.837665  0.837941 -0.608679  0.669269 -0.658827 -0.674808  0.675758 -0.023072 -0.413483  0.823963  0.770423  0.737828  0.827967 -0.662397 -0.410960  0.861008  0.781734 -1.089152  0.738606 -0.144794 -0.823868  0.729188  0.725940 -0.783655 -0.639835  0.852012 -1.031053  0.772244  0.810012  0.265465  0.758054  0.529153  0.866735  0.158484  0.551069 -0.526007 -0.252063  0.422602 -0.653381 -1.067983  0.866475  0.149841  0.265848  0.399830 -0.659165  0.158925 -0.669481  0.528747 -1.017442 -0.208013  0.669517  0.648251  0.266898  0.471811  0.799245  0.745780 -0.670459  0.088770 -0.441600 -1.084100  0.694486  0.776322 -0.890840  0.658694  0.415985  0.439139  0.748403  0.841603  0.772842  0.514888 -0.602058 -0.666015 -0.681031
        -0.190510 -0.050715 -0.026153  0.454401 -0.059812  0.201875  0.284921  0.437747  0.401821  0.102595  0.070263  0.324872  0.247371  0.541828 -0.280475 -0.164737  0.187876 -0.220990 -0.070411  0.140304  0.221112  0.240657  0.057567 -0.090941  0.323642 -0.233599  0.107525  0.478011 -0.060868  0.336329  0.177932  0.340224  0.259323  0.046248 -0.003143  0.251556  0.252485  0.196482  0.081866 -0.043998  0.432436  0.303303  0.377523 -0.121355  0.480980 -0.143496  0.035238  0.249720 -0.194298 -0.212615 -0.039831  0.073887  0.194818  0.087381 -0.166387  0.260132  0.246284 -0.141387  0.247737  0.308888  0.566913  0.242149  0.048156  0.258737 -0.035537  0.382888  0.488916 -0.190805  0.292242 -0.184756  0.263070  0.297960  0.354246  0.257107  0.420645 -0.057036  0.387282  0.264272  0.321613  0.204018  0.119141 -0.147375  0.300838  0.263561  0.287639  0.190315  0.191550  0.215624  0.249100  0.496040  0.105912  0.060787  0.082698  0.419290 -0.005061  0.113338  0.504394  0.068957 -0.111929 -0.043263 -0.236545 -0.021729  0.325819  0.256606  0.305113 -0.161560  0.243946  0.242746  0.242349  0.298236  0.315690 -0.173483 -0.050405  0.066665  0.490353  0.284301  0.227376  0.271480  0.179633  0.287870  0.435403  0.192242 -0.084307  0.310994  0.265808  0.197394  0.391704  0.180692 -0.166866 -0.039313  0.483732  0.282207  0.158512  0.253327  0.285662  0.249020  0.226081  0.222748 -0.033706 -0.166200  0.228307  0.179349 -0.055021  0.400248  0.099982  0.107368 -0.097502  0.196064  0.338812  0.016641  0.168422 -0.014849  0.039584 -0.023253  0.431264 -0.274010 -0.233720  0.378543  0.266620 -0.109047 -0.261292  0.393692 -0.163730  0.156344  0.186319  0.214858  0.245926  0.404643 -0.110195  0.107634 -0.158171  0.280788  0.249805  0.493759  0.267015  0.202587  0.211625  0.410942  0.262387  0.205830  0.317499 -0.249312 -0.217348  0.292013  0.292674  0.283672  0.389078  0.235153  0.624182  0.397245 -0.046030  0.237558  0.025972  0.091045  0.233655  0.091910  0.247725  0.330440  0.058163  0.073628 -0.025992  0.232512  0.215390  0.085019  0.175785  0.257896  0.149695  0.257600  0.115350 -0.084781  0.123926  0.145030  0.369672  0.133381  0.045571  0.136428  0.003533  0.373872  0.502310  0.007437  0.449425 -0.223420 -0.077627  0.139406  0.053861  0.369195  0.457721  0.246471  0.305367 -0.131465  0.047282 -0.231182  0.393831  0.269811  0.376844  0.345995  0.327484  0.037993  0.133974 -0.055112  0.061985  0.530081 -0.196842  0.369778  0.119452 -0.242370  0.374810  0.377077  0.479235  0.113786  0.054182  0.254863 -0.013274  0.407846  0.249088 -0.093403
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  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  = [  0.002723 -0.029723 -0.040484 -0.032766  0.009199  0.007384  0.013169  0.017745 -0.024568 -0.025825  0.016319  0.010493 -0.017457  0.022409 -0.035592  0.024935 -0.020588 -0.003922 -0.029559 -0.023710 -0.040683  0.028026  0.006732  0.002536 -0.002376  0.007014  0.004229  0.015874 -0.011378  0.005173 -0.028171 -0.039025  0.017169  0.008481 -0.005207 -0.033273 -0.021587 -0.028373 -0.028437 -0.003563 -0.039601 -0.035608 -0.002812 -0.016839 -0.004583  0.024070 -0.035414  0.020239 -0.025619 -0.034561 -0.025097 -0.031099 -0.010500 -0.035279  0.022906 -0.039989 -0.013681 -0.023936  0.012245 -0.030016  0.009596  0.025775  0.016287  0.017365 -0.041587 -0.002284 -0.007922 -0.041096  0.004454 -0.020680 -0.027978 -0.010762 -0.019623  0.001820  0.001584  0.004856 -0.011541 -0.013911  0.016287  0.004638 -0.006078  0.019302 -0.013136 -0.005871  0.016184 -0.005031  0.017469  0.013103  0.020132  0.013188 -0.041572 -0.013459 -0.040684 -0.002429  0.006885  0.000071 -0.040964 -0.029787 -0.003170 -0.025694 -0.012727  0.016112  0.016322 -0.027041 -0.030256 -0.004492  0.002455 -0.041987 -0.020830  0.001789 -0.039956 -0.020691 -0.028843 -0.039468 -0.003469 -0.011012  0.020244 -0.013950 -0.012373 -0.033726  0.016194 -0.019449  0.012271 -0.019588  0.016127 -0.010519 -0.027883 -0.009065 -0.038535  0.009294  0.012241 -0.041548  0.000226  0.016838 -0.021868 -0.005894  0.020989 -0.018181  0.024173 -0.041731 -0.040926 -0.033703 -0.041965 -0.014298 -0.022218 -0.037178 -0.034837 -0.039798 -0.000963  0.014512  0.016851 -0.000231 -0.022004  0.000345 -0.002088 -0.006941 -0.041857 -0.040183  0.023545 -0.021609  0.020862 -0.022694 -0.005024  0.018662  0.013999  0.010793 -0.038314 -0.017748 -0.041033 -0.041107  0.020781  0.021769 -0.041941 -0.038785 -0.038351 -0.039939 -0.000327 -0.011541 -0.018910  0.026535  0.004898  0.000123  0.025336  0.011235 -0.019840 -0.020756  0.004344 -0.015687  0.006469  0.021337  0.014624  0.003121  0.025761 -0.005409 -0.041901  0.010595 -0.004381 -0.013922 -0.007096 -0.027669 -0.038120 -0.021771 -0.041432 -0.019511 -0.003161 -0.008975  0.026416  0.013668 -0.017063 -0.006255 -0.000947 -0.015428 -0.011959 -0.037778  0.004461  0.003800 -0.035464 -0.039449 -0.008588 -0.016054 -0.013818  0.020227 -0.006378 -0.041437 -0.030848 -0.019233  0.012857  0.000636 -0.029092 -0.027999 -0.010523  0.005466  0.010296 -0.010965 -0.006155 -0.039985  0.002199 -0.041055 -0.023113 -0.027935 -0.000276 -0.039703 -0.007143  0.015690 -0.041759 -0.004905 -0.034937  0.017657 -0.034322 -0.041640 -0.039178  0.019334  0.024199 -0.003708  0.014920  0.024377
         0.023530 -0.040296 -0.018589 -0.037353 -0.085608 -0.084950  0.038927 -0.095847 -0.047388  0.011562 -0.094481  0.032152  0.007505  0.077641 -0.030439  0.063006 -0.048548  0.060463 -0.039283  0.039994 -0.016954 -0.112690 -0.089888 -0.085277  0.050680  0.024505 -0.078876  0.070385  0.029681  0.059544  0.022806  0.026691 -0.091633 -0.089975 -0.068576 -0.036430  0.039806 -0.033570  0.034794 -0.070147 -0.022824 -0.028003 -0.076744 -0.058031  0.016233  0.048665 -0.034810  0.043175 -0.044543 -0.027440  0.001653  0.017392 -0.066158 -0.033639 -0.107176 -0.001480 -0.061462  0.016516  0.070197 -0.002078 -0.093018  0.050594 -0.096461  0.075691  0.008369 -0.069562  0.054113  0.008996  0.045873 -0.052972 -0.042740  0.015976 -0.053590 -0.082287 -0.083476  0.024941  0.015510 -0.061805 -0.095566  0.021368  0.038656  0.033180  0.008746 -0.066688  0.035541 -0.073092  0.061405 -0.091394  0.062286  0.071156 -0.007374  0.040381 -0.016827  0.048556 -0.084135  0.054682  0.001524 -0.037228  0.027185 -0.045922  0.017976 -0.093380  0.078339 -0.044512  0.015605 -0.072044  0.034372  0.013420 -0.049469  0.041066 -0.023057 -0.050905 -0.037490 -0.020460 -0.073505 -0.065876 -0.104688 -0.056647 -0.057345  0.022277  0.072137  0.045247 -0.090131 -0.044920  0.033572  0.055283  0.039629 -0.066514 -0.023727  0.036579 -0.093435  0.002632 -0.072800 -0.100291  0.002707 -0.069260  0.057203 -0.050397  0.039771  0.017175  0.004307 -0.025123  0.003300  0.007266 -0.051951 -0.020634 -0.030299 -0.013880  0.054305 -0.092505 -0.094638  0.045409  0.022096  0.039075 -0.074938 -0.070429 -0.001550 -0.023325 -0.103765 -0.051716  0.060219  0.031145 -0.074275  0.032539  0.034857 -0.090663  0.009002 -0.052091 -0.012400 -0.016790 -0.102154  0.069895  0.000281 -0.010988 -0.025054 -0.020337  0.051964 -0.058942  0.016218 -0.111184  0.041501  0.061857 -0.110379 -0.088828 -0.053519  0.040961  0.049424 -0.057035  0.022124 -0.098553 -0.096989  0.026868  0.079562  0.055724 -0.001138  0.026466 -0.073052  0.031017 -0.064407 -0.039524  0.019836 -0.050652 -0.009012 -0.053840 -0.069400  0.022371 -0.101756  0.053875 -0.057654  0.031124 -0.074928 -0.059108 -0.064137  0.018442 -0.081265 -0.079935  0.029126 -0.009330 -0.064931  0.014886  0.050511  0.078820  0.021772  0.004711 -0.036136  0.041540 -0.095283 -0.081027 -0.038470  0.020796 -0.061417 -0.085903  0.050933 -0.062280 -0.066227 -0.005704  0.020096  0.012039 -0.051120  0.028003  0.024870  0.012651 -0.068365 -0.099618 -0.004622  0.013315 -0.029694  0.032731 -0.034627 -0.006785 -0.011624 -0.098944 -0.105047  0.014111 -0.093111 -0.103165
         0.089371  0.026538  0.046099  0.018190  0.085520  0.048563  0.083656  0.038432  0.015859  0.061413  0.008093  0.088979  0.081564  0.038643  0.028758  0.069624  0.001577  0.022030  0.076247  0.026115  0.010574  0.067048  0.063097  0.065277  0.044975  0.095955 -0.002084  0.045010  0.059265  0.044417  0.043383  0.017445 -0.005277  0.024595  0.035203  0.023161  0.029991  0.091177  0.026169  0.036383  0.012940  0.039051  0.059863  0.071279  0.090035  0.087074  0.066960  0.088741  0.029766  0.084287  0.076546  0.046071  0.016322  0.070183  0.075467  0.053429  0.013914  0.057776  0.037781  0.073789  0.063145  0.087061  0.082081  0.032618  0.030361  0.047658  0.029703  0.033802  0.061669  0.020534  0.025664  0.079251  0.057396  0.021554  0.068114  0.090624  0.078504  0.020605  0.032480  0.097597  0.055467  0.106382  0.089888  0.050152  0.093589  0.071027  0.060763  0.036873  0.063553  0.037547  0.046018  0.042294  0.043751  0.047847  0.006585  0.043063  0.044144  0.079493  0.074842  0.015464  0.072647  0.005550  0.018220  0.023034  0.049629  0.029535  0.073619  0.015413  0.032783  0.063961  0.052061  0.009789  0.037095  0.070314  0.029220  0.069491  0.070089  0.036586  0.044830  0.035729  0.042193  0.023670  0.039134  0.092275  0.097296  0.022026  0.016064  0.028631  0.006738  0.080916  0.055128  0.036626  0.043750  0.061867  0.081419  0.031709  0.071403  0.084509  0.100593  0.016204  0.040990  0.089911  0.025396  0.090691  0.068072  0.084788  0.032865  0.067602  0.041969  0.045624  0.042414  0.055355  0.053402  0.064408  0.011284  0.061537  0.013164  0.055866  0.053348  0.019403  0.067300  0.040668  0.065668  0.106787  0.090898  0.012244  0.044971  0.047872  0.033556  0.053441  0.055946  0.055746  0.021680  0.068772  0.009404  0.022802  0.046425  0.038572  0.065600  0.076653  0.067987  0.028317  0.072254  0.039055  0.072848  0.029544  0.056909  0.008395  0.101242  0.039764  0.057546  0.084601  0.035760  0.031074  0.017746  0.100775  0.027481  0.053780  0.039178  0.045312  0.030830  0.056597  0.032869  0.057831  0.085732  0.072558  0.030161  0.064907  0.071622  0.064960  0.052467  0.013949  0.071593  0.033889  0.035378  0.037722  0.022724  0.064714  0.080181  0.071789  0.025556  0.025986  0.077593  0.035228  0.046825  0.031276  0.021325  0.071218  0.033350  0.046239  0.050721  0.016376  0.063741  0.079228  0.000786  0.058282  0.095037  0.030208  0.065458  0.036996  0.082505  0.036018  0.055876  0.070908  0.014751  0.096423  0.033734  0.103682  0.054420  0.042565  0.068026  0.026279  0.085718  0.096685  0.007760  0.049566
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  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  = [ -0.652715 -0.816336 -0.998628 -0.839232 -0.753673 -0.791515 -0.657485 -0.603021 -0.804861 -0.695668 -0.641323 -0.680633 -0.721937 -0.428033 -0.926332 -0.632599 -0.798590 -0.605077 -0.813838 -0.689240 -1.026474 -0.653467 -0.732344 -0.798042 -0.676795 -0.694389 -0.773686 -0.619124 -0.681271 -0.691323 -0.698157 -0.904458 -0.574431 -0.707873 -0.767570 -0.853748 -0.690978 -0.835189 -0.717708 -0.779103 -0.988721 -0.903272 -0.819708 -0.786207 -0.604425 -0.644816 -0.910086 -0.655503 -0.800457 -0.920546 -0.708830 -0.701408 -0.799717 -0.879494 -0.737155 -0.992959 -0.792190 -0.694140 -0.645631 -0.715897 -0.729480 -0.618110 -0.745578 -0.555951 -1.026486 -0.758727 -0.619790 -1.008354 -0.665793 -0.823219 -0.814591 -0.700877 -0.761136 -0.779010 -0.798994 -0.672294 -0.701657 -0.810942 -0.645510 -0.696765 -0.676435 -0.605182 -0.677615 -0.732770 -0.654265 -0.778180 -0.654059 -0.723276 -0.647323 -0.597188 -1.041256 -0.681262 -1.033402 -0.676848 -0.738667 -0.677060 -0.990321 -0.814066 -0.663434 -0.805987 -0.689299 -0.641529 -0.395000 -0.814368 -0.700565 -0.778808 -0.665325 -1.041785 -0.786905 -0.668040 -0.973153 -0.798425 -0.811326 -1.022826 -0.777784 -0.796961 -0.715998 -0.780779 -0.753479 -0.750463 -0.598670 -0.680446 -0.741562 -0.782888 -0.668492 -0.695579 -0.700833 -0.773298 -1.004792 -0.660838 -0.695522 -1.037106 -0.809958 -0.687213 -0.739718 -0.768257 -0.646643 -0.781022 -0.625629 -1.033364 -1.014798 -0.879785 -1.040656 -0.678777 -0.799719 -0.892636 -0.871026 -1.030030 -0.678094 -0.714906 -0.660902 -0.672280 -0.691870 -0.669541 -0.765655 -0.819117 -1.041122 -0.998226 -0.635621 -0.813804 -0.646593 -0.694767 -0.855643 -0.646171 -0.676228 -0.695417 -0.887692 -0.752515 -1.028660 -1.029001 -0.634416 -0.624520 -1.041091 -0.930156 -0.937550 -1.018060 -0.674746 -0.780128 -0.691329 -0.689977 -0.664956 -0.651920 -0.720529 -0.742598 -0.789209 -0.690146 -0.665504 -0.787502 -0.692901 -0.551844 -0.665880 -0.657975 -0.373042 -0.617278 -1.041166 -0.685622 -0.776131 -0.683867 -0.782695 -0.766147 -0.841892 -0.765679 -1.036168 -0.763419 -0.766033 -0.689245 -0.350343 -0.656110 -0.786431 -0.677263 -0.777671 -0.793937 -0.792387 -0.841550 -0.758166 -0.758827 -0.775726 -0.963493 -0.771476 -0.687142 -0.693613 -0.435784 -0.661620 -1.036995 -0.807956 -0.703263 -0.650656 -0.787369 -0.834298 -0.697750 -0.748846 -0.743053 -0.659480 -0.773564 -0.792543 -0.947247 -0.653238 -1.025953 -0.800795 -0.694591 -0.640465 -0.942671 -0.755718 -0.726034 -1.040310 -0.591493 -0.871125 -0.647176 -0.833966 -1.040999 -0.930548 -0.430859 -0.731570 -0.590297 -0.642721 -0.605823
         0.692885 -0.645668 -0.284237 -0.627737 -0.670921 -0.637508  0.643932 -0.871662 -0.665345  0.600154 -0.803640  0.653180  0.655999  0.936302 -0.437169  0.664278 -0.667801  0.828679 -0.595049  0.691753 -0.183714 -0.834233 -0.758150 -0.678896  0.652692  0.686969 -0.706297  0.772940  0.617323  0.676182  0.610367  0.507336 -0.897047 -0.779836 -0.656081 -0.593522  0.694816 -0.533246  0.649547 -0.649201 -0.327764 -0.521912 -0.578182 -0.671090  0.735468  0.640692 -0.504152  0.653713 -0.640369 -0.447566  0.608926  0.604560 -0.668547 -0.520076 -0.741177  0.232578 -0.659552  0.605214  0.751477  0.599632 -0.761280  0.655404 -0.684520  0.867077  0.142607 -0.695176  0.777667  0.206263  0.633887 -0.646187 -0.648112  0.632034 -0.671043 -0.706355 -0.677095  0.680174  0.631568 -0.661088 -0.819728  0.683832  0.626512  0.762498  0.717318 -0.687881  0.673676 -0.678450  0.653464 -0.742560  0.652158  0.831722 -0.020038  0.637796 -0.131656  0.650568 -0.728150  0.689100  0.248243 -0.592994  0.636502 -0.663878  0.615802 -0.802539  0.947887 -0.658031  0.602773 -0.663659  0.624535  0.033403 -0.641121  0.628726 -0.353701 -0.647579 -0.656483 -0.150756 -0.665121 -0.674707 -0.780555 -0.663692 -0.704841  0.588915  0.804637  0.754479 -0.747187 -0.629998  0.689922  0.766187  0.750501 -0.656175 -0.266472  0.630061 -0.749602  0.068634 -0.645439 -0.799594  0.644307 -0.656765  0.647352 -0.635751  0.727061  0.143657  0.186604 -0.186083  0.034748  0.715838 -0.673422  0.146417 -0.541474  0.033706  0.688723 -0.764273 -0.829407  0.634470  0.609713  0.626707 -0.689717 -0.594482 -0.039886 -0.306750 -0.811118 -0.661889  0.650091  0.622885 -0.597013  0.741467  0.657939 -0.755451  0.425690 -0.689589 -0.168119 -0.167122 -0.809933  0.723567 -0.040922  0.326410 -0.440296 -0.221622  0.653975 -0.688854  0.607399 -0.801553  0.629141  0.774922 -0.774703 -0.745884 -0.666578  0.695971  0.637073 -0.657595  0.718970 -0.917534 -0.786483  0.650817  0.991181  0.779278 -0.039473  0.695053 -0.682675  0.618834 -0.682194 -0.674655  0.500353 -0.684275 -0.111272 -0.687463 -0.654680  0.615520 -1.027235  0.641601 -0.670712  0.620859 -0.566834 -0.657198 -0.663798  0.498959 -0.697609 -0.696279  0.616354  0.278735 -0.650189  0.625385  0.718873  0.947339  0.655453  0.070713 -0.624294  0.689741 -0.843260 -0.647300 -0.582976  0.608494 -0.676980 -0.718366  0.638636 -0.652962 -0.682504  0.314185  0.689451  0.146277 -0.679479  0.620601  0.666732  0.359831 -0.654209 -0.768905 -0.058072  0.774484 -0.540869  0.741659 -0.590198 -0.042450  0.325774 -0.983483 -0.695275  0.775281 -0.802269 -0.842469
         0.439180  0.148048 -0.060623 -0.014365  0.360175 -0.189006  0.512833  0.151396 -0.080433  0.514037 -0.246076  0.458667  0.369944  0.283191  0.231621  0.523629 -0.104435  0.242157  0.351984  0.389820 -0.009647 -0.055185 -0.021711  0.147078  0.472457  0.358967  0.032436  0.366246  0.513050  0.411364  0.497135  0.158885 -0.041575  0.129140  0.306569  0.151491  0.380530  0.406411  0.409554  0.287846 -0.065690 -0.017637 -0.225162  0.250811  0.440592  0.536625  0.188067  0.501798  0.240992  0.280563  0.481181  0.499856 -0.103109  0.295303  0.218120  0.245953 -0.176379  0.509729  0.358805  0.483070 -0.021663  0.555694  0.353646  0.244788  0.139702 -0.143133  0.349213  0.193484  0.514449 -0.042911  0.147175  0.459005 -0.205111 -0.007472  0.149916  0.425493  0.458259  0.095450  0.226426  0.360609  0.508288  0.385873  0.327363 -0.242657  0.472115  0.260190  0.506315  0.220531  0.518037  0.258862  0.067694  0.486293  0.007362  0.475330 -0.164869  0.415900  0.238695  0.355230  0.513913 -0.080828  0.502595 -0.248619  0.291534  0.083948  0.503414  0.254094  0.527245  0.017815  0.283934  0.517817 -0.088715 -0.187976  0.104684  0.196923  0.253778  0.177238  0.036129  0.245081 -0.132685  0.442191  0.334403  0.268765  0.035445  0.366239  0.414318  0.181114  0.220513  0.289875 -0.079406  0.526675 -0.206630  0.103765  0.168998 -0.061779  0.351681  0.303075  0.525265  0.359162  0.425231  0.042004  0.176416  0.598081  0.065736  0.328166  0.164335  0.574978  0.231583  0.198655  0.414805 -0.083520  0.014726  0.504084  0.507260  0.518214 -0.186230 -0.194858  0.013805  0.013167 -0.201899  0.030116  0.521784  0.485821  0.009155  0.342197  0.458804 -0.231320  0.368896 -0.183890  0.052153  0.015136 -0.208186  0.449478  0.020551  0.371463 -0.128491  0.075376  0.473907  0.150311  0.510975  0.176658  0.521831  0.285957  0.120811  0.035366  0.252379  0.380084  0.510751 -0.200478  0.260257  0.066854 -0.190468  0.501300  0.135299  0.350584  0.018388  0.362067  0.208485  0.507263  0.168736 -0.181089  0.381621 -0.155824  0.026419 -0.154590  0.360457  0.503148  0.069418  0.518753  0.251154  0.514360 -0.340889 -0.176344  0.248627  0.384680  0.231645  0.233989  0.350101  0.316034  0.354909  0.492422  0.327500  0.220223  0.488819  0.102368 -0.177171  0.365847  0.038080  0.312845  0.268206  0.500160 -0.224888 -0.182898  0.517620  0.342928 -0.041592  0.331313  0.444846  0.139548  0.046083  0.489098  0.504610  0.289226 -0.254644  0.114509  0.021015  0.373070  0.232452  0.339093 -0.173417  0.039374  0.370716  0.148416  0.369345  0.373333 -0.246408 -0.187663
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  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  = [ -0.046347 -0.085157 -0.063794  0.048145 -0.036464  0.028975 -0.048351 -0.088060 -0.040428 -0.021295 -0.038116  0.050872  0.023204  0.028475 -0.055416 -0.098345  0.083153 -0.084796 -0.096755 -0.106055 -0.089903 -0.018312 -0.034958 -0.020609  0.015108 -0.046378 -0.058777 -0.063573  0.028856 -0.005206 -0.064816 -0.058857 -0.100672 -0.033013 -0.093069 -0.030848  0.083516 -0.050714 -0.069718  0.038782 -0.045791 -0.094001  0.029453 -0.035642 -0.049575  0.091210 -0.086498 -0.061753  0.060384  0.001207 -0.023898 -0.083560  0.087171  0.021213  0.012328  0.057705 -0.004360 -0.045531 -0.097297 -0.039676 -0.043734 -0.026327 -0.017864 -0.031431 -0.055886 -0.018464 -0.074091  0.035798 -0.042668  0.065195  0.032465 -0.063326 -0.087880 -0.057284 -0.035695 -0.078332  0.066341 -0.037581  0.097335  0.039511 -0.048695 -0.012296 -0.096796  0.016206 -0.091073  0.089171 -0.037437  0.016039 -0.031989  0.025214 -0.022799 -0.107440 -0.106356  0.106812 -0.046706 -0.027959 -0.027264 -0.034237 -0.042153  0.116577  0.055777 -0.012078  0.068007  0.009946 -0.095213  0.061460 -0.045984 -0.032768 -0.010195 -0.070728  0.075377 -0.008960 -0.047728 -0.012526 -0.014417  0.052268 -0.077151  0.066565 -0.022142 -0.059551 -0.027562 -0.061216 -0.034190 -0.120892  0.062397  0.071434  0.036731  0.057441 -0.051019 -0.043919  0.067244  0.054868 -0.105596 -0.048894 -0.049926 -0.030373  0.060782 -0.105438 -0.004438 -0.061376 -0.101271 -0.019094 -0.001803  0.096310 -0.031491 -0.033095  0.087643  0.058336  0.014766  0.106577 -0.039669 -0.102596 -0.106025  0.021292  0.006279 -0.098833 -0.074808  0.045231 -0.065772  0.004644 -0.004463  0.062320 -0.030047 -0.113733  0.084651 -0.084500  0.069281 -0.050885  0.093539 -0.095661  0.000517 -0.038079  0.078795 -0.015744 -0.118811  0.075900 -0.036083 -0.077720 -0.071157 -0.093844  0.061605 -0.028593 -0.039426 -0.013808  0.066662 -0.032922  0.043095 -0.062031  0.071411  0.061731 -0.033641 -0.054714 -0.071388  0.025651 -0.034770 -0.041180  0.000809  0.070774 -0.023130 -0.112382 -0.065859 -0.096570 -0.111955 -0.055872 -0.054228 -0.092061  0.066598  0.063357 -0.016183 -0.114198 -0.070330  0.061074 -0.022176 -0.062719 -0.096605  0.012325 -0.046267 -0.021226  0.003294 -0.088578 -0.093114 -0.118424 -0.079111 -0.013464  0.056924 -0.056456 -0.045390 -0.035993 -0.008184 -0.051668 -0.052765 -0.021327 -0.078269  0.091535 -0.071546 -0.048344 -0.054999 -0.041663  0.110070  0.019298  0.076375 -0.032356 -0.013825 -0.032390  0.018415  0.069670 -0.032410 -0.014130 -0.054254 -0.016453  0.078722 -0.056744 -0.004965 -0.071986 -0.075068 -0.063351  0.064857  0.072366 -0.067537 -0.097619 -0.045514 -0.035173  0.082369 -0.016293  0.080683  0.018419 -0.027801  0.008657  0.037816  0.037539 -0.051632  0.087364  0.109599  0.027504  0.051340  0.016598  0.018908 -0.102788 -0.054644 -0.078094 -0.068904  0.017213 -0.076161 -0.029671  0.057820 -0.082553 -0.022378 -0.008801 -0.062063 -0.056262  0.027449 -0.019867 -0.017473 -0.047203  0.091736  0.004049 -0.041099 -0.023632  0.049015 -0.046482 -0.035729  0.069263 -0.038100 -0.073213 -0.046742  0.048906  0.062589  0.071654 -0.033529 -0.033878 -0.037449  0.057360  0.092933  0.073732 -0.031693 -0.058500 -0.008821 -0.013345  0.039717 -0.069960 -0.082802  0.006902 -0.103936 -0.022565 -0.016034  0.041708 -0.022415 -0.023589 -0.006863  0.083132  0.050351  0.073451  0.025742 -0.100352  0.009712  0.011271 -0.081340 -0.094527 -0.078998  0.104343 -0.062429  0.041191 -0.013869  0.056454  0.025137 -0.079844 -0.052177 -0.017357 -0.078086  0.103121 -0.073708 -0.026133  0.035572 -0.015457  0.069772  0.013028  0.005799 -0.111644  0.054002 -0.051341 -0.127197 -0.021579 -0.106906 -0.036144 -0.005187  0.048625  0.030447  0.009599 -0.052199 -0.106734 -0.061026 -0.002572  0.036552 -0.012969  0.067144 -0.073337  0.016457 -0.019975  0.111056 -0.034477  0.028446 -0.017919 -0.026238 -0.054931 -0.035832 -0.053536 -0.083322 -0.005648  0.103811 -0.014126  0.032695  0.035020  0.087666 -0.021508 -0.080304 -0.088439  0.030840 -0.080296 -0.076101  0.016056  0.008264  0.030523 -0.114339 -0.086756 -0.065765 -0.020237  0.061851  0.061342  0.032036 -0.025622 -0.093601 -0.024808 -0.080488  0.060680  0.073844  0.110862 -0.094820 -0.006013 -0.054889 -0.073310  0.018580 -0.050989 -0.042684 -0.020444  0.033540 -0.029536 -0.059078  0.071329  0.023943 -0.022708  0.075288  0.037422 -0.015223 -0.003757 -0.011093  0.063169  0.000325  0.065105  0.079726 -0.112550  0.097849  0.019469 -0.042125 -0.010185  0.006046 -0.046365 -0.019316 -0.030345 -0.114928 -0.041432 -0.062246 -0.000894 -0.098880  0.000431  0.002885 -0.042022  0.016440 -0.029020 -0.032127  0.060075 -0.021590 -0.078319 -0.090901 -0.098977 -0.055928  0.071433  0.000937 -0.019321 -0.038893  0.003987  0.007786 -0.067703  0.003008 -0.037152  0.061224  0.080871 -0.050585  0.018730 -0.051883 -0.010736  0.013124  0.030362  0.056053 -0.026918 -0.109313 -0.036214 -0.086268 -0.012502 -0.066872  0.025037 -0.040425  0.108004 -0.027261 -0.060149  0.089158 -0.036475 -0.004070  0.008794 -0.044013 -0.096651  0.002108  0.085443  0.024030 -0.009598 -0.030311 -0.030759 -0.049362  0.109550 -0.051153  0.080006 -0.005601  0.066788
        -0.005729  0.005159  0.021154 -0.098919 -0.083725 -0.071772  0.030108 -0.007687  0.023207  0.030438 -0.070997 -0.099235 -0.091606 -0.052069  0.020273 -0.005752 -0.049526 -0.045458 -0.016022 -0.000949 -0.015713  0.031737 -0.082591  0.013448 -0.097391  0.030417 -0.014732 -0.098339 -0.049035  0.010168  0.037268 -0.097740 -0.096326 -0.041964  0.031382 -0.082665 -0.040557  0.030246 -0.105614 -0.096622 -0.078368  0.006283 -0.086551 -0.002124 -0.091470 -0.059252 -0.062588 -0.016036 -0.061097  0.037765 -0.010071 -0.093361 -0.029764 -0.042683 -0.110223 -0.053478  0.030043 -0.004647  0.001900 -0.113976  0.024263 -0.121573 -0.039579  0.006961 -0.010360 -0.001997  0.032447 -0.045535  0.024819 -0.072896 -0.049241  0.015220 -0.014666 -0.014636  0.003351  0.031196 -0.051336  0.025943 -0.064346  0.003556  0.033416 -0.053690 -0.007054 -0.064703 -0.012220 -0.023869 -0.100710 -0.010232  0.034347  0.011955 -0.079520 -0.009737  0.033521 -0.018254 -0.110519 -0.028584  0.020540 -0.001359 -0.089211 -0.008531 -0.077329 -0.105541 -0.026571  0.026373  0.005050 -0.085386 -0.089132 -0.077064 -0.021454  0.032494 -0.056041 -0.057056 -0.085730 -0.016816 -0.046240 -0.092446 -0.043557 -0.082836 -0.032058 -0.014968 -0.078168 -0.102777 -0.079318 -0.029783 -0.078305 -0.070884 -0.098798 -0.026491  0.028437 -0.095748  0.003267 -0.014000  0.017802 -0.110645  0.023365 -0.092335 -0.002244  0.008432 -0.049584  0.022920  0.012714 -0.096740  0.032161 -0.061726  0.005992 -0.090570 -0.072811 -0.028032 -0.076026 -0.003632 -0.110801  0.042411 -0.007414 -0.087515 -0.111674  0.008796  0.035167 -0.094633 -0.032987 -0.077173 -0.120046 -0.026212 -0.095142 -0.069506 -0.051948 -0.081332 -0.015305  0.030057 -0.029007  0.035523 -0.001730 -0.071585 -0.060840 -0.079930 -0.007363 -0.004732 -0.082105  0.014463  0.016907  0.032396 -0.065984 -0.010297 -0.115006 -0.095959 -0.009431 -0.112865 -0.087423 -0.007263 -0.072298 -0.012848 -0.078477 -0.090855  0.026263 -0.064441 -0.081123 -0.088626 -0.016339  0.009464 -0.091567 -0.056534 -0.105683 -0.001609  0.021326  0.032654  0.027912 -0.082627 -0.049914 -0.090223  0.011004 -0.022027  0.026708 -0.044879 -0.041505  0.013720  0.016058 -0.047231 -0.093536 -0.067409  0.004876 -0.034881  0.041121 -0.004526 -0.075094  0.026748 -0.089421 -0.024669 -0.088826  0.035020 -0.105715 -0.107575 -0.097937 -0.099486  0.018695 -0.003003 -0.053699 -0.085519  0.019791  0.020493 -0.048678  0.020281 -0.002090  0.030425  0.023961 -0.092438 -0.092642 -0.049670 -0.008235 -0.068493 -0.101201  0.030959 -0.061048  0.017533  0.012498 -0.105416  0.035697 -0.060977 -0.072413 -0.006368 -0.105866  0.040303 -0.106066  0.013651 -0.029371 -0.025093 -0.077518 -0.099492 -0.007293 -0.001323 -0.086157 -0.096870 -0.104604 -0.041323 -0.055318 -0.021948 -0.072058 -0.105290 -0.022706 -0.075028 -0.101751  0.037649  0.015170 -0.011740  0.027331  0.029273 -0.018176  0.026121 -0.108082 -0.015853 -0.103229 -0.100361  0.006048 -0.020849 -0.071472 -0.113117 -0.071664 -0.115220 -0.106192 -0.057145 -0.063544 -0.005916  0.034904  0.007420 -0.115763 -0.103303 -0.113679 -0.098824 -0.034788 -0.015439 -0.062503 -0.084106  0.005285  0.011279 -0.052437 -0.055542  0.006048  0.024093  0.032051  0.029589 -0.067546 -0.094876  0.016368 -0.103185 -0.094671  0.007214 -0.003441 -0.024254 -0.062269 -0.009688 -0.004736 -0.045253 -0.051731 -0.070882  0.015468  0.017820 -0.081131 -0.109109 -0.009341 -0.085068  0.037916 -0.062549 -0.070028 -0.015189 -0.007533 -0.055133  0.006626 -0.020851 -0.093766 -0.096122 -0.088187 -0.046990  0.021490 -0.003029 -0.095298 -0.120638  0.010017 -0.093758 -0.105403 -0.008539  0.008335  0.034575 -0.007848 -0.121546  0.021818  0.010194  0.037213 -0.001613 -0.096858 -0.021577  0.028906  0.022584  0.036315 -0.116645 -0.036207 -0.021538 -0.091939 -0.054146 -0.045904 -0.005693 -0.062668  0.032224 -0.017447  0.023501 -0.114076 -0.016146 -0.046746  0.030702  0.018174 -0.039207 -0.060164 -0.070831 -0.072631 -0.035423 -0.068652  0.025203 -0.002983 -0.046775 -0.017124 -0.087873 -0.074415 -0.049113  0.016491  0.011851  0.005973  0.022425  0.030421  0.003856 -0.082226 -0.063274 -0.082673 -0.067027 -0.002836 -0.120154  0.036539 -0.001574 -0.040759 -0.061027  0.016636  0.028519  0.035547 -0.080953 -0.022537  0.017938  0.001749 -0.061991 -0.044552 -0.048186 -0.103651 -0.043204 -0.093319 -0.120785 -0.074438 -0.007595 -0.055968 -0.027583  0.010554 -0.080538 -0.104353 -0.069149 -0.041512 -0.057615 -0.060556 -0.089969 -0.068365 -0.070962 -0.012334 -0.090797 -0.054517  0.029562 -0.007521  0.012109  0.004469  0.035728 -0.018928 -0.066001  0.002216 -0.114055 -0.049011  0.021589  0.005748 -0.098475 -0.097291  0.037953 -0.056744  0.032880 -0.099546 -0.005726 -0.104675  0.028363 -0.115494  0.017457 -0.019292  0.017648  0.038642 -0.084224 -0.048093 -0.000976  0.037876 -0.002596  0.002487 -0.049809 -0.090436 -0.018185 -0.033806 -0.077175 -0.021747 -0.074252 -0.069639  0.030334  0.036595 -0.092865 -0.112461 -0.060020  0.022768 -0.017878 -0.033282  0.008060 -0.102257 -0.086595  0.004669 -0.002577 -0.084703 -0.007370 -0.019740 -0.054687 -0.031981 -0.037680  0.028102 -0.062316 -0.054336 -0.083673  0.029644 -0.088901
         0.170059  0.191985  0.201272  0.204496  0.259928  0.229904  0.254941  0.181534  0.267389  0.203882  0.165596  0.203662  0.210100  0.245619  0.198839  0.184834  0.264945  0.177949  0.177015  0.194251  0.175957  0.219949  0.259236  0.261146  0.204838  0.205331  0.167589  0.270799  0.247628  0.245683  0.235656  0.261680  0.219944  0.306524  0.223968  0.167552  0.266407  0.205797  0.221872  0.207985  0.287938  0.196705  0.216339  0.303020  0.259518  0.261957  0.188100  0.167847  0.251154  0.205397  0.288637  0.205334  0.266609  0.249891  0.186393  0.253614  0.228233  0.169204  0.194021  0.191007  0.200213  0.200771  0.285865  0.182805  0.172708  0.271653  0.256203  0.248902  0.200486  0.240928  0.248088  0.195545  0.176374  0.165455  0.173284  0.261530  0.257146  0.200806  0.241801  0.223476  0.242259  0.270289  0.183107  0.234895  0.178382  0.265577  0.218717  0.237379  0.210754  0.214485  0.234835  0.182933  0.227153  0.266804  0.194857  0.303816  0.258182  0.299772  0.238674  0.257236  0.233896  0.169299  0.256611  0.218628  0.196093  0.225875  0.260533  0.273049  0.272385  0.254978  0.258801  0.262558  0.280457  0.272910  0.278595  0.218556  0.172874  0.229041  0.294414  0.167829  0.244589  0.239219  0.271310  0.190346  0.233865  0.247725  0.199321  0.249387  0.263199  0.224453  0.239052  0.239945  0.214398  0.208366  0.277810  0.173525  0.238824  0.205135  0.264458  0.202508  0.207576  0.221704  0.199903  0.256447  0.179565  0.226178  0.234633  0.251155  0.224422  0.255414  0.214097  0.233682  0.184813  0.213946  0.187492  0.201918  0.247457  0.215342  0.161458  0.226102  0.178140  0.253435  0.174825  0.207716  0.264825  0.197308  0.251341  0.258090  0.269709  0.227212  0.247212  0.285366  0.256148  0.230967  0.192421  0.246673  0.268059  0.198145  0.198337  0.224714  0.247698  0.296814  0.192114  0.222539  0.247299  0.214766  0.222033  0.178827  0.244699  0.246351  0.271962  0.184588  0.209353  0.235972  0.268815  0.176704  0.256322  0.235491  0.167856  0.200095  0.247514  0.189539  0.218029  0.209648  0.204405  0.202658  0.257491  0.219523  0.257909  0.184099  0.209265  0.255731  0.291229  0.194320  0.209566  0.252475  0.181182  0.268280  0.239875  0.174653  0.236586  0.196262  0.190202  0.197987  0.221523  0.153747  0.266613  0.210963  0.211736  0.209821  0.187837  0.220017  0.202890  0.251058  0.174924  0.281600  0.198393  0.197319  0.273575  0.212924  0.245109  0.231358  0.194372  0.223088  0.208794  0.258627  0.301794  0.247064  0.224548  0.226158  0.255942  0.196676  0.243866  0.221701  0.224427  0.174027  0.241539  0.246784  0.253709  0.231608  0.188740  0.283190  0.263333  0.282781  0.231745  0.201788  0.293353  0.238571  0.221050  0.206307  0.193424  0.268437  0.272811  0.235799  0.237548  0.195551  0.241666  0.204234  0.223118  0.231039  0.196231  0.237160  0.213177  0.233312  0.245206  0.214951  0.216596  0.267278  0.241692  0.230124  0.218784  0.287575  0.242765  0.207072  0.230934  0.178308  0.185801  0.281358  0.244288  0.166990  0.210691  0.236520  0.191615  0.214602  0.206899  0.206421  0.256250  0.251993  0.288800  0.237763  0.299382  0.225799  0.269414  0.258428  0.178452  0.280250  0.203822  0.233316  0.237760  0.198883  0.202134  0.203516  0.220284  0.270455  0.268776  0.241677  0.275193  0.287720  0.257566  0.266053  0.252093  0.248199  0.211655  0.212795  0.221620  0.191229  0.179492  0.205953  0.237224  0.249012  0.177625  0.235466  0.268684  0.252680  0.218647  0.171527  0.255039  0.222196  0.198360  0.274015  0.204920  0.286813  0.209332  0.192959  0.234836  0.208895  0.201494  0.185449  0.225363  0.240403  0.196560  0.195030  0.217604  0.290389  0.214808  0.228716  0.203406  0.250757  0.204832  0.218166  0.238549  0.184940  0.247294  0.276318  0.215380  0.176088  0.251188  0.277331  0.250263  0.227723  0.233254  0.245398  0.213934  0.158498  0.306234  0.256666  0.204829  0.271180  0.267280  0.238213  0.230829  0.246149  0.243281  0.198262  0.184446  0.180740  0.233430  0.199533  0.187814  0.249623  0.227469  0.214407  0.206966  0.212108  0.260797  0.269919  0.229775  0.249886  0.221204  0.275114  0.186984  0.208137  0.227839  0.238247  0.262172  0.266164  0.209262  0.197407  0.213493  0.190127  0.241884  0.196412  0.180729  0.273043  0.248452  0.296738  0.223476  0.260823  0.207764  0.202588  0.240158  0.229726  0.271871  0.267033  0.252304  0.231543  0.206707  0.246285  0.264634  0.200771  0.262158  0.212255  0.294233  0.234990  0.248480  0.244492  0.278259  0.232585  0.189209  0.190769  0.187583  0.203496  0.176950  0.237394  0.242049  0.193633  0.249670  0.196654  0.181838  0.209294  0.171031  0.233948  0.187796  0.225819  0.233317  0.246119  0.205879  0.234000  0.192303  0.230837  0.251157  0.198356  0.212196  0.243677  0.255758  0.245940  0.225502  0.230036  0.184429  0.271681  0.212589  0.233923  0.251734  0.250238  0.181596  0.280832  0.191675  0.231583  0.221694  0.208582  0.189887  0.269203  0.252967  0.163413  0.268833  0.294621  0.212038  0.218071  0.185421  0.188166  0.222691  0.252607  0.235375  0.265923  0.307155  0.306168  0.263225  0.258525  0.163863  0.221357  0.199527  0.220419
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  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  = [ -0.830556 -0.336983 -0.210495 -0.103778  0.522668 -0.202680  0.112054 -0.198090  0.360733 -0.069720 -0.560896 -0.030589 -0.075311 -0.136186 -0.183221 -0.216027 -0.338511 -0.523295 -0.335824 -0.384287 -0.234195 -0.139725  0.524175  0.611013  0.294119 -0.155741 -0.504970  0.396871  0.032533  0.679424 -0.008412  0.516140 -0.506806  0.698643 -0.257797 -0.557501 -0.398533 -0.210505 -0.025504 -0.171055  0.570580 -0.431199 -0.270517  0.772223  0.498375 -0.122669 -0.557491 -0.481808 -0.272266 -0.347100  0.820430 -0.494805 -0.428512  0.317748  0.226127 -0.244234  0.314838 -0.829740 -0.406952 -0.603772 -0.123109  0.059387  0.764148 -0.605100 -0.359754  0.774452  0.059404 -0.066532 -0.122044 -0.193912 -0.069865 -0.150224 -0.187908 -0.503477 -0.537576  0.112122 -0.243833 -0.122348  0.449218 -0.163344  0.155459  0.657276 -0.214478 -0.014553 -0.206239 -0.377649 -0.029773  0.596080  0.165149  0.369016  0.294357 -0.316653 -0.200074  0.255118 -0.647908  0.800201  0.344892  0.772405  0.530315  0.656898 -0.059613 -0.632341 -0.330558  0.616410 -0.423686  0.122505  0.449909  0.653236  0.748879  0.062766 -0.211007  0.661827  0.496241  0.762437  0.693247  0.114001 -0.513585  0.073135  0.846885 -0.505744  0.438824  0.504916  0.642079 -0.541134 -0.045323 -0.101927  0.145417 -0.577115  0.221915  0.381428 -0.245114 -0.595131 -0.277256 -0.611377  0.182032 -0.438871 -0.590240 -0.437915  0.651294 -0.295733 -0.377957 -0.116171 -0.616432  0.025239 -0.595367  0.012543  0.505328 -0.453925  0.088541  0.060248 -0.427259 -0.078133 -0.315238  0.084618  0.310143 -0.427858  0.060453 -0.127455 -0.589859  0.275513 -0.169304 -0.480450 -0.438544 -0.585226 -0.353726 -0.529418 -0.146390  0.109519 -0.195907 -0.103261  0.670689  0.632303 -0.033758  0.272891 -0.499861 -0.182349  0.579357 -0.295151 -0.251224 -0.258571 -0.280589  0.775127 -0.634224  0.002588 -0.154379 -0.071047 -0.160104 -0.234267 -0.005085 -0.476341  0.652362 -0.485997 -0.387591 -0.101730  0.580670 -0.405807  0.659052 -0.165194 -0.629341 -0.607227  0.499966 -0.311640 -0.197706 -0.276943 -0.225777 -0.537414 -0.309025  0.143497  0.674706 -0.570043 -0.386533 -0.287061  0.754219 -0.149617 -0.373758  0.371483 -0.429142  0.678767  0.658098 -0.494003  0.165842 -0.462680 -0.553775 -0.262881  0.104923 -0.698564  0.464263  0.060219  0.431439 -0.472174 -0.581541 -0.054293 -0.346541 -0.115603 -0.517419  0.495624 -0.182804 -0.133208  0.183526  0.590125 -0.181875  0.267219 -0.263242  0.013248  0.149110 -0.305953  0.794161  0.514575  0.299319 -0.236141 -0.033831 -0.138943  0.679665 -0.145001 -0.267070 -0.466701 -0.194250 -0.135930  0.443944 -0.088838 -0.617093  0.644479 -0.374783  0.826057  0.409073  0.216416  0.783180  0.635291 -0.295741 -0.172298 -0.658609 -0.394685  0.263211  0.117922 -0.104399  0.288156  0.609298 -0.556928  0.284650 -0.024830 -0.192530  0.597254 -0.417265  0.269904 -0.576280 -0.379906  0.087633  0.731162  0.504069  0.448376  0.330078  0.849099  0.565094 -0.685777  0.581326  0.508625 -0.578853  0.661323 -0.255112 -0.814772  0.060483 -0.166705 -0.632899 -0.259623 -0.685317 -0.061139 -0.506711 -0.180546  0.650980  0.527865  0.763206 -0.551161 -0.386550 -0.202162 -0.595569  0.076354 -0.329217  0.013311 -0.216192 -0.537140 -0.410537  0.410330 -0.492934  0.698737  0.764271 -0.208644  0.671873  0.820740  0.695658 -0.344086 -0.206077 -0.099910  0.375769 -0.384999  0.236000  0.225069 -0.164540 -0.539880  0.082048  0.090041 -0.454413 -0.202093  0.766436 -0.245486  0.327767 -0.291197  0.545121 -0.000962 -0.531804 -0.044253 -0.295873  0.770782 -0.236811  0.296952 -0.166196  0.305494  0.371653 -0.471915 -0.479777  0.152812 -0.400296  0.102655 -0.236275  0.636519 -0.140516 -0.199928 -0.100695  0.665664 -0.223748 -0.236103  0.025962  0.503793 -0.285924  0.780172  0.321310 -0.519210  0.436002  0.808842  0.100754  0.319898  0.022931  0.273852  0.203235 -0.694350  0.676701  0.046736 -0.411057  0.743477 -0.197060  0.497697 -0.282372 -0.272618  0.563251 -0.142123 -0.200564 -0.526938  0.025325 -0.445612 -0.548513  0.375214  0.629199 -0.267984 -0.416614 -0.357247 -0.025399  0.767790  0.009624 -0.280852 -0.316964  0.651415 -0.252815  0.223406 -0.124122 -0.590343 -0.345025  0.289516 -0.427742 -0.292995 -0.237760 -0.548912  0.608970 -0.141233 -0.296840  0.673844 -0.068789  0.684987  0.280217 -0.347540 -0.008067  0.063006  0.171395 -0.170867  0.671561  0.718603  0.669109  0.010943  0.430890 -0.297568 -0.307219 -0.607395 -0.114249  0.091988  0.630800  0.385563  0.650103  0.514753  0.667468  0.269230 -0.541074 -0.175206 -0.141042 -0.439920 -0.472518  0.290018  0.657688 -0.606118  0.375598 -0.138658 -0.605797  0.162620 -0.567575 -0.025055 -0.544088 -0.186048  0.475633 -0.136863  0.431502 -0.120729 -0.633691  0.629587  0.663852 -0.206615  0.493142  0.493265 -0.286911 -0.189417  0.129706  0.571543 -0.159521  0.667165  0.309088  0.120780 -0.456208  0.566454 -0.565159  0.616498 -0.571134  0.014154 -0.291376 -0.006974 -0.604520  0.073205  0.344895 -0.614894 -0.356392  0.723756  0.424075  0.368070 -0.182091 -0.255864  0.343983 -0.218760  0.397525  0.659974  0.774841  0.735902  0.223572  0.138812 -0.515249  0.552865 -0.292584  0.276131
         0.540205  0.601230  0.722370 -1.074075 -0.912755 -0.735472  0.996411  0.655380  0.882780  0.797596 -0.514545 -1.095191 -0.844837 -0.635770  0.685179  0.698226 -0.336813 -0.472556  0.341538  0.773665  0.462364  1.006970 -0.911622  0.577352 -0.742472  0.656262  0.824492 -0.948612 -0.356291  0.431845  1.017200 -0.901185 -0.855533 -0.485370  0.606921 -0.531503 -0.019723  0.755753 -1.094203 -1.042832 -0.632247  0.688025 -0.736026  0.363113 -0.925915 -0.914245 -0.463481  0.693244 -0.590771  0.867970  0.316080 -0.675665  0.266450 -0.052126 -1.048561 -0.425566  0.810218  0.541287  0.651819 -0.729229  0.612711 -1.114026 -0.261987  0.738493  0.758951  0.379455  0.979417 -0.126308  0.613267 -0.845174 -0.130013  0.609254  0.554534  0.824587  0.858857  0.948319 -0.285460  0.618225 -0.933264  0.527481  0.976518 -0.566801  0.696925 -0.835905  0.521421  0.387728 -0.581869  0.383773  0.999047  0.595862 -0.777706  0.703062  0.574272  0.421039 -0.792736 -0.021420  0.858680  0.395196 -0.888323  0.485969 -0.746247 -0.637874  0.303767  0.535334  0.639564 -0.893041 -0.956826 -0.698403  0.293460  0.979463 -0.569433 -0.598619 -0.801845  0.323008 -0.451256 -0.803306 -0.446415 -0.847047 -0.050526  0.824256 -0.931171 -0.926400 -0.763440 -0.406134 -0.791022 -0.845244 -1.030508  0.310998  0.932117 -0.832178  0.556051  0.392509  0.649160 -0.734029  0.956194 -0.515484  0.420420  0.617512 -0.545087  0.671670  0.752564 -0.669813  0.605300 -1.030655  0.819911 -0.891662 -0.920462  0.285024 -0.697148  0.790643 -0.578664  0.876545  0.705384 -0.702321 -1.026776  0.689988  0.993824 -0.866782 -0.301720 -0.555877 -1.050673  0.265788 -0.518291 -0.487330 -0.439555 -0.563633  0.468261  0.996360  0.286461  0.731925  0.406609 -0.595461 -0.766278 -0.645343  0.768890  0.533947 -0.837868  0.648375  0.768276  0.607935 -0.702007  0.353667 -0.800306 -0.622684  0.497205 -0.477463 -0.749392  0.639921 -0.986810  0.382747 -0.699816 -0.505086  0.694764 -0.746049 -0.836886 -0.473111  0.376103  0.615844 -0.625654 -0.468266 -0.928580  0.735892  0.612355  0.833451  0.662554 -0.565029 -0.206676 -0.874973  0.472430 -0.160490  0.695209 -0.130322 -0.327804  0.607753  0.722261 -0.597401 -0.510312 -0.636001  0.419869 -0.340919  0.973686  0.688324 -0.538599  0.847063 -0.816728 -0.054083 -0.945653  0.967250 -0.716843 -0.964207 -0.622050 -0.613889  0.778566  0.712028 -0.453299 -0.801634  0.684698  0.626086 -0.096192  0.426780  0.536589  0.954768  0.844276 -0.893530 -0.828421 -0.206432  0.320117 -0.890519 -0.932926  0.975016 -0.766486  0.677470  0.434176 -1.091844  0.906088 -0.438686 -0.844691  0.510863 -0.959562  0.728603 -0.697707  0.654641  0.258606  0.200063 -0.926181 -0.805485  0.345685  0.429132 -0.738838 -1.043081 -0.745579 -0.020489 -0.223598  0.464146 -0.705505 -0.889779  0.418438 -0.531931 -0.991352  1.030793  0.664488  0.382266  0.734099  0.953616  0.366974  0.775065 -0.530421  0.343504 -0.926851 -0.937674  0.608656  0.215283 -0.837417 -0.853805 -0.895475 -0.916924 -0.634548 -0.526090 -0.709758  0.633391  0.967134  0.613800 -0.801063 -1.045833 -0.854368 -1.071663  0.094325  0.467681 -0.550449 -0.842823  0.425020  0.482483 -0.420615 -0.437413  0.819967  0.973623  0.861101  0.925719 -0.608789 -0.718709  0.752682 -0.777869 -0.799988  0.509987  0.362309  0.508693 -0.566242  0.316464  0.382717 -0.165002 -0.254563 -0.845242  0.504007  0.690217 -0.676841 -1.047447  0.597453 -0.567470  1.013899 -1.059241 -0.450851  0.507294  0.358216 -0.427221  0.609233  0.484503 -0.891989 -0.622847 -0.585778 -0.143286  0.806043  0.401489 -0.957473 -1.051444  0.616397 -0.747472 -0.862702  0.584229  0.472287  0.977678  0.729268 -1.111488  0.610967  0.651606  0.942739  0.494475 -0.986412  0.344785  0.663549  0.611734  0.999322 -0.913574  0.329957  0.264785 -0.913248 -0.453746 -0.255289  0.340305 -1.062597  0.942252  0.435539  0.854546 -0.593884  0.584966 -0.501087  1.000774  0.754488 -0.151147 -0.920152 -0.806483 -0.719015  0.423980 -0.818663  0.714577  0.664596 -0.473873  0.435863 -0.707018 -0.528740 -0.599283  0.449046  0.558383  0.619192  0.784894  0.993093  0.427260 -0.798804 -0.699297 -0.756178 -0.581247  0.739339 -0.913075  0.975140  0.421090 -0.140151 -0.888864  0.734812  0.848895  0.922279 -0.577873  0.418607  0.637165  0.836764 -0.565964 -0.125325 -0.487804 -0.993252 -0.142596 -0.881989 -1.113237 -0.975035  0.504206 -0.537665  0.262176  0.456662 -0.797116 -0.796377 -0.805089  0.076858 -0.469347 -0.936442 -0.862173 -0.615918 -0.728306  0.400927 -0.908167 -0.536214  0.953904  0.685538  0.592985  0.600843  0.834250  0.051838 -0.892202  0.417208 -0.729308 -0.599181  0.609883  0.737279 -1.044768 -0.574548  1.031097 -0.479625  0.593175 -0.937526  0.511505 -0.796699  0.993287 -0.800794  0.455422  0.347070  0.765280  0.815182 -0.902703 -0.133535  0.557226  1.004857  0.470895  0.656722 -0.486006 -0.783403  0.467908  0.279250 -0.867196 -0.160209 -0.581723 -0.478013  0.926464  0.935334 -0.881535 -0.727714 -0.978405  0.860908  0.602296  0.121665  0.523423 -0.760704 -0.652519  0.783176  0.739598 -0.587859  0.595621  0.448997 -0.567798 -0.116414 -0.410804  0.931783 -1.055343 -0.501096 -0.862424  0.850020 -0.918552
        -0.124854 -0.570434 -0.496421  0.365710  0.268849  0.941127  0.456262 -0.558895  0.583938 -0.435747 -0.562392  0.241544  0.860437  1.040717 -0.537072 -0.515570  1.124983 -0.612814 -0.725756 -0.373692 -0.690428  0.404828  0.268157  0.793186  0.916191 -0.566911 -0.143242  0.525803  1.199248  0.840216  0.426837  0.416128 -0.288643  0.824280 -0.577044 -0.554377  1.142303 -0.463610  0.077868  0.454265  0.847675 -0.452545  0.915052  0.765573  0.318267  0.734442 -0.597680 -0.398258  1.031404 -0.229851  0.713765 -0.495950  1.070555  1.204866  0.458076  1.131329  0.766228 -0.125709 -0.500039 -0.359683 -0.604417  0.288473  0.868096 -0.185659 -0.389274  0.746813  0.548485  1.240368 -0.604144  0.820972  1.239554 -0.604188 -0.639718 -0.145376  0.300660  0.611691  1.178546 -0.600453  0.589882  1.050732  0.504706  0.807309 -0.517297  0.870742 -0.659451  1.048307  1.095317  0.950339  0.036138  0.949911  0.876667 -0.486506 -0.608793  1.152821 -0.221238  0.864262  0.656956  0.738033  0.422251  0.938062  0.968221 -0.406804  1.112194  0.829497 -0.503548  0.812361  0.225940  0.651647  0.842153  0.547260  1.067759  0.769267  0.717809  0.805782  0.857537  0.919175 -0.631632  0.873973  0.788833 -0.143002  0.478833  0.272991  0.544508 -0.635339  0.926995  0.856258  0.545880  0.944685  0.593152  0.750524  1.011620  0.882014 -0.541856  0.751509  0.553539 -0.635224  0.869320 -0.514922  0.834100 -0.521509 -0.405668  1.035438 -0.342078  0.493357  0.319492  0.822977  0.561784  1.050895  1.004656  0.861204  1.008376 -0.317337 -0.484625  1.000079  0.452547 -0.452085  0.497818  0.826869 -0.646698  1.061250 -0.148605  1.040923 -0.633924 -0.568891  1.075742 -0.557300  1.099663  0.459410  1.173424 -0.490399  0.866994  0.810858  0.955926  1.003623 -0.309807  1.048628  0.491788 -0.544068 -0.436501 -0.576298  0.939347  0.767520 -0.228098  1.072417  1.080642  1.145151  0.943496 -0.563794  0.641960  0.990651  0.650560 -0.616916 -0.463790  0.956517  0.492545 -0.671364  0.898743  0.994848 -0.421431 -0.565153  0.299314 -0.450646 -0.584050 -0.346996 -0.549120 -0.551629  1.170910  0.834133  0.814469 -0.695124 -0.463877  1.189273  0.852696 -0.605414 -0.441943  1.006344 -0.643260  0.700382  0.871551 -0.686725 -0.014941 -0.437336 -0.558034 -0.316671  0.906155 -0.612303  0.344732 -0.137877  0.869957  0.508746 -0.479772  1.076932 -0.389247  0.918759 -0.626024  0.718953 -0.537518 -0.593172  1.269741  0.926308  1.047064  0.467675 -0.320286  0.819887  0.873285  1.172045  0.758920  0.458594  0.652589  0.472110  0.955720 -0.550135  0.838399  0.074634 -0.228954 -0.659427  0.821583  1.076895  0.351639 -0.493765 -0.379818  0.639848  1.104809  0.772424  0.646391  0.881767  0.759955  0.888216  0.901306  0.452587 -0.276394  1.144334  1.246508  1.105016  0.995500  0.753076  0.917558 -0.560617  0.528880  0.126984 -0.554171  0.950120 -0.406603  0.469629  0.915711 -0.377218  1.116333  0.835888  0.275464  0.440473  0.957214  0.722476  0.514692  0.415883  0.516657  0.498735 -0.471208  0.838966  0.944227  0.198879 -0.138149  0.995876 -0.228597 -0.062684  0.415710  0.410073  1.068178  1.090438  0.830424  0.567601  0.726904  0.864288  1.065995  1.140503  0.318379  0.563462 -0.254460  0.676307  1.038738 -0.427676 -0.389840  0.821616 -0.372344  0.746839  0.776074  1.049941  0.788979  0.712849  0.854512  1.162236  1.197135  0.856732  1.010910 -0.470476  0.992284  0.462912 -0.611000 -0.548335  0.383928  0.329025 -0.659824  1.052671  0.775982  1.130394  0.957078 -0.665101  0.332981  1.072074 -0.540925  1.258397 -0.373976  0.735469  0.636487  0.382697  0.994193  0.906836  0.742465 -0.534850  0.932348  0.502851 -0.421564  0.262715 -0.579996  0.659329  0.616940  1.060652  0.641007  0.910572 -0.548693 -0.579434  0.493599  0.514334  1.120182  0.813855  0.726115 -0.624860  1.134443  0.717045  0.256168  0.442821  1.124754  0.718932  1.060767 -0.320886  0.840902  0.477815 -0.387144  0.924083  0.679467  0.681894  0.925754  1.079401  0.702956 -0.516032 -0.550316 -0.610023  1.124930 -0.495595 -0.567445  1.003492  0.881179  0.996837 -0.522823 -0.375664  0.528440  0.716844  0.925323  0.941535  0.872810  0.801612 -0.464036  0.764614 -0.114394  0.868744  1.164763  0.797923 -0.401792 -0.297189 -0.211083 -0.535734  0.917777 -0.583596 -0.307281  0.786828  1.239918  0.840974  0.529238  1.163414  0.821747  0.290290  0.664054  1.063198  0.816201  0.894915  0.833950  0.927092  0.786118  0.818002  1.179108 -0.564478  0.695560  0.843477  0.791584  0.876303  0.892224  0.375080  0.822589  0.468902 -0.392228 -0.612155 -0.611246 -0.208351 -0.747921  0.720644  0.873724 -0.357057  1.003539 -0.604526 -0.186626  0.515913 -0.517537  0.129892 -0.596929 -0.597885  0.356739  1.076231  0.785290  0.476151 -0.227909  0.876446  0.910972 -0.451066  0.608119  0.464470  1.189300  1.030385  0.405619  0.915751 -0.564164  0.863443  0.870010  1.103139  1.051474  0.404434 -0.697627  0.843363 -0.581717  0.674573 -0.154956  0.822565 -0.360803  0.663358  0.651741 -0.391242  1.150579  0.690160  0.831020  0.960129 -0.426837 -0.462854  1.016388  0.990078  1.035867  0.802943  0.894183  0.828670  0.593177  0.372724 -0.601004  0.633608 -0.295068  0.737966
         1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  1.000000  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 = [-0.999166 0.040392 0.005912]';
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 = [0.908565 -0.130276 0.396909]';
q1c = [0.015708 0.048890 -0.312476]';
t1c = twist_matrix_fast(w1c,q1c,Theta(1));

w1d = [-0.413727 -0.149197 0.898092]';
q1d = [0.015708 0.048890 -0.312476]';
t1d = twist_matrix_fast(w1d,q1d,Theta(2));

w1e = [-0.057782 -0.980188 -0.189454]';
q1e = [0.015708 0.048890 -0.312476]';
t1e = twist_matrix_fast(w1e,q1e,Theta(3));

w4a = [0.003701 -0.986748 -0.162220]';
q4a = [-0.049932 0.025219 -0.169989]';
t4a = twist_matrix_fast(w4a,q4a,Theta(4));

w4b = [0.296280 -0.153856 0.942627]';
q4b = [-0.049932 0.025219 -0.169989]';
t4b = twist_matrix_fast(w4b,q4b,Theta(5));

w4c = [0.955094 0.051551 -0.291784]';
q4c = [-0.049932 0.025219 -0.169989]';
t4c = twist_matrix_fast(w4c,q4c,Theta(6));

w5a = [-0.151657 -0.981997 -0.112614]';
q5a = [0.002680 -0.002102 -0.002603]';
t5a = twist_matrix_fast(w5a,q5a,Theta(7));

w5b = [0.033589 -0.118986 0.992328]';
q5b = [0.002680 -0.002102 -0.002603]';
t5b = twist_matrix_fast(w5b,q5b,Theta(8));

w5c = [0.987862 -0.146710 -0.051029]';
q5c = [0.002680 -0.002102 -0.002603]';
t5c = twist_matrix_fast(w5c,q5c,Theta(9));

w6a = [0.068498 -0.990279 -0.121059]';
q6a = [0.006943 -0.017204 0.123346]';
t6a = twist_matrix_fast(w6a,q6a,Theta(10));

w6b = [-0.541912 -0.138815 0.828892]';
q6b = [0.006943 -0.017204 0.123346]';
t6b = twist_matrix_fast(w6b,q6b,Theta(11));

w6c = [0.837639 -0.008826 0.546153]';
q6c = [0.006943 -0.017204 0.123346]';
t6c = twist_matrix_fast(w6c,q6c,Theta(12));

w7a = [0.014132 -0.987631 -0.156159]';
q7a = [-0.027136 -0.025934 0.175473]';
t7a = twist_matrix_fast(w7a,q7a,Theta(13));

w7b = [0.848419 -0.070802 0.524569]';
q7b = [-0.027136 -0.025934 0.175473]';
t7b = twist_matrix_fast(w7b,q7b,Theta(14));

w7c = [0.529136 0.139902 -0.836924]';
q7c = [-0.027136 -0.025934 0.175473]';
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
