MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: smallinvSNPr1b100-110

Small Investor Mean-Variance Portfolio Optimization
This is a natural extension of the standard Markovitz Mean-Variance-Optimization
(MVO) model by constraints for small investors. The variables in the standard
Markovitz model determine which fraction of the investment is made in the
repective assets. When the investment is bounded within a range that is not very
much bigger than the prices of the assets, one has to take into account that
each asset has a minimum unit of which only integer multiples can be traded,
e.g. 1, 0.1, or 0.01. Hence, the optimization problem for the small investor has
integer variables in addition to the budget constraints that define lower and
upper bounds on the investment.
Update (2018-08-07): After a fix to the convexity check routines, it was found that
the smallest eigenvalue of the quadratic coefficients matrix in the quadratic constraint
is slightly negative (about -2e-7). Though these instances were originally intended to be
convex, a loss of precision in the process of creating the original POLIP instance lead to
a loss of positive semi-definiteness in the coefficients matrix.
Formats ams gms lp mod nl osil pip
Primal Bounds (infeas ≤ 1e-08)
5.81307796 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
4.38157755 (ANTIGONE)
5.81307796 (BARON)
5.81307796 (COUENNE)
5.81307796 (LINDO)
-0.99660118 (SCIP)
Source POLIP instance portfolio/small-investor-MVO-SNP100-return_0.0010-budget_10000-11000
Application Portfolio Optimization
Added to library 26 Feb 2014
Problem type MIQCP
#Variables 101
#Binary Variables 0
#Integer Variables 100
#Nonlinear Variables 100
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 100
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 4
#Linear Constraints 3
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 401
#Nonlinear Nonzeros in Jacobian 100
#Nonzeros in (Upper-Left) Hessian of Lagrangian 10000
#Nonzeros in Diagonal of Hessian of Lagrangian 100
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 100
Maximal blocksize in Hessian of Lagrangian 100
Average blocksize in Hessian of Lagrangian 100.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1e+04
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        0        2        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        101        1        0      100        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        401      301      100        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
          ,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35,i36
          ,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,i53
          ,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,i64,i65,i66,i67,i68,i69,i70
          ,i71,i72,i73,i74,i75,i76,i77,i78,i79,i80,i81,i82,i83,i84,i85,i86,i87
          ,i88,i89,i90,i91,i92,i93,i94,i95,i96,i97,i98,i99,i100,objvar;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17
          ,i18,i19,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34
          ,i35,i36,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51
          ,i52,i53,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,i64,i65,i66,i67,i68
          ,i69,i70,i71,i72,i73,i74,i75,i76,i77,i78,i79,i80,i81,i82,i83,i84,i85
          ,i86,i87,i88,i89,i90,i91,i92,i93,i94,i95,i96,i97,i98,i99,i100;

Equations  e1,e2,e3,e4;


e1.. 0.00841507*sqr(i1) + 0.0222536*sqr(i2) + 0.0056479*sqr(i3) + 0.00333322*
     sqr(i4) + 0.00490963*sqr(i5) + 0.0221034*sqr(i6) + 0.00509899*sqr(i7) + 
     0.049464*sqr(i8) + 0.0171508*sqr(i9) + 0.0064643*sqr(i10) + 0.0218437*sqr(
     i11) + 0.00346366*sqr(i12) + 0.0458502*sqr(i13) + 0.0747061*sqr(i14) + 
     0.0196511*sqr(i15) + 0.014222*sqr(i16) + 0.0147535*sqr(i17) + 0.00398615*
     sqr(i18) + 0.00644484*sqr(i19) + 0.0322232*sqr(i20) + 0.00887889*sqr(i21)
      + 0.0434025*sqr(i22) + 0.00981376*sqr(i23) + 0.0133193*sqr(i24) + 
     0.00471036*sqr(i25) + 0.00359843*sqr(i26) + 0.0112312*sqr(i27) + 
     0.00476479*sqr(i28) + 0.00356255*sqr(i29) + 0.0730121*sqr(i30) + 
     0.00785721*sqr(i31) + 0.0243787*sqr(i32) + 0.0171188*sqr(i33) + 0.00439547
     *sqr(i34) + 0.00502594*sqr(i35) + 0.0580619*sqr(i36) + 0.0135984*sqr(i37)
      + 0.00254137*sqr(i38) + 0.0153341*sqr(i39) + 0.109758*sqr(i40) + 
     0.0346065*sqr(i41) + 0.0127589*sqr(i42) + 0.011147*sqr(i43) + 0.0156318*
     sqr(i44) + 0.00556588*sqr(i45) + 0.00302864*sqr(i46) + 0.0214898*sqr(i47)
      + 0.00499587*sqr(i48) + 0.00864393*sqr(i49) + 0.0228248*sqr(i50) + 
     0.0077726*sqr(i51) + 0.00992767*sqr(i52) + 0.0184506*sqr(i53) + 0.0113481*
     sqr(i54) + 0.0067583*sqr(i55) + 0.0150416*sqr(i56) + 0.00324193*sqr(i57)
      + 0.00478196*sqr(i58) + 0.0132471*sqr(i59) + 0.00273446*sqr(i60) + 
     0.0282459*sqr(i61) + 0.0230221*sqr(i62) + 0.0240972*sqr(i63) + 0.00829946*
     sqr(i64) + 0.00688665*sqr(i65) + 0.00858803*sqr(i66) + 0.00778038*sqr(i67)
      + 0.0082583*sqr(i68) + 0.022885*sqr(i69) + 0.00568332*sqr(i70) + 
     0.0234021*sqr(i71) + 0.00924249*sqr(i72) + 0.00669675*sqr(i73) + 0.0109501
     *sqr(i74) + 0.00663385*sqr(i75) + 0.00328058*sqr(i76) + 0.0112814*sqr(i77)
      + 0.00341076*sqr(i78) + 0.0400653*sqr(i79) + 0.00876827*sqr(i80) + 
     0.0138276*sqr(i81) + 0.00246987*sqr(i82) + 0.0406516*sqr(i83) + 0.00947194
     *sqr(i84) + 0.00647449*sqr(i85) + 0.0107715*sqr(i86) + 0.00803069*sqr(i87)
      + 0.106502*sqr(i88) + 0.00815263*sqr(i89) + 0.0171707*sqr(i90) + 
     0.0163522*sqr(i91) + 0.00911726*sqr(i92) + 0.00287317*sqr(i93) + 
     0.00360309*sqr(i94) + 0.00699161*sqr(i95) + 0.0340959*sqr(i96) + 
     0.00958446*sqr(i97) + 0.0147951*sqr(i98) + 0.0177595*sqr(i99) + 0.0208523*
     sqr(i100) + 0.00692522*i1*i2 + 0.00066464*i1*i3 + 0.00388744*i1*i4 + 
     0.001108218*i1*i5 + 0.0046712*i1*i6 + 0.00771824*i1*i7 + 0.0020653*i1*i8
      + 0.001524626*i1*i9 + 0.00484724*i1*i10 + 0.00733242*i1*i11 + 0.00556218*
     i1*i12 + 0.0052571*i1*i13 + 0.0218926*i1*i14 + 0.01352862*i1*i15 + 
     0.00549784*i1*i16 + 0.00235342*i1*i17 + 0.00448206*i1*i18 + 0.0072148*i1*
     i19 + 0.00958894*i1*i20 + 0.00376328*i1*i21 + 0.0117501*i1*i22 + 
     0.00575998*i1*i23 - 0.000109147*i1*i24 + 0.000604944*i1*i25 + 0.00473296*
     i1*i26 + 0.000356572*i1*i27 - 0.001552262*i1*i28 + 0.00119092*i1*i29 + 
     0.01373684*i1*i30 + 0.0059113*i1*i31 + 0.00623524*i1*i32 + 0.00801204*i1*
     i33 + 0.00108736*i1*i34 + 0.001491474*i1*i35 + 0.01080356*i1*i36 + 
     0.00559202*i1*i37 + 7.8057e-6*i1*i38 + 0.00831004*i1*i39 + 0.001096208*i1*
     i40 + 0.001136658*i1*i41 + 0.0073715*i1*i42 + 0.000726938*i1*i43 + 
     0.00621872*i1*i44 + 0.00646596*i1*i45 + 0.00441466*i1*i46 + 0.001262528*i1
     *i47 + 0.00567366*i1*i48 + 0.00690472*i1*i49 + 0.01140754*i1*i50 + 
     0.00275514*i1*i51 + 0.00633434*i1*i52 + 0.00842252*i1*i53 + 0.00674544*i1*
     i54 + 0.00577156*i1*i55 + 0.000723972*i1*i56 + 0.00617654*i1*i57 + 
     0.00426758*i1*i58 + 0.00581362*i1*i59 + 0.00305964*i1*i60 + 0.00915838*i1*
     i61 + 0.00408204*i1*i62 + 0.00526036*i1*i63 + 0.00641708*i1*i64 + 
     0.001311362*i1*i65 + 0.00589896*i1*i66 + 0.001450664*i1*i67 + 0.0054669*i1
     *i68 + 0.00759698*i1*i69 + 0.0069591*i1*i70 + 0.0023689*i1*i71 + 0.0026146
     *i1*i72 + 0.00520422*i1*i73 + 0.00959956*i1*i74 + 0.00799166*i1*i75 + 
     0.00256248*i1*i76 + 0.01210352*i1*i77 + 0.00469514*i1*i78 + 0.00329676*i1*
     i79 + 0.0068214*i1*i80 + 0.00190637*i1*i81 + 0.00256972*i1*i82 - 
     0.00577696*i1*i83 + 0.00245394*i1*i84 + 0.00585966*i1*i85 + 0.00330078*i1*
     i86 + 0.00362852*i1*i87 + 0.0064137*i1*i88 + 0.00375038*i1*i89 + 
     0.00666048*i1*i90 + 0.00942176*i1*i91 + 0.00379828*i1*i92 + 0.00246526*i1*
     i93 + 0.0029997*i1*i94 + 0.00592606*i1*i95 + 0.0136565*i1*i96 + 0.00562112
     *i1*i97 + 0.0031101*i1*i98 + 0.00328418*i1*i99 + 0.00992138*i1*i100 + 
     0.01159836*i2*i3 + 0.00432612*i2*i4 + 0.01055774*i2*i5 + 0.0235592*i2*i6
      + 0.0053913*i2*i7 + 0.01748966*i2*i8 + 0.01322526*i2*i9 + 0.01103896*i2*
     i10 + 0.001420928*i2*i11 + 0.00303766*i2*i12 + 0.0325414*i2*i13 + 
     0.0528886*i2*i14 + 0.0344486*i2*i15 + 0.01889664*i2*i16 + 0.01085498*i2*
     i17 + 0.01133696*i2*i18 + 0.0105108*i2*i19 + 0.041965*i2*i20 + 0.01908526*
     i2*i21 + 0.0438608*i2*i22 + 0.01760436*i2*i23 + 0.0177692*i2*i24 + 
     0.01401386*i2*i25 + 0.01130076*i2*i26 + 0.0201926*i2*i27 + 0.00893526*i2*
     i28 + 0.01013464*i2*i29 + 0.0522552*i2*i30 + 0.00674062*i2*i31 + 0.0386894
     *i2*i32 + 0.01840562*i2*i33 + 0.0079061*i2*i34 + 0.01050574*i2*i35 + 
     0.038882*i2*i36 + 0.0209782*i2*i37 + 0.00569346*i2*i38 + 0.0259324*i2*i39
      + 0.0472088*i2*i40 + 0.0282636*i2*i41 + 0.0225892*i2*i42 + 0.01104052*i2*
     i43 + 0.0218496*i2*i44 + 0.00682534*i2*i45 + 0.01022898*i2*i46 + 0.0273094
     *i2*i47 + 0.01045064*i2*i48 + 0.01767338*i2*i49 + 0.0311902*i2*i50 + 
     0.0126455*i2*i51 + 0.0206168*i2*i52 + 0.0261894*i2*i53 + 0.024527*i2*i54
      + 0.01734138*i2*i55 + 0.01224052*i2*i56 + 0.01152072*i2*i57 + 0.01028864*
     i2*i58 + 0.01883544*i2*i59 + 0.00908648*i2*i60 + 0.0449708*i2*i61 + 
     0.0363664*i2*i62 + 0.01577062*i2*i63 + 0.01266282*i2*i64 + 0.01385216*i2*
     i65 + 0.00440902*i2*i66 + 0.01711764*i2*i67 + 0.0110787*i2*i68 + 0.0341778
     *i2*i69 + 0.0156542*i2*i70 + 0.01891112*i2*i71 + 0.0216326*i2*i72 + 
     0.01534328*i2*i73 + 0.01661334*i2*i74 + 0.01534594*i2*i75 + 0.01116732*i2*
     i76 + 0.01402982*i2*i77 + 0.00963242*i2*i78 + 0.0200668*i2*i79 + 
     0.01379116*i2*i80 + 0.01910046*i2*i81 + 0.0077605*i2*i82 - 0.000954558*i2*
     i83 + 0.01255918*i2*i84 + 0.0126639*i2*i85 + 0.0201936*i2*i86 + 0.017931*
     i2*i87 + 0.0389418*i2*i88 + 0.00845916*i2*i89 + 0.0267914*i2*i90 + 
     0.0193905*i2*i91 + 0.01261014*i2*i92 + 0.0069012*i2*i93 + 0.00876014*i2*
     i94 + 0.01829908*i2*i95 + 0.0373396*i2*i96 + 0.0211262*i2*i97 + 0.01549032
     *i2*i98 + 0.0247114*i2*i99 + 0.0324248*i2*i100 - 0.000720538*i3*i4 + 
     0.00453322*i3*i5 + 0.00638226*i3*i6 + 0.000938158*i3*i7 + 0.0035154*i3*i8
      + 0.00681962*i3*i9 + 0.006345*i3*i10 + 0.00232904*i3*i11 - 0.00054599*i3*
     i12 + 0.01850556*i3*i13 + 0.01892336*i3*i14 + 0.00820906*i3*i15 + 
     0.00848796*i3*i16 + 0.0100743*i3*i17 + 0.00327798*i3*i18 + 0.000498452*i3*
     i19 + 0.01775572*i3*i20 + 0.00919688*i3*i21 + 0.01282772*i3*i22 + 
     0.00853066*i3*i23 + 0.00506148*i3*i24 + 0.004557*i3*i25 + 0.001737768*i3*
     i26 + 0.00560326*i3*i27 + 0.00374962*i3*i28 + 0.000427408*i3*i29 + 
     0.01831098*i3*i30 + 0.00791496*i3*i31 + 0.01306*i3*i32 + 0.0143109*i3*i33
      + 0.00324578*i3*i34 + 0.00289704*i3*i35 + 0.01899172*i3*i36 + 0.00855898*
     i3*i37 + 0.000764782*i3*i38 + 0.01045622*i3*i39 + 0.0241684*i3*i40 + 
     0.01022702*i3*i41 + 0.0096569*i3*i42 + 0.00605256*i3*i43 + 0.0087656*i3*
     i44 + 0.00231868*i3*i45 + 0.003075*i3*i46 + 0.00904418*i3*i47 + 0.00346386
     *i3*i48 + 0.00970054*i3*i49 + 0.0107517*i3*i50 + 0.00833706*i3*i51 + 
     0.00601022*i3*i52 + 0.00885472*i3*i53 + 0.0087269*i3*i54 + 0.00799796*i3*
     i55 + 0.0077742*i3*i56 + 0.00233028*i3*i57 + 0.00392772*i3*i58 + 
     0.00960436*i3*i59 + 0.000506858*i3*i60 + 0.01485036*i3*i61 + 0.01172454*i3
     *i62 + 0.00763564*i3*i63 + 0.00510368*i3*i64 + 0.00739458*i3*i65 + 
     0.00321864*i3*i66 + 0.00506992*i3*i67 + 0.001582392*i3*i68 + 0.0133327*i3*
     i69 + 0.00346984*i3*i70 + 0.00591914*i3*i71 + 0.0050918*i3*i72 + 
     0.00762942*i3*i73 + 0.0072567*i3*i74 + 0.0028432*i3*i75 + 0.00258746*i3*
     i76 + 0.00665946*i3*i77 + 0.001559716*i3*i78 + 0.0114221*i3*i79 + 
     0.00359546*i3*i80 + 0.00675946*i3*i81 + 0.001328782*i3*i82 + 0.00450512*i3
     *i83 + 0.00859628*i3*i84 + 0.00541618*i3*i85 + 0.01126372*i3*i86 + 
     0.00604642*i3*i87 + 0.01802074*i3*i88 + 0.0056414*i3*i89 + 0.00952436*i3*
     i90 + 0.00568388*i3*i91 + 0.0086732*i3*i92 + 0.001482822*i3*i93 + 
     0.0026677*i3*i94 + 0.00675394*i3*i95 + 0.01169216*i3*i96 + 0.0076724*i3*
     i97 + 0.00761804*i3*i98 + 0.01192344*i3*i99 + 0.01326866*i3*i100 + 
     0.00169903*i4*i5 + 0.00300136*i4*i6 + 0.00385392*i4*i7 + 0.00382362*i4*i8
      + 0.00575034*i4*i9 + 0.00125203*i4*i10 + 0.000828078*i4*i11 + 0.00404896*
     i4*i12 - 0.001180878*i4*i13 + 0.00956206*i4*i14 + 0.00571904*i4*i15 + 
     0.0047927*i4*i16 + 0.001736122*i4*i17 + 0.001900434*i4*i18 + 0.00498296*i4
     *i19 + 0.0055112*i4*i20 + 0.00199047*i4*i21 + 0.00302926*i4*i22 + 
     0.001107052*i4*i23 + 0.0032099*i4*i24 + 0.00202704*i4*i25 + 0.0049441*i4*
     i26 + 0.00296714*i4*i27 + 0.001430786*i4*i28 + 0.00335542*i4*i29 + 
     0.0072271*i4*i30 + 0.001983328*i4*i31 + 0.00263338*i4*i32 + 0.0034098*i4*
     i33 + 0.001978102*i4*i34 + 0.00248436*i4*i35 + 0.001037234*i4*i36 + 
     0.001931824*i4*i37 + 0.00154955*i4*i38 + 0.00293776*i4*i39 - 0.01282698*i4
     *i40 + 0.001937926*i4*i41 + 0.0052959*i4*i42 + 0.001856036*i4*i43 + 
     0.000740384*i4*i44 + 0.00372246*i4*i45 + 0.00362974*i4*i46 + 0.001687258*
     i4*i47 + 0.00297792*i4*i48 + 0.0024381*i4*i49 + 0.00581304*i4*i50 + 
     0.000775592*i4*i51 + 0.00512872*i4*i52 + 0.00302932*i4*i53 + 0.00451004*i4
     *i54 + 0.00355054*i4*i55 + 0.000365898*i4*i56 + 0.00396452*i4*i57 + 
     0.00218522*i4*i58 + 0.001602712*i4*i59 + 0.00378946*i4*i60 + 0.00528342*i4
     *i61 + 0.00345546*i4*i62 + 0.0072364*i4*i63 + 0.00460504*i4*i64 + 
     0.00362066*i4*i65 + 0.00176825*i4*i66 + 0.00326082*i4*i67 + 0.00494324*i4*
     i68 + 0.00478058*i4*i69 + 0.0047424*i4*i70 + 0.00406804*i4*i71 + 
     0.00356438*i4*i72 + 0.0039191*i4*i73 + 0.00506266*i4*i74 + 0.005213*i4*i75
      + 0.00334114*i4*i76 + 0.00410168*i4*i77 + 0.00325268*i4*i78 + 0.000621396
     *i4*i79 + 0.00679868*i4*i80 + 0.001665408*i4*i81 + 0.00231708*i4*i82 - 
     0.0025243*i4*i83 + 0.00277762*i4*i84 + 0.0040202*i4*i85 + 0.001500566*i4*
     i86 + 0.001680814*i4*i87 + 0.00640404*i4*i88 + 0.00397656*i4*i89 + 
     0.000508164*i4*i90 + 0.00565534*i4*i91 + 0.0031999*i4*i92 + 0.0007233*i4*
     i93 + 0.001347788*i4*i94 + 0.00386662*i4*i95 + 0.0056032*i4*i96 + 
     0.00392786*i4*i97 + 0.0032706*i4*i98 + 0.000716722*i4*i99 + 0.00200998*i4*
     i100 + 0.00725878*i5*i6 + 0.000634496*i5*i7 + 0.0112129*i5*i8 + 0.006535*
     i5*i9 + 0.0076756*i5*i10 - 0.00455426*i5*i11 + 0.001111236*i5*i12 + 
     0.01473142*i5*i13 + 0.01556352*i5*i14 + 0.00889148*i5*i15 + 0.00833956*i5*
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     i55 + 0.01114364*i5*i56 + 0.00464056*i5*i57 + 0.00294786*i5*i58 + 
     0.01085566*i5*i59 + 0.00324938*i5*i60 + 0.01321296*i5*i61 + 0.00956118*i5*
     i62 + 0.00799502*i5*i63 + 0.00255928*i5*i64 + 0.00635808*i5*i65 + 
     0.00425494*i5*i66 + 0.00743456*i5*i67 + 0.003997*i5*i68 + 0.01327542*i5*
     i69 + 0.00624764*i5*i70 + 0.00544782*i5*i71 + 0.00583882*i5*i72 + 
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     i76 + 0.0064726*i5*i77 + 0.0043073*i5*i78 + 0.01376458*i5*i79 + 0.00590054
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     i87 + 0.01858866*i5*i88 + 0.00588762*i5*i89 + 0.00671372*i5*i90 + 
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     i94 + 0.00692006*i5*i95 + 0.0082357*i5*i96 + 0.00798976*i5*i97 + 
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     0.0257432*i6*i15 + 0.01758104*i6*i16 + 0.01908054*i6*i17 + 0.00928378*i6*
     i18 + 0.00320468*i6*i19 + 0.0315536*i6*i20 + 0.01792788*i6*i21 + 0.0231518
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     0.00771848*i6*i26 + 0.0203708*i6*i27 + 0.00861336*i6*i28 + 0.00733064*i6*
     i29 + 0.0211284*i6*i30 + 0.01136376*i6*i31 + 0.0298052*i6*i32 + 0.01763386
     *i6*i33 + 0.01196962*i6*i34 + 0.00970124*i6*i35 + 0.0426536*i6*i36 + 
     0.0162704*i6*i37 + 0.00511032*i6*i38 + 0.0211034*i6*i39 + 0.0536216*i6*i40
      + 0.0314338*i6*i41 + 0.0212846*i6*i42 + 0.01544516*i6*i43 + 0.0203852*i6*
     i44 + 0.00711214*i6*i45 + 0.01012528*i6*i46 + 0.0378006*i6*i47 + 
     0.00769828*i6*i48 + 0.01043538*i6*i49 + 0.0235092*i6*i50 + 0.00574084*i6*
     i51 + 0.01540822*i6*i52 + 0.01066192*i6*i53 + 0.01947344*i6*i54 + 
     0.01212224*i6*i55 + 0.01841288*i6*i56 + 0.00863178*i6*i57 + 0.0123986*i6*
     i58 + 0.01033934*i6*i59 + 0.00473636*i6*i60 + 0.0271978*i6*i61 + 0.0244978
     *i6*i62 + 0.0206042*i6*i63 + 0.0123061*i6*i64 + 0.00969592*i6*i65 + 
     0.0105285*i6*i66 + 0.01296694*i6*i67 + 0.00467684*i6*i68 + 0.0206522*i6*
     i69 + 0.01181216*i6*i70 + 0.034569*i6*i71 + 0.01713412*i6*i72 + 0.00997084
     *i6*i73 + 0.00934556*i6*i74 + 0.00446476*i6*i75 + 0.00591468*i6*i76 + 
     0.00902732*i6*i77 + 0.00684842*i6*i78 + 0.000346556*i6*i79 + 0.01344964*i6
     *i80 + 0.028585*i6*i81 + 0.00365848*i6*i82 + 0.0233826*i6*i83 + 0.01097966
     *i6*i84 + 0.01159854*i6*i85 + 0.0132315*i6*i86 + 0.00973116*i6*i87 + 
     0.01749474*i6*i88 + 0.00153948*i6*i89 + 0.01386412*i6*i90 + 0.01199914*i6*
     i91 + 0.0141917*i6*i92 + 0.001321806*i6*i93 + 0.00438272*i6*i94 + 
     0.01131596*i6*i95 + 0.01535776*i6*i96 + 0.01709068*i6*i97 + 0.024088*i6*
     i98 + 0.0176488*i6*i99 + 0.0244376*i6*i100 + 0.00488516*i7*i8 + 0.00626372
     *i7*i9 + 0.001990118*i7*i10 + 0.00360408*i7*i11 + 0.0044488*i7*i12 + 
     0.00345036*i7*i13 + 0.01022598*i7*i14 + 0.00914736*i7*i15 + 0.00744612*i7*
     i16 + 0.0041386*i7*i17 + 0.00439536*i7*i18 + 0.00478826*i7*i19 + 
     0.00946126*i7*i20 + 0.00383118*i7*i21 + 0.00577738*i7*i22 + 0.0023517*i7*
     i23 + 0.0050588*i7*i24 + 0.0021953*i7*i25 + 0.00304582*i7*i26 + 0.0025687*
     i7*i27 + 0.001019412*i7*i28 + 0.001803492*i7*i29 + 0.00840076*i7*i30 + 
     0.00405006*i7*i31 + 0.00330894*i7*i32 + 0.00379124*i7*i33 + 0.00297878*i7*
     i34 + 0.00257924*i7*i35 + 0.00710268*i7*i36 + 0.00290856*i7*i37 + 
     0.00084645*i7*i38 + 0.00616224*i7*i39 + 0.00012188*i7*i40 + 0.00931498*i7*
     i41 + 0.00783*i7*i42 + 0.00769852*i7*i43 + 0.00783756*i7*i44 + 0.0049081*
     i7*i45 + 0.00379762*i7*i46 + 0.00691856*i7*i47 + 0.00516014*i7*i48 + 
     0.00525658*i7*i49 + 0.00529626*i7*i50 + 0.00103022*i7*i51 + 0.00545452*i7*
     i52 + 0.00609146*i7*i53 + 0.0066465*i7*i54 + 0.0057959*i7*i55 + 0.00384568
     *i7*i56 + 0.00518642*i7*i57 + 0.0049888*i7*i58 + 0.00240984*i7*i59 + 
     0.001870666*i7*i60 + 0.00856542*i7*i61 + 0.00433228*i7*i62 + 0.00926318*i7
     *i63 + 0.00802564*i7*i64 + 0.002679*i7*i65 + 0.00656044*i7*i66 + 
     0.00189873*i7*i67 + 0.00559974*i7*i68 + 0.0059088*i7*i69 + 0.00502274*i7*
     i70 + 0.00714092*i7*i71 + 0.00451814*i7*i72 + 0.0055096*i7*i73 + 0.0054579
     *i7*i74 + 0.00428152*i7*i75 + 0.00201372*i7*i76 + 0.00763776*i7*i77 + 
     0.001767634*i7*i78 - 0.00404984*i7*i79 + 0.00693072*i7*i80 + 0.00453578*i7
     *i81 + 0.001431356*i7*i82 + 0.001000832*i7*i83 + 0.00363592*i7*i84 + 
     0.00399748*i7*i85 + 0.00244412*i7*i86 - 0.00038172*i7*i87 + 0.00670104*i7*
     i88 + 0.00351634*i7*i89 + 0.000192176*i7*i90 + 0.00766242*i7*i91 + 
     0.00431432*i7*i92 + 0.00099522*i7*i93 + 0.00215394*i7*i94 + 0.00467712*i7*
     i95 + 0.00551306*i7*i96 + 0.00524514*i7*i97 + 0.00715168*i7*i98 + 
     0.00269474*i7*i99 + 0.006577*i7*i100 + 0.01497394*i8*i9 + 0.0108969*i8*i10
      + 0.00659842*i8*i11 + 0.00635336*i8*i12 + 0.0313098*i8*i13 + 0.0387588*i8
     *i14 + 0.01963812*i8*i15 + 0.00587206*i8*i16 + 0.0158028*i8*i17 + 
     0.00433344*i8*i18 + 0.01027216*i8*i19 + 0.0310764*i8*i20 + 0.01480666*i8*
     i21 + 0.0292324*i8*i22 + 0.01097454*i8*i23 + 0.01637932*i8*i24 + 0.0081932
     *i8*i25 + 0.00625414*i8*i26 + 0.01206926*i8*i27 + 0.00960586*i8*i28 + 
     0.00767454*i8*i29 + 0.0389634*i8*i30 + 0.01047056*i8*i31 + 0.0243166*i8*
     i32 + 0.01490526*i8*i33 + 0.0048023*i8*i34 + 0.00582726*i8*i35 + 0.0310084
     *i8*i36 + 0.01520046*i8*i37 + 0.00435652*i8*i38 + 0.01820518*i8*i39 + 
     0.028962*i8*i40 + 0.0236162*i8*i41 + 0.0089807*i8*i42 + 0.01679084*i8*i43
      + 0.01575264*i8*i44 - 0.00596962*i8*i45 + 0.0045504*i8*i46 + 0.0135935*i8
     *i47 + 0.00528224*i8*i48 + 0.01215584*i8*i49 + 0.01116408*i8*i50 + 
     0.00976906*i8*i51 + 0.01011206*i8*i52 + 0.0224104*i8*i53 + 0.01007602*i8*
     i54 + 0.01583128*i8*i55 + 0.00761084*i8*i56 + 0.00804396*i8*i57 + 
     0.01038608*i8*i58 + 0.01602498*i8*i59 + 0.00380248*i8*i60 + 0.0227414*i8*
     i61 + 0.0208778*i8*i62 + 0.01278874*i8*i63 + 0.00882622*i8*i64 + 
     0.01253422*i8*i65 + 0.00938202*i8*i66 + 0.0132364*i8*i67 + 0.00341364*i8*
     i68 + 0.0217686*i8*i69 + 0.01082106*i8*i70 + 0.0109575*i8*i71 + 0.01032418
     *i8*i72 + 0.01203924*i8*i73 + 0.01820078*i8*i74 + 0.00454846*i8*i75 + 
     0.00699592*i8*i76 + 0.017175*i8*i77 + 0.00418326*i8*i78 + 0.003044*i8*i79
      + 0.00913958*i8*i80 + 0.01058642*i8*i81 + 0.00609436*i8*i82 + 0.00939194*
     i8*i83 + 0.01860882*i8*i84 + 0.00544766*i8*i85 + 0.00672898*i8*i86 + 
     0.00847128*i8*i87 + 0.0399532*i8*i88 + 0.00230258*i8*i89 + 0.00647968*i8*
     i90 + 0.00663734*i8*i91 + 0.00723392*i8*i92 + 0.0028363*i8*i93 + 
     0.01094692*i8*i94 + 0.01122622*i8*i95 + 0.01922686*i8*i96 + 0.0178042*i8*
     i97 + 0.00987488*i8*i98 + 0.0201768*i8*i99 + 0.00916962*i8*i100 + 
     0.00380196*i9*i10 + 0.000241806*i9*i11 + 0.00422182*i9*i12 + 0.01745366*i9
     *i13 + 0.01560378*i9*i14 + 0.01797116*i9*i15 + 0.0104377*i9*i16 + 
     0.01789532*i9*i17 + 0.0058031*i9*i18 + 0.00524852*i9*i19 + 0.0217664*i9*
     i20 + 0.0137801*i9*i21 + 0.00556924*i9*i22 + 0.00707894*i9*i23 + 
     0.00383446*i9*i24 + 0.00797136*i9*i25 + 0.00671112*i9*i26 + 0.00962638*i9*
     i27 + 0.00548282*i9*i28 + 0.00537842*i9*i29 + 0.01125578*i9*i30 + 
     0.01033708*i9*i31 + 0.01741482*i9*i32 + 0.01282666*i9*i33 + 0.00490948*i9*
     i34 + 0.00344028*i9*i35 + 0.01643714*i9*i36 + 0.00871578*i9*i37 + 0.002884
     *i9*i38 + 0.01596496*i9*i39 + 0.0171071*i9*i40 + 0.0282184*i9*i41 + 
     0.0157083*i9*i42 + 0.01908622*i9*i43 + 0.01887462*i9*i44 + 0.00621506*i9*
     i45 + 0.00706654*i9*i46 + 0.01685764*i9*i47 + 0.0046064*i9*i48 + 
     0.01393082*i9*i49 + 0.01366172*i9*i50 + 0.00974224*i9*i51 + 0.01117786*i9*
     i52 + 0.0105042*i9*i53 + 0.01603942*i9*i54 + 0.01154502*i9*i55 + 0.0187017
     *i9*i56 + 0.0063051*i9*i57 + 0.01180982*i9*i58 + 0.01148738*i9*i59 + 
     0.0045111*i9*i60 + 0.01782442*i9*i61 + 0.01261594*i9*i62 + 0.0275116*i9*
     i63 + 0.01370986*i9*i64 + 0.01301448*i9*i65 + 0.00909146*i9*i66 + 
     0.00880956*i9*i67 + 0.00542126*i9*i68 + 0.0173699*i9*i69 + 0.0063573*i9*
     i70 + 0.01464082*i9*i71 + 0.01030184*i9*i72 + 0.01342364*i9*i73 + 
     0.01050302*i9*i74 + 0.00580926*i9*i75 + 0.00669824*i9*i76 + 0.0154461*i9*
     i77 + 0.00331996*i9*i78 - 0.00117976*i9*i79 + 0.0134427*i9*i80 + 
     0.01200946*i9*i81 + 0.00261992*i9*i82 + 0.01802554*i9*i83 + 0.01281546*i9*
     i84 + 0.00817562*i9*i85 + 0.01353278*i9*i86 + 0.0065419*i9*i87 + 0.0287756
     *i9*i88 + 0.00438656*i9*i89 + 0.006514*i9*i90 + 0.00948704*i9*i91 + 
     0.01460712*i9*i92 + 0.00442406*i9*i93 + 0.00525338*i9*i94 + 0.01080594*i9*
     i95 + 0.007284*i9*i96 + 0.01145784*i9*i97 + 0.01167366*i9*i98 + 0.01306896
     *i9*i99 + 0.01230056*i9*i100 + 0.00390108*i10*i11 + 0.00306506*i10*i12 + 
     0.0266658*i10*i13 + 0.027667*i10*i14 + 0.01278752*i10*i15 + 0.01031474*i10
     *i16 + 0.01126594*i10*i17 + 0.00489102*i10*i18 + 0.00513038*i10*i19 + 
     0.01899656*i10*i20 + 0.01116072*i10*i21 + 0.0218888*i10*i22 + 0.01101148*
     i10*i23 + 0.00938786*i10*i24 + 0.00495956*i10*i25 + 0.00409492*i10*i26 + 
     0.00774196*i10*i27 + 0.00563678*i10*i28 + 0.00452506*i10*i29 + 0.0234496*
     i10*i30 + 0.00879878*i10*i31 + 0.01816086*i10*i32 + 0.01204676*i10*i33 + 
     0.00474448*i10*i34 + 0.00478426*i10*i35 + 0.0297012*i10*i36 + 0.0151832*
     i10*i37 + 0.00256504*i10*i38 + 0.01482468*i10*i39 + 0.0351312*i10*i40 + 
     0.00722204*i10*i41 + 0.00911442*i10*i42 + 0.00459148*i10*i43 + 0.00643892*
     i10*i44 + 0.00232242*i10*i45 + 0.00525016*i10*i46 + 0.00918898*i10*i47 + 
     0.00604914*i10*i48 + 0.00855226*i10*i49 + 0.01758968*i10*i50 + 0.00905476*
     i10*i51 + 0.0076611*i10*i52 + 0.01159398*i10*i53 + 0.00933998*i10*i54 + 
     0.00932956*i10*i55 + 0.0077777*i10*i56 + 0.00585234*i10*i57 + 0.00494612*
     i10*i58 + 0.01267098*i10*i59 + 0.0025072*i10*i60 + 0.01652258*i10*i61 + 
     0.0113132*i10*i62 + 0.00647572*i10*i63 + 0.00509638*i10*i64 + 0.00796924*
     i10*i65 + 0.00671784*i10*i66 + 0.00876736*i10*i67 + 0.00330284*i10*i68 + 
     0.0143256*i10*i69 + 0.00658518*i10*i70 + 0.00751304*i10*i71 + 0.00447272*
     i10*i72 + 0.00707326*i10*i73 + 0.01022514*i10*i74 + 0.00629098*i10*i75 + 
     0.00437386*i10*i76 + 0.0069722*i10*i77 + 0.00631338*i10*i78 + 0.01475202*
     i10*i79 + 0.00722624*i10*i80 + 0.00973154*i10*i81 + 0.00371556*i10*i82 + 
     0.00253096*i10*i83 + 0.008833*i10*i84 + 0.00871744*i10*i85 + 0.0101816*i10
     *i86 + 0.01000738*i10*i87 + 0.01974334*i10*i88 + 0.00587674*i10*i89 + 
     0.0124516*i10*i90 + 0.00915752*i10*i91 + 0.00913708*i10*i92 + 0.00200378*
     i10*i93 + 0.00536928*i10*i94 + 0.00823672*i10*i95 + 0.01736144*i10*i96 + 
     0.01105742*i10*i97 + 0.01023842*i10*i98 + 0.01685104*i10*i99 + 0.01457986*
     i10*i100 + 0.000833086*i11*i12 + 0.00999478*i11*i13 + 0.01344484*i11*i14
      + 0.0031808*i11*i15 + 0.01117228*i11*i16 + 0.000697152*i11*i17 + 
     0.000585828*i11*i18 + 0.00585952*i11*i19 + 0.00859976*i11*i20 + 0.00502902
     *i11*i21 + 0.00447154*i11*i22 + 0.001969568*i11*i23 + 0.0049358*i11*i24 - 
     0.00029705*i11*i25 + 0.0008833*i11*i26 + 0.00788936*i11*i27 + 0.00223564*
     i11*i28 - 0.001370818*i11*i29 + 0.0148367*i11*i30 + 0.01084338*i11*i31 + 
     0.000606756*i11*i32 + 0.00591896*i11*i33 - 0.00408456*i11*i34 - 0.002724*
     i11*i35 + 0.01495302*i11*i36 + 0.0001528802*i11*i37 + 0.000200858*i11*i38
      + 0.00843216*i11*i39 + 0.01341476*i11*i40 + 0.01160686*i11*i41 + 
     0.00464728*i11*i42 + 0.00803576*i11*i43 + 0.00270742*i11*i44 - 0.00352162*
     i11*i45 + 0.000947796*i11*i46 + 0.00388898*i11*i47 + 0.00557236*i11*i48 + 
     0.00208008*i11*i49 + 0.000931698*i11*i50 + 0.000654446*i11*i51 + 
     0.00650504*i11*i52 + 0.000501194*i11*i53 + 0.00681518*i11*i54 + 0.00601122
     *i11*i55 - 0.00507122*i11*i56 + 0.000483176*i11*i57 + 0.00482018*i11*i58
      + 0.0064067*i11*i59 - 0.000166498*i11*i60 + 0.00575774*i11*i61 + 
     0.00725456*i11*i62 + 0.00219412*i11*i63 + 0.0084673*i11*i64 + 0.000333436*
     i11*i65 + 0.00655332*i11*i66 - 0.00257168*i11*i67 + 0.01199786*i11*i68 + 
     0.0059299*i11*i69 + 0.001843394*i11*i70 + 0.01060724*i11*i71 + 0.00647206*
     i11*i72 + 0.00231676*i11*i73 + 0.00580344*i11*i74 + 0.00620538*i11*i75 - 
     0.000334258*i11*i76 + 0.00656424*i11*i77 - 0.001286316*i11*i78 + 
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     0.01336936*i15*i24 + 0.01153424*i15*i25 + 0.01291552*i15*i26 + 0.01571376*
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     0.01589948*i15*i80 + 0.01996746*i15*i81 + 0.00616376*i15*i82 + 0.00905236*
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     0.01662354*i15*i87 + 0.0326642*i15*i88 + 0.00648876*i15*i89 + 0.0255582*
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     0.01190474*i16*i31 + 0.01955462*i16*i32 + 0.0138212*i16*i33 + 0.00642106*
     i16*i34 + 0.00665524*i16*i35 + 0.0380492*i16*i36 + 0.01602708*i16*i37 + 
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     i16*i55 + 0.01166912*i16*i56 + 0.00870972*i16*i57 + 0.00719416*i16*i58 + 
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     i16*i90 + 0.01898344*i16*i91 + 0.01310136*i16*i92 + 0.00293122*i16*i93 + 
     0.00548746*i16*i94 + 0.01674526*i16*i95 + 0.0263504*i16*i96 + 0.0187966*
     i16*i97 + 0.0198675*i16*i98 + 0.0160833*i16*i99 + 0.01885334*i16*i100 + 
     0.00599666*i17*i18 + 0.0047675*i17*i19 + 0.0265872*i17*i20 + 0.01628802*
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     0.00989432*i17*i25 + 0.00330258*i17*i26 + 0.0116841*i17*i27 + 0.0079471*
     i17*i28 + 0.0045994*i17*i29 + 0.0254766*i17*i30 + 0.01659406*i17*i31 + 
     0.0220846*i17*i32 + 0.01861566*i17*i33 + 0.00948066*i17*i34 + 0.0090429*
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     i17*i63 + 0.01054316*i17*i64 + 0.01114578*i17*i65 + 0.010706*i17*i66 + 
     0.01057722*i17*i67 + 0.00541042*i17*i68 + 0.022045*i17*i69 + 0.00933892*
     i17*i70 + 0.0217256*i17*i71 + 0.010527*i17*i72 + 0.01245986*i17*i73 + 
     0.01462496*i17*i74 + 0.00471612*i17*i75 + 0.00385082*i17*i76 + 0.0150046*
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     0.0167981*i17*i81 + 0.00275656*i17*i82 + 0.0264668*i17*i83 + 0.01754616*
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     0.0334656*i17*i88 + 0.0100102*i17*i89 + 0.00830234*i17*i90 + 0.00830522*
     i17*i91 + 0.01347376*i17*i92 + 0.00371114*i17*i93 + 0.00721878*i17*i94 + 
     0.01197232*i17*i95 + 0.01097582*i17*i96 + 0.0153446*i17*i97 + 0.01911512*
     i17*i98 + 0.0158341*i17*i99 + 0.01647016*i17*i100 + 0.0038501*i18*i19 + 
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     i18*i23 + 0.00577628*i18*i24 + 0.00353166*i18*i25 + 0.00406754*i18*i26 + 
     0.00586712*i18*i27 + 0.00246394*i18*i28 + 0.00208424*i18*i29 + 0.00868042*
     i18*i30 + 0.00488392*i18*i31 + 0.01139774*i18*i32 + 0.00652178*i18*i33 + 
     0.00514824*i18*i34 + 0.00420068*i18*i35 + 0.01314078*i18*i36 + 0.00738678*
     i18*i37 + 0.00212172*i18*i38 + 0.00767338*i18*i39 + 0.01491396*i18*i40 + 
     0.00689198*i18*i41 + 0.00941516*i18*i42 + 0.00703674*i18*i43 + 0.00623926*
     i18*i44 + 0.0042213*i18*i45 + 0.00377366*i18*i46 + 0.01005392*i18*i47 + 
     0.00385304*i18*i48 + 0.0061538*i18*i49 + 0.00828744*i18*i50 + 0.00452496*
     i18*i51 + 0.00647618*i18*i52 + 0.00595912*i18*i53 + 0.00909974*i18*i54 + 
     0.00683082*i18*i55 + 0.00696058*i18*i56 + 0.00489492*i18*i57 + 0.00399036*
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     0.01002278*i18*i69 + 0.00498708*i18*i70 + 0.00467346*i18*i71 + 0.00622154*
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     i18*i79 + 0.007017*i18*i80 + 0.00647242*i18*i81 + 0.00407958*i18*i82 - 
     0.000888864*i18*i83 + 0.00537106*i18*i84 + 0.00634694*i18*i85 + 0.00514234
     *i18*i86 + 0.00350408*i18*i87 - 0.00202898*i18*i88 + 0.001751682*i18*i89
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     i18*i93 + 0.00436006*i18*i94 + 0.00715274*i18*i95 + 0.00776482*i18*i96 + 
     0.00710082*i18*i97 + 0.00609606*i18*i98 + 0.00652362*i18*i99 + 0.01247386*
     i18*i100 + 0.01204848*i19*i20 + 0.00628788*i19*i21 + 0.00938206*i19*i22 + 
     0.00540152*i19*i23 + 0.00366816*i19*i24 + 0.00424804*i19*i25 + 0.00443146*
     i19*i26 + 0.00550836*i19*i27 + 0.00441186*i19*i28 + 0.00464964*i19*i29 + 
     0.0215394*i19*i30 + 0.00534434*i19*i31 + 0.01089826*i19*i32 + 0.00384858*
     i19*i33 + 0.00271286*i19*i34 + 0.00459438*i19*i35 + 0.00753494*i19*i36 + 
     0.00675858*i19*i37 + 0.00330138*i19*i38 + 0.01012594*i19*i39 + 0.00097236*
     i19*i40 + 0.00697634*i19*i41 + 0.0055734*i19*i42 + 0.00439042*i19*i43 + 
     0.00466626*i19*i44 + 0.0056599*i19*i45 + 0.00343664*i19*i46 + 0.00191227*
     i19*i47 + 0.00409474*i19*i48 + 0.00728426*i19*i49 + 0.0118005*i19*i50 + 
     0.00439032*i19*i51 + 0.00819602*i19*i52 + 0.00683532*i19*i53 + 0.00927236*
     i19*i54 + 0.00638082*i19*i55 + 0.0049778*i19*i56 + 0.0064092*i19*i57 + 
     0.00332368*i19*i58 + 0.00797006*i19*i59 + 0.00515114*i19*i60 + 0.0140857*
     i19*i61 + 0.00824548*i19*i62 + 0.00645382*i19*i63 + 0.00492056*i19*i64 + 
     0.0040063*i19*i65 + 0.00621702*i19*i66 + 0.00486474*i19*i67 + 0.01089728*
     i19*i68 + 0.01064856*i19*i69 + 0.00763898*i19*i70 + 0.00304924*i19*i71 + 
     0.00746516*i19*i72 + 0.0073895*i19*i73 + 0.008372*i19*i74 + 0.0096269*i19*
     i75 + 0.00403824*i19*i76 + 0.00896868*i19*i77 + 0.00369816*i19*i78 + 
     0.01338638*i19*i79 + 0.00702566*i19*i80 + 0.00204776*i19*i81 + 0.0040369*
     i19*i82 - 0.00617474*i19*i83 + 0.00664876*i19*i84 + 0.00640014*i19*i85 + 
     0.00537574*i19*i86 + 0.00744762*i19*i87 + 0.0288232*i19*i88 + 0.0089059*
     i19*i89 + 0.00438344*i19*i90 + 0.01192674*i19*i91 + 0.00326376*i19*i92 + 
     0.00330764*i19*i93 + 0.00649262*i19*i94 + 0.0076392*i19*i95 + 0.01075072*
     i19*i96 + 0.00749846*i19*i97 + 0.00563188*i19*i98 + 0.00430788*i19*i99 + 
     0.00505074*i19*i100 + 0.026993*i20*i21 + 0.0407142*i20*i22 + 0.0262048*i20
     *i23 + 0.0233804*i20*i24 + 0.01566388*i20*i25 + 0.01254316*i20*i26 + 
     0.0230746*i20*i27 + 0.01228074*i20*i28 + 0.01141404*i20*i29 + 0.046979*i20
     *i30 + 0.01956928*i20*i31 + 0.0444886*i20*i32 + 0.0345924*i20*i33 + 
     0.01450852*i20*i34 + 0.01607032*i20*i35 + 0.0534276*i20*i36 + 0.027915*i20
     *i37 + 0.00446976*i20*i38 + 0.0310128*i20*i39 + 0.0617194*i20*i40 + 
     0.0418284*i20*i41 + 0.0284554*i20*i42 + 0.0202322*i20*i43 + 0.0309222*i20*
     i44 + 0.00850138*i20*i45 + 0.01226594*i20*i46 + 0.0355744*i20*i47 + 
     0.01044628*i20*i48 + 0.0261968*i20*i49 + 0.0353182*i20*i50 + 0.01768812*
     i20*i51 + 0.0227266*i20*i52 + 0.0229416*i20*i53 + 0.0285392*i20*i54 + 
     0.024215*i20*i55 + 0.0227*i20*i56 + 0.01349126*i20*i57 + 0.01576804*i20*
     i58 + 0.0251472*i20*i59 + 0.00678918*i20*i60 + 0.0460104*i20*i61 + 
     0.0362612*i20*i62 + 0.0246576*i20*i63 + 0.01897386*i20*i64 + 0.021042*i20*
     i65 + 0.01449872*i20*i66 + 0.01901978*i20*i67 + 0.01289314*i20*i68 + 
     0.04318*i20*i69 + 0.0192612*i20*i70 + 0.0319956*i20*i71 + 0.0241418*i20*
     i72 + 0.0231068*i20*i73 + 0.0232748*i20*i74 + 0.01394672*i20*i75 + 
     0.01233534*i20*i76 + 0.0250086*i20*i77 + 0.01003866*i20*i78 + 0.01782134*
     i20*i79 + 0.0175231*i20*i80 + 0.0266842*i20*i81 + 0.00899148*i20*i82 + 
     0.01916166*i20*i83 + 0.0237898*i20*i84 + 0.01674726*i20*i85 + 0.0243836*
     i20*i86 + 0.0205712*i20*i87 + 0.0526016*i20*i88 + 0.01299922*i20*i89 + 
     0.0223216*i20*i90 + 0.0221722*i20*i91 + 0.0200512*i20*i92 + 0.00605128*i20
     *i93 + 0.01422172*i20*i94 + 0.0209666*i20*i95 + 0.0316224*i20*i96 + 
     0.0278754*i20*i97 + 0.0266692*i20*i98 + 0.032317*i20*i99 + 0.0372718*i20*
     i100 + 0.0225584*i21*i22 + 0.01330824*i21*i23 + 0.01120138*i21*i24 + 
     0.00988644*i21*i25 + 0.0053562*i21*i26 + 0.01171726*i21*i27 + 0.0075308*
     i21*i28 + 0.0062293*i21*i29 + 0.028151*i21*i30 + 0.01116532*i21*i31 + 
     0.024731*i21*i32 + 0.01403094*i21*i33 + 0.0053378*i21*i34 + 0.0062169*i21*
     i35 + 0.0322338*i21*i36 + 0.0173092*i21*i37 + 0.00310282*i21*i38 + 
     0.01943686*i21*i39 + 0.0397312*i21*i40 + 0.0227668*i21*i41 + 0.01402322*
     i21*i42 + 0.01184862*i21*i43 + 0.01574106*i21*i44 + 0.00351088*i21*i45 + 
     0.00692094*i21*i46 + 0.01710158*i21*i47 + 0.00581758*i21*i48 + 0.013985*
     i21*i49 + 0.0205976*i21*i50 + 0.01286968*i21*i51 + 0.01222018*i21*i52 + 
     0.01492284*i21*i53 + 0.01502328*i21*i54 + 0.01279528*i21*i55 + 0.01443928*
     i21*i56 + 0.00711002*i21*i57 + 0.00897148*i21*i58 + 0.0175601*i21*i59 + 
     0.00366562*i21*i60 + 0.0240206*i21*i61 + 0.01871124*i21*i62 + 0.01471548*
     i21*i63 + 0.00910326*i21*i64 + 0.01121548*i21*i65 + 0.0093615*i21*i66 + 
     0.0129081*i21*i67 + 0.0055548*i21*i68 + 0.0214638*i21*i69 + 0.00932128*i21
     *i70 + 0.01654162*i21*i71 + 0.01150414*i21*i72 + 0.01130758*i21*i73 + 
     0.01195864*i21*i74 + 0.00685764*i21*i75 + 0.00673976*i21*i76 + 0.01092518*
     i21*i77 + 0.00610126*i21*i78 + 0.0166491*i21*i79 + 0.00973956*i21*i80 + 
     0.01360816*i21*i81 + 0.00413938*i21*i82 + 0.01295166*i21*i83 + 0.01359658*
     i21*i84 + 0.0100056*i21*i85 + 0.01591198*i21*i86 + 0.01302584*i21*i87 + 
     0.0321888*i21*i88 + 0.0069057*i21*i89 + 0.01467542*i21*i90 + 0.0104985*i21
     *i91 + 0.01203108*i21*i92 + 0.00438602*i21*i93 + 0.0064228*i21*i94 + 
     0.0109577*i21*i95 + 0.01683074*i21*i96 + 0.01510662*i21*i97 + 0.013665*i21
     *i98 + 0.01994166*i21*i99 + 0.0184821*i21*i100 + 0.01713984*i22*i23 + 
     0.0290628*i22*i24 + 0.01659484*i22*i25 + 0.01330504*i22*i26 + 0.0220338*
     i22*i27 + 0.0096401*i22*i28 + 0.01336178*i22*i29 + 0.0794522*i22*i30 + 
     0.00912184*i22*i31 + 0.0466568*i22*i32 + 0.0203942*i22*i33 + 0.00695226*
     i22*i34 + 0.0125215*i22*i35 + 0.0728992*i22*i36 + 0.0354588*i22*i37 + 
     0.00691112*i22*i38 + 0.037201*i22*i39 + 0.0756082*i22*i40 + 0.0292772*i22*
     i41 + 0.0266054*i22*i42 + 0.01269282*i22*i43 + 0.0230306*i22*i44 + 
     0.000804368*i22*i45 + 0.01545384*i22*i46 + 0.0296748*i22*i47 + 0.0193381*
     i22*i48 + 0.0200644*i22*i49 + 0.0450946*i22*i50 + 0.01567104*i22*i51 + 
     0.0202574*i22*i52 + 0.0456018*i22*i53 + 0.024727*i22*i54 + 0.01871804*i22*
     i55 + 0.01574656*i22*i56 + 0.01426746*i22*i57 + 0.0112117*i22*i58 + 
     0.0237092*i22*i59 + 0.01100176*i22*i60 + 0.0484136*i22*i61 + 0.0477626*i22
     *i62 + 0.01715072*i22*i63 + 0.01569402*i22*i64 + 0.0163363*i22*i65 + 
     0.00819194*i22*i66 + 0.0250362*i22*i67 + 0.01191736*i22*i68 + 0.0445474*
     i22*i69 + 0.0208408*i22*i70 + 0.0196514*i22*i71 + 0.01993902*i22*i72 + 
     0.01317816*i22*i73 + 0.0290184*i22*i74 + 0.022028*i22*i75 + 0.01241074*i22
     *i76 + 0.01467528*i22*i77 + 0.0179883*i22*i78 + 0.040464*i22*i79 + 
     0.01646476*i22*i80 + 0.0251454*i22*i81 + 0.00665554*i22*i82 - 0.00094782*
     i22*i83 + 0.01809638*i22*i84 + 0.01658492*i22*i85 + 0.0242392*i22*i86 + 
     0.0215874*i22*i87 + 0.0229098*i22*i88 + 0.01114584*i22*i89 + 0.046945*i22*
     i90 + 0.0230318*i22*i91 + 0.01381346*i22*i92 + 0.0100301*i22*i93 + 
     0.00837496*i22*i94 + 0.0250054*i22*i95 + 0.0620424*i22*i96 + 0.0302296*i22
     *i97 + 0.0248336*i22*i98 + 0.0372288*i22*i99 + 0.0441042*i22*i100 + 
     0.00618108*i23*i24 + 0.00567144*i23*i25 + 0.0048866*i23*i26 + 0.00839514*
     i23*i27 + 0.00487436*i23*i28 + 0.004356*i23*i29 + 0.024299*i23*i30 + 
     0.00996842*i23*i31 + 0.0204928*i23*i32 + 0.01726232*i23*i33 + 0.00564344*
     i23*i34 + 0.00506272*i23*i35 + 0.027322*i23*i36 + 0.01648718*i23*i37 + 
     0.001813512*i23*i38 + 0.0143408*i23*i39 + 0.0410642*i23*i40 + 0.00822668*
     i23*i41 + 0.01397884*i23*i42 + 0.00751294*i23*i43 + 0.01081252*i23*i44 + 
     0.00375058*i23*i45 + 0.00488444*i23*i46 + 0.01210078*i23*i47 + 0.0050334*
     i23*i48 + 0.01042672*i23*i49 + 0.01834872*i23*i50 + 0.0122672*i23*i51 + 
     0.01291522*i23*i52 + 0.01243908*i23*i53 + 0.01372984*i23*i54 + 0.0114482*
     i23*i55 + 0.0105593*i23*i56 + 0.00644542*i23*i57 + 0.00648944*i23*i58 + 
     0.01543002*i23*i59 + 0.0037869*i23*i60 + 0.0214726*i23*i61 + 0.01495998*
     i23*i62 + 0.00692592*i23*i63 + 0.00648514*i23*i64 + 0.00794602*i23*i65 + 
     0.00558232*i23*i66 + 0.0093087*i23*i67 + 0.000819996*i23*i68 + 0.01512186*
     i23*i69 + 0.0070338*i23*i70 + 0.00840292*i23*i71 + 0.00668858*i23*i72 + 
     0.00956292*i23*i73 + 0.00972254*i23*i74 + 0.00409738*i23*i75 + 0.00544566*
     i23*i76 + 0.01207296*i23*i77 + 0.00561846*i23*i78 + 0.01639358*i23*i79 + 
     0.00769632*i23*i80 + 0.01062502*i23*i81 + 0.0060578*i23*i82 + 0.00866906*
     i23*i83 + 0.00707332*i23*i84 + 0.01006612*i23*i85 + 0.01147664*i23*i86 + 
     0.0127172*i23*i87 + 0.01718458*i23*i88 + 0.00499896*i23*i89 + 0.01300446*
     i23*i90 + 0.00824348*i23*i91 + 0.01100222*i23*i92 + 0.00359882*i23*i93 + 
     0.00760194*i23*i94 + 0.01026304*i23*i95 + 0.01748628*i23*i96 + 0.01222018*
     i23*i97 + 0.00656104*i23*i98 + 0.01929844*i23*i99 + 0.01526792*i23*i100 + 
     0.01061256*i24*i25 + 0.00390748*i24*i26 + 0.0176534*i24*i27 + 0.00973526*
     i24*i28 + 0.00580416*i24*i29 + 0.0308904*i24*i30 + 0.00564094*i24*i31 + 
     0.0202996*i24*i32 + 0.00846578*i24*i33 + 0.00878324*i24*i34 + 0.0092725*
     i24*i35 + 0.0386418*i24*i36 + 0.01405906*i24*i37 + 0.0050169*i24*i38 + 
     0.01753958*i24*i39 + 0.0277342*i24*i40 + 0.0200538*i24*i41 + 0.0160148*i24
     *i42 + 0.01157484*i24*i43 + 0.0097945*i24*i44 + 0.00047637*i24*i45 + 
     0.0074696*i24*i46 + 0.0232922*i24*i47 + 0.0064693*i24*i48 + 0.0076863*i24*
     i49 + 0.01970906*i24*i50 + 0.00539232*i24*i51 + 0.01285448*i24*i52 + 
     0.0120141*i24*i53 + 0.0124346*i24*i54 + 0.00898946*i24*i55 + 0.00726448*
     i24*i56 + 0.0065436*i24*i57 + 0.00501008*i24*i58 + 0.01101314*i24*i59 + 
     0.00470396*i24*i60 + 0.0237074*i24*i61 + 0.0228986*i24*i62 + 0.01228188*
     i24*i63 + 0.01100376*i24*i64 + 0.00915078*i24*i65 + 0.0069269*i24*i66 + 
     0.01206108*i24*i67 + 0.00908652*i24*i68 + 0.0217466*i24*i69 + 0.00887002*
     i24*i70 + 0.022452*i24*i71 + 0.0139555*i24*i72 + 0.00715706*i24*i73 + 
     0.01096546*i24*i74 + 0.00744888*i24*i75 + 0.0028668*i24*i76 + 0.0036177*
     i24*i77 + 0.00580328*i24*i78 + 0.0086669*i24*i79 + 0.00929752*i24*i80 + 
     0.01854944*i24*i81 + 0.0023229*i24*i82 + 0.01207648*i24*i83 + 0.01205652*
     i24*i84 + 0.0096674*i24*i85 + 0.0108503*i24*i86 + 0.00597266*i24*i87 + 
     0.0190243*i24*i88 + 0.00640978*i24*i89 + 0.01034642*i24*i90 + 0.01193214*
     i24*i91 + 0.00822214*i24*i92 + 0.00070224*i24*i93 + 0.00307244*i24*i94 + 
     0.01092084*i24*i95 + 0.0203774*i24*i96 + 0.01743418*i24*i97 + 0.0232524*
     i24*i98 + 0.01437366*i24*i99 + 0.01998814*i24*i100 + 0.00270846*i25*i26 + 
     0.00878244*i25*i27 + 0.00564506*i25*i28 + 0.00404084*i25*i29 + 0.0227806*
     i25*i30 + 0.00477484*i25*i31 + 0.016725*i25*i32 + 0.00496432*i25*i33 + 
     0.00361518*i25*i34 + 0.00462338*i25*i35 + 0.0204146*i25*i36 + 0.01087624*
     i25*i37 + 0.00256388*i25*i38 + 0.01236456*i25*i39 + 0.01769162*i25*i40 + 
     0.01576792*i25*i41 + 0.00928236*i25*i42 + 0.00793946*i25*i43 + 0.00966756*
     i25*i44 + 0.00248138*i25*i45 + 0.00485932*i25*i46 + 0.0122764*i25*i47 + 
     0.0023089*i25*i48 + 0.00859364*i25*i49 + 0.01421118*i25*i50 + 0.00733214*
     i25*i51 + 0.00816206*i25*i52 + 0.00960248*i25*i53 + 0.00866518*i25*i54 + 
     0.00692386*i25*i55 + 0.00882586*i25*i56 + 0.00434948*i25*i57 + 0.0041589*
     i25*i58 + 0.01055232*i25*i59 + 0.00330494*i25*i60 + 0.01561392*i25*i61 + 
     0.0126551*i25*i62 + 0.00815092*i25*i63 + 0.00612506*i25*i64 + 0.0070869*
     i25*i65 + 0.00424002*i25*i66 + 0.00879504*i25*i67 + 0.0058829*i25*i68 + 
     0.01439048*i25*i69 + 0.00610238*i25*i70 + 0.01131906*i25*i71 + 0.00889538*
     i25*i72 + 0.00612414*i25*i73 + 0.00846104*i25*i74 + 0.0057198*i25*i75 + 
     0.00393476*i25*i76 + 0.00432972*i25*i77 + 0.00446968*i25*i78 + 0.0141591*
     i25*i79 + 0.00681524*i25*i80 + 0.00839778*i25*i81 + 0.00242412*i25*i82 + 
     0.0061299*i25*i83 + 0.00821362*i25*i84 + 0.0059951*i25*i85 + 0.01036166*
     i25*i86 + 0.0075501*i25*i87 + 0.0208316*i25*i88 + 0.00461656*i25*i89 + 
     0.01024232*i25*i90 + 0.00541446*i25*i91 + 0.0058998*i25*i92 + 0.00419408*
     i25*i93 + 0.0034525*i25*i94 + 0.00742618*i25*i95 + 0.01117296*i25*i96 + 
     0.00976304*i25*i97 + 0.01005714*i25*i98 + 0.00997578*i25*i99 + 0.01119052*
     i25*i100 + 0.0054348*i26*i27 + 0.00158545*i26*i28 + 0.00507804*i26*i29 + 
     0.01115184*i26*i30 + 0.00280118*i26*i31 + 0.0103351*i26*i32 + 0.00796856*
     i26*i33 + 0.00322344*i26*i34 + 0.00410686*i26*i35 + 0.00922294*i26*i36 + 
     0.00708292*i26*i37 + 0.00218796*i26*i38 + 0.00667316*i26*i39 + 0.00604564*
     i26*i40 + 0.00774532*i26*i41 + 0.00814596*i26*i42 + 0.0026451*i26*i43 + 
     0.00582206*i26*i44 + 0.00332382*i26*i45 + 0.00451686*i26*i46 + 0.00733916*
     i26*i47 + 0.00476946*i26*i48 + 0.00485772*i26*i49 + 0.0100103*i26*i50 + 
     0.00280844*i26*i51 + 0.00687248*i26*i52 + 0.00732458*i26*i53 + 0.00815206*
     i26*i54 + 0.00612236*i26*i55 + 0.00307146*i26*i56 + 0.0049056*i26*i57 + 
     0.00412472*i26*i58 + 0.0040935*i26*i59 + 0.0040596*i26*i60 + 0.01138906*
     i26*i61 + 0.00976836*i26*i62 + 0.0087752*i26*i63 + 0.00574374*i26*i64 + 
     0.00539202*i26*i65 + 0.0020772*i26*i66 + 0.00535872*i26*i67 + 0.0041987*
     i26*i68 + 0.00941624*i26*i69 + 0.00708368*i26*i70 + 0.00623148*i26*i71 + 
     0.0059506*i26*i72 + 0.00509138*i26*i73 + 0.00640786*i26*i74 + 0.00599214*
     i26*i75 + 0.00535234*i26*i76 + 0.0061449*i26*i77 + 0.0049639*i26*i78 + 
     0.00212662*i26*i79 + 0.00709762*i26*i80 + 0.00556936*i26*i81 + 0.0033022*
     i26*i82 - 0.0001706112*i26*i83 + 0.0042184*i26*i84 + 0.00533878*i26*i85 + 
     0.00407216*i26*i86 + 0.0050287*i26*i87 + 0.00492458*i26*i88 + 0.00236614*
     i26*i89 + 0.0069424*i26*i90 + 0.00767098*i26*i91 + 0.00534286*i26*i92 + 
     0.001624812*i26*i93 + 0.00309366*i26*i94 + 0.00617648*i26*i95 + 0.01108742
     *i26*i96 + 0.0068572*i26*i97 + 0.00411952*i26*i98 + 0.00653102*i26*i99 + 
     0.00944332*i26*i100 + 0.01236278*i27*i28 + 0.00615174*i27*i29 + 0.0284656*
     i27*i30 + 0.00531366*i27*i31 + 0.0227234*i27*i32 + 0.01239532*i27*i33 + 
     0.00873604*i27*i34 + 0.01006162*i27*i35 + 0.0244272*i27*i36 + 0.01206064*
     i27*i37 + 0.00764146*i27*i38 + 0.01638042*i27*i39 + 0.0281728*i27*i40 + 
     0.0236864*i27*i41 + 0.01394576*i27*i42 + 0.01151236*i27*i43 + 0.00967762*
     i27*i44 + 0.0001345884*i27*i45 + 0.00656542*i27*i46 + 0.0226088*i27*i47 + 
     0.00665866*i27*i48 + 0.00867994*i27*i49 + 0.01519986*i27*i50 + 0.00516678*
     i27*i51 + 0.01290734*i27*i52 + 0.00750112*i27*i53 + 0.015481*i27*i54 + 
     0.00918208*i27*i55 + 0.01133662*i27*i56 + 0.00655584*i27*i57 + 0.00645326*
     i27*i58 + 0.01022706*i27*i59 + 0.00655942*i27*i60 + 0.0230718*i27*i61 + 
     0.0200196*i27*i62 + 0.01214952*i27*i63 + 0.00996324*i27*i64 + 0.00982212*
     i27*i65 + 0.00606814*i27*i66 + 0.00854006*i27*i67 + 0.00819936*i27*i68 + 
     0.01608286*i27*i69 + 0.00821942*i27*i70 + 0.0230626*i27*i71 + 0.01648106*
     i27*i72 + 0.00833058*i27*i73 + 0.0119455*i27*i74 + 0.0073591*i27*i75 + 
     0.00553444*i27*i76 + 0.00629646*i27*i77 + 0.00406434*i27*i78 + 0.00760068*
     i27*i79 + 0.00662478*i27*i80 + 0.0198678*i27*i81 + 0.0044671*i27*i82 + 
     0.01205228*i27*i83 + 0.0106948*i27*i84 + 0.00763694*i27*i85 + 0.01122432*
     i27*i86 + 0.00899094*i27*i87 + 0.0237458*i27*i88 + 0.00548044*i27*i89 + 
     0.01135562*i27*i90 + 0.01131762*i27*i91 + 0.00767916*i27*i92 + 0.00281062*
     i27*i93 + 0.00450634*i27*i94 + 0.01029564*i27*i95 + 0.01573164*i27*i96 + 
     0.01494338*i27*i97 + 0.01900252*i27*i98 + 0.01470772*i27*i99 + 0.01866828*
     i27*i100 + 0.00362518*i28*i29 + 0.01640256*i28*i30 + 0.00349192*i28*i31 + 
     0.0129237*i28*i32 + 0.00538584*i28*i33 + 0.00533474*i28*i34 + 0.00643216*
     i28*i35 + 0.01292206*i28*i36 + 0.00798078*i28*i37 + 0.0054977*i28*i38 + 
     0.00885966*i28*i39 + 0.016828*i28*i40 + 0.01167374*i28*i41 + 0.00549216*
     i28*i42 + 0.00692364*i28*i43 + 0.00370672*i28*i44 + 0.000284348*i28*i45 + 
     0.00277668*i28*i46 + 0.00936392*i28*i47 + 0.00267238*i28*i48 + 0.00522892*
     i28*i49 + 0.00779258*i28*i50 + 0.0043462*i28*i51 + 0.00591302*i28*i52 + 
     0.00320368*i28*i53 + 0.00698682*i28*i54 + 0.00560018*i28*i55 + 0.0075828*
     i28*i56 + 0.00361162*i28*i57 + 0.00229658*i28*i58 + 0.00780328*i28*i59 + 
     0.0033416*i28*i60 + 0.01168298*i28*i61 + 0.0082366*i28*i62 + 0.00465746*
     i28*i63 + 0.00328332*i28*i64 + 0.00685966*i28*i65 + 0.00386632*i28*i66 + 
     0.0053142*i28*i67 + 0.00432904*i28*i68 + 0.00791276*i28*i69 + 0.0040137*
     i28*i70 + 0.01081358*i28*i71 + 0.00841874*i28*i72 + 0.00534694*i28*i73 + 
     0.00677544*i28*i74 + 0.00391198*i28*i75 + 0.00308942*i28*i76 + 0.00250778*
     i28*i77 + 0.00189916*i28*i78 + 0.00856184*i28*i79 + 0.00337182*i28*i80 + 
     0.00959416*i28*i81 + 0.00329038*i28*i82 + 0.00388664*i28*i83 + 0.00685968*
     i28*i84 + 0.00406002*i28*i85 + 0.00658126*i28*i86 + 0.00646838*i28*i87 + 
     0.0218548*i28*i88 + 0.00541992*i28*i89 + 0.00503116*i28*i90 + 0.00418236*
     i28*i91 + 0.0040874*i28*i92 + 0.0022624*i28*i93 + 0.00392254*i28*i94 + 
     0.00482686*i28*i95 + 0.00726382*i28*i96 + 0.00767472*i28*i97 + 0.01066418*
     i28*i98 + 0.00883358*i28*i99 + 0.0070211*i28*i100 + 0.0147917*i29*i30 + 
     0.001068816*i29*i31 + 0.0105712*i29*i32 + 0.00407766*i29*i33 + 0.00300076*
     i29*i34 + 0.00524794*i29*i35 + 0.01016322*i29*i36 + 0.00841674*i29*i37 + 
     0.00258632*i29*i38 + 0.00698836*i29*i39 + 0.01223674*i29*i40 + 0.01128912*
     i29*i41 + 0.00481604*i29*i42 + 0.00316394*i29*i43 + 0.00690116*i29*i44 + 
     0.00082418*i29*i45 + 0.00343988*i29*i46 + 0.00660586*i29*i47 + 0.00315994*
     i29*i48 + 0.004109*i29*i49 + 0.01072766*i29*i50 + 0.00295018*i29*i51 + 
     0.00574084*i29*i52 + 0.00735384*i29*i53 + 0.00646518*i29*i54 + 0.00437712*
     i29*i55 + 0.0050201*i29*i56 + 0.00428602*i29*i57 + 0.00339284*i29*i58 + 
     0.00395186*i29*i59 + 0.00369852*i29*i60 + 0.01069104*i29*i61 + 0.00877524*
     i29*i62 + 0.00780122*i29*i63 + 0.00319846*i29*i64 + 0.00522668*i29*i65 + 
     0.00318906*i29*i66 + 0.00765554*i29*i67 + 0.00353436*i29*i68 + 0.0090668*
     i29*i69 + 0.0062235*i29*i70 + 0.00879038*i29*i71 + 0.00661754*i29*i72 + 
     0.00355728*i29*i73 + 0.0041974*i29*i74 + 0.00530048*i29*i75 + 0.00543652*
     i29*i76 + 0.00436164*i29*i77 + 0.00450742*i29*i78 + 0.00725294*i29*i79 + 
     0.00491692*i29*i80 + 0.00689594*i29*i81 + 0.00288614*i29*i82 + 0.005327*
     i29*i83 + 0.00356482*i29*i84 + 0.00320232*i29*i85 + 0.00401206*i29*i86 + 
     0.00746968*i29*i87 + 0.01484586*i29*i88 + 0.00405332*i29*i89 + 0.00646554*
     i29*i90 + 0.00398186*i29*i91 + 0.0045419*i29*i92 + 0.00249602*i29*i93 + 
     0.00344506*i29*i94 + 0.0046313*i29*i95 + 0.01012898*i29*i96 + 0.00666118*
     i29*i97 + 0.00510452*i29*i98 + 0.00865974*i29*i99 + 0.00556162*i29*i100 + 
     0.01432038*i30*i31 + 0.048762*i30*i32 + 0.03246*i30*i33 + 0.00510162*i30*
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     0.001838718*i30*i45 + 0.01735792*i30*i46 + 0.0257124*i30*i47 + 0.01952576*
     i30*i48 + 0.0285968*i30*i49 + 0.0597966*i30*i50 + 0.0235442*i30*i51 + 
     0.0356002*i30*i52 + 0.056815*i30*i53 + 0.031993*i30*i54 + 0.0256864*i30*
     i55 + 0.012682*i30*i56 + 0.01927838*i30*i57 + 0.0132181*i30*i58 + 
     0.0308396*i30*i59 + 0.01646776*i30*i60 + 0.0691402*i30*i61 + 0.0539688*i30
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     0.01199066*i30*i66 + 0.0301278*i30*i67 + 0.0209952*i30*i68 + 0.0484514*i30
     *i69 + 0.0226726*i30*i70 + 0.02153*i30*i71 + 0.023498*i30*i72 + 0.0217474*
     i30*i73 + 0.0363548*i30*i74 + 0.0290864*i30*i75 + 0.01738014*i30*i76 + 
     0.0248066*i30*i77 + 0.01560782*i30*i78 + 0.0735134*i30*i79 + 0.0216582*i30
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     0.02421*i30*i84 + 0.01903928*i30*i85 + 0.0384208*i30*i86 + 0.0308632*i30*
     i87 + 0.112101*i30*i88 + 0.0313082*i30*i89 + 0.0480838*i30*i90 + 0.0265036
     *i30*i91 + 0.0219052*i30*i92 + 0.01243318*i30*i93 + 0.00866336*i30*i94 + 
     0.0318698*i30*i95 + 0.0809696*i30*i96 + 0.0362056*i30*i97 + 0.0307602*i30*
     i98 + 0.0452826*i30*i99 + 0.0359652*i30*i100 + 0.01352968*i31*i32 + 
     0.01461656*i31*i33 + 0.00410226*i31*i34 + 0.00308616*i31*i35 + 0.0221942*
     i31*i36 + 0.0095014*i31*i37 + 0.0001894118*i31*i38 + 0.01328104*i31*i39 + 
     0.0207254*i31*i40 + 0.01363894*i31*i41 + 0.01129202*i31*i42 + 0.0108266*
     i31*i43 + 0.01097008*i31*i44 + 0.00461712*i31*i45 + 0.00463752*i31*i46 + 
     0.00929264*i31*i47 + 0.00473752*i31*i48 + 0.0114599*i31*i49 + 0.0117742*
     i31*i50 + 0.0088573*i31*i51 + 0.0075837*i31*i52 + 0.00658756*i31*i53 + 
     0.0113218*i31*i54 + 0.00930362*i31*i55 + 0.01063604*i31*i56 + 0.00432704*
     i31*i57 + 0.00804616*i31*i58 + 0.01180986*i31*i59 + 0.0009047*i31*i60 + 
     0.01200762*i31*i61 + 0.00940268*i31*i62 + 0.01417994*i31*i63 + 0.0076164*
     i31*i64 + 0.00575322*i31*i65 + 0.00834872*i31*i66 + 0.00454676*i31*i67 + 
     0.00544346*i31*i68 + 0.0132866*i31*i69 + 0.00553084*i31*i70 + 0.01147094*
     i31*i71 + 0.00577578*i31*i72 + 0.00887008*i31*i73 + 0.01059428*i31*i74 + 
     0.0040723*i31*i75 + 0.00207936*i31*i76 + 0.01175316*i31*i77 + 0.00278464*
     i31*i78 + 0.00880162*i31*i79 + 0.0087823*i31*i80 + 0.00669872*i31*i81 + 
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     i31*i85 + 0.01080682*i31*i86 + 0.00523332*i31*i87 + 0.0207656*i31*i88 + 
     0.00591302*i31*i89 + 0.00439716*i31*i90 + 0.0115743*i31*i91 + 0.00995262*
     i31*i92 + 0.000428388*i31*i93 + 0.00464012*i31*i94 + 0.00813868*i31*i95 + 
     0.00570582*i31*i96 + 0.00954936*i31*i97 + 0.01038358*i31*i98 + 0.00920842*
     i31*i99 + 0.01146966*i31*i100 + 0.0209668*i32*i33 + 0.0108011*i32*i34 + 
     0.01248282*i32*i35 + 0.0530038*i32*i36 + 0.0301486*i32*i37 + 0.00760388*
     i32*i38 + 0.0317898*i32*i39 + 0.0642986*i32*i40 + 0.0332684*i32*i41 + 
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     i32*i59 + 0.00772776*i32*i60 + 0.0424102*i32*i61 + 0.0330624*i32*i62 + 
     0.0190237*i32*i63 + 0.01185726*i32*i64 + 0.01593976*i32*i65 + 0.00931156*
     i32*i66 + 0.01976096*i32*i67 + 0.00940704*i32*i68 + 0.0353824*i32*i69 + 
     0.01637874*i32*i70 + 0.0234414*i32*i71 + 0.01981882*i32*i72 + 0.01518934*
     i32*i73 + 0.0206944*i32*i74 + 0.01368518*i32*i75 + 0.01085922*i32*i76 + 
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     i32*i87 + 0.0404024*i32*i88 + 0.00700416*i32*i89 + 0.0284686*i32*i90 + 
     0.01764584*i32*i91 + 0.01747106*i32*i92 + 0.00781272*i32*i93 + 0.01173676*
     i32*i94 + 0.01901852*i32*i95 + 0.032411*i32*i96 + 0.0238232*i32*i97 + 
     0.021198*i32*i98 + 0.0300116*i32*i99 + 0.0354006*i32*i100 + 0.0090127*i33*
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     i33*i41 + 0.01859662*i33*i42 + 0.00949822*i33*i43 + 0.0173394*i33*i44 + 
     0.00462026*i33*i45 + 0.0076766*i33*i46 + 0.0195887*i33*i47 + 0.00677792*
     i33*i48 + 0.01593666*i33*i49 + 0.0205366*i33*i50 + 0.01028686*i33*i51 + 
     0.01380638*i33*i52 + 0.0139701*i33*i53 + 0.016589*i33*i54 + 0.0139115*i33*
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     0.01414764*i33*i73 + 0.01623304*i33*i74 + 0.00580254*i33*i75 + 0.00688906*
     i33*i76 + 0.01955742*i33*i77 + 0.0043617*i33*i78 + 0.0110714*i33*i79 + 
     0.00837212*i33*i80 + 0.0186224*i33*i81 + 0.0038599*i33*i82 + 0.01828456*
     i33*i83 + 0.01460176*i33*i84 + 0.00984126*i33*i85 + 0.01375926*i33*i86 + 
     0.01081848*i33*i87 + 0.0294078*i33*i88 + 0.00904426*i33*i89 + 0.01335384*
     i33*i90 + 0.00944562*i33*i91 + 0.01586856*i33*i92 + 0.00253356*i33*i93 + 
     0.00579828*i33*i94 + 0.01264366*i33*i95 + 0.0212436*i33*i96 + 0.014968*i33
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     0.00838326*i34*i42 + 0.00601354*i34*i43 + 0.00621002*i34*i44 + 0.00388646*
     i34*i45 + 0.00291464*i34*i46 + 0.01279302*i34*i47 + 0.001590652*i34*i48 + 
     0.00546164*i34*i49 + 0.00756668*i34*i50 + 0.00255946*i34*i51 + 0.00586752*
     i34*i52 - 0.0001086844*i34*i53 + 0.00756758*i34*i54 + 0.00472132*i34*i55
      + 0.0090114*i34*i56 + 0.00404276*i34*i57 + 0.00259172*i34*i58 + 0.0043188
     *i34*i59 + 0.00265148*i34*i60 + 0.00988174*i34*i61 + 0.00773706*i34*i62 + 
     0.00871216*i34*i63 + 0.0051719*i34*i64 + 0.005674*i34*i65 + 0.0042472*i34*
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     0.00528678*i34*i70 + 0.01141144*i34*i71 + 0.00731358*i34*i72 + 0.00557996*
     i34*i73 + 0.00428558*i34*i74 + 0.00214164*i34*i75 + 0.001888024*i34*i76 + 
     0.00450712*i34*i77 + 0.001974898*i34*i78 + 0.000555542*i34*i79 + 0.004826*
     i34*i80 + 0.01009798*i34*i81 + 0.00342408*i34*i82 + 0.0066259*i34*i83 + 
     0.00557372*i34*i84 + 0.00493326*i34*i85 + 0.0033431*i34*i86 + 0.00355798*
     i34*i87 + 0.0070914*i34*i88 + 0.00319452*i34*i89 + 0.001165088*i34*i90 + 
     0.00330168*i34*i91 + 0.00487072*i34*i92 + 0.001039364*i34*i93 + 0.00462638
     *i34*i94 + 0.00474964*i34*i95 + 0.00307738*i34*i96 + 0.00634158*i34*i97 + 
     0.0093911*i34*i98 + 0.00479968*i34*i99 + 0.00945466*i34*i100 + 0.00886108*
     i35*i36 + 0.008324*i35*i37 + 0.0042517*i35*i38 + 0.0063195*i35*i39 + 
     0.00897334*i35*i40 + 0.01438534*i35*i41 + 0.00707384*i35*i42 + 0.00524994*
     i35*i43 + 0.00729354*i35*i44 + 0.00231104*i35*i45 + 0.00317018*i35*i46 + 
     0.01095322*i35*i47 + 0.00256082*i35*i48 + 0.0066693*i35*i49 + 0.00896786*
     i35*i50 + 0.00243944*i35*i51 + 0.00542922*i35*i52 + 0.001853016*i35*i53 + 
     0.0080304*i35*i54 + 0.004194*i35*i55 + 0.00944224*i35*i56 + 0.0044097*i35*
     i57 + 0.00234874*i35*i58 + 0.0045055*i35*i59 + 0.00387194*i35*i60 + 
     0.01070194*i35*i61 + 0.01020854*i35*i62 + 0.00869604*i35*i63 + 0.0038381*
     i35*i64 + 0.00566828*i35*i65 + 0.00392276*i35*i66 + 0.00493806*i35*i67 + 
     0.00543634*i35*i68 + 0.01090284*i35*i69 + 0.00744802*i35*i70 + 0.01323476*
     i35*i71 + 0.00994186*i35*i72 + 0.00554564*i35*i73 + 0.00631474*i35*i74 + 
     0.00456554*i35*i75 + 0.00357674*i35*i76 + 0.00520436*i35*i77 + 0.0030095*
     i35*i78 + 0.0057729*i35*i79 + 0.00411204*i35*i80 + 0.00953392*i35*i81 + 
     0.00378046*i35*i82 + 0.00572152*i35*i83 + 0.00613732*i35*i84 + 0.00382166*
     i35*i85 + 0.00356476*i35*i86 + 0.00634394*i35*i87 + 0.0111758*i35*i88 + 
     0.00567884*i35*i89 + 0.00368822*i35*i90 + 0.00382434*i35*i91 + 0.00295216*
     i35*i92 + 0.00261056*i35*i93 + 0.00538486*i35*i94 + 0.00508518*i35*i95 + 
     0.00571674*i35*i96 + 0.00749186*i35*i97 + 0.00986618*i35*i98 + 0.00565378*
     i35*i99 + 0.0094721*i35*i100 + 0.0440606*i36*i37 + 0.0069763*i36*i38 + 
     0.0493166*i36*i39 + 0.121634*i36*i40 + 0.0358136*i36*i41 + 0.0380066*i36*
     i42 + 0.0240066*i36*i43 + 0.0315302*i36*i44 + 0.00778714*i36*i45 + 
     0.01711478*i36*i46 + 0.0433014*i36*i47 + 0.01592312*i36*i48 + 0.0219624*
     i36*i49 + 0.0584382*i36*i50 + 0.0237454*i36*i51 + 0.030079*i36*i52 + 
     0.0450814*i36*i53 + 0.0285826*i36*i54 + 0.0266392*i36*i55 + 0.01830758*i36
     *i56 + 0.01364522*i36*i57 + 0.01568*i36*i58 + 0.0359108*i36*i59 + 
     0.00643528*i36*i60 + 0.056249*i36*i61 + 0.0503568*i36*i62 + 0.0221574*i36*
     i63 + 0.023432*i36*i64 + 0.0219264*i36*i65 + 0.01946022*i36*i66 + 
     0.0301552*i36*i67 + 0.00986666*i36*i68 + 0.0496472*i36*i69 + 0.0177644*i36
     *i70 + 0.0308856*i36*i71 + 0.01899074*i36*i72 + 0.01805938*i36*i73 + 
     0.0273694*i36*i74 + 0.01662774*i36*i75 + 0.00832596*i36*i76 + 0.0203852*
     i36*i77 + 0.0174271*i36*i78 + 0.039217*i36*i79 + 0.0232082*i36*i80 + 
     0.0357644*i36*i81 + 0.00331724*i36*i82 + 0.0276304*i36*i83 + 0.0267904*i36
     *i84 + 0.02756*i36*i85 + 0.0320374*i36*i86 + 0.0222598*i36*i87 + 0.0496644
     *i36*i88 + 0.01118028*i36*i89 + 0.0432572*i36*i90 + 0.027434*i36*i91 + 
     0.0293774*i36*i92 + 0.0055352*i36*i93 + 0.00852418*i36*i94 + 0.028037*i36*
     i95 + 0.0642512*i36*i96 + 0.0386458*i36*i97 + 0.040981*i36*i98 + 0.04604*
     i36*i99 + 0.0478424*i36*i100 + 0.00525362*i37*i38 + 0.0212576*i37*i39 + 
     0.0543916*i37*i40 + 0.018282*i37*i41 + 0.01700698*i37*i42 + 0.00953368*i37
     *i43 + 0.0147155*i37*i44 + 0.00425042*i37*i45 + 0.00777022*i37*i46 + 
     0.01646346*i37*i47 + 0.00740598*i37*i48 + 0.01274586*i37*i49 + 0.0282742*
     i37*i50 + 0.01506898*i37*i51 + 0.01409464*i37*i52 + 0.01916222*i37*i53 + 
     0.01572296*i37*i54 + 0.01361714*i37*i55 + 0.01302042*i37*i56 + 0.00807862*
     i37*i57 + 0.00701644*i37*i58 + 0.0201438*i37*i59 + 0.00497496*i37*i60 + 
     0.0259544*i37*i61 + 0.01982096*i37*i62 + 0.01082904*i37*i63 + 0.00909066*
     i37*i64 + 0.0112364*i37*i65 + 0.0089483*i37*i66 + 0.01522148*i37*i67 + 
     0.00459152*i37*i68 + 0.0214858*i37*i69 + 0.01075074*i37*i70 + 0.0132224*
     i37*i71 + 0.00980738*i37*i72 + 0.00885252*i37*i73 + 0.01427422*i37*i74 + 
     0.00903996*i37*i75 + 0.00768272*i37*i76 + 0.0103221*i37*i77 + 0.01082002*
     i37*i78 + 0.0248284*i37*i79 + 0.01098172*i37*i80 + 0.01335848*i37*i81 + 
     0.00545734*i37*i82 + 0.00921544*i37*i83 + 0.0110069*i37*i84 + 0.01385998*
     i37*i85 + 0.01437348*i37*i86 + 0.01621552*i37*i87 + 0.01981332*i37*i88 + 
     0.00549314*i37*i89 + 0.0210958*i37*i90 + 0.0116061*i37*i91 + 0.01444326*
     i37*i92 + 0.00631646*i37*i93 + 0.00847398*i37*i94 + 0.0132838*i37*i95 + 
     0.0257442*i37*i96 + 0.01746728*i37*i97 + 0.01331586*i37*i98 + 0.0246618*
     i37*i99 + 0.0231186*i37*i100 + 0.00427726*i38*i39 + 0.00960742*i38*i40 + 
     0.00588794*i38*i41 + 0.0040899*i38*i42 + 0.00370486*i38*i43 + 0.001581616*
     i38*i44 + 0.00157779*i38*i45 + 0.001517842*i38*i46 + 0.00577098*i38*i47 + 
     0.00184948*i38*i48 + 0.001412132*i38*i49 + 0.00473326*i38*i50 + 
     0.001265572*i38*i51 + 0.00389392*i38*i52 + 0.00195541*i38*i53 + 0.0045747*
     i38*i54 + 0.003024*i38*i55 + 0.00322834*i38*i56 + 0.00240162*i38*i57 + 
     0.000494648*i38*i58 + 0.0035117*i38*i59 + 0.00302272*i38*i60 + 0.0067192*
     i38*i61 + 0.00576934*i38*i62 + 0.00236514*i38*i63 + 0.00208302*i38*i64 + 
     0.00359594*i38*i65 + 0.001590092*i38*i66 + 0.00239398*i38*i67 + 0.00302224
     *i38*i68 + 0.00326928*i38*i69 + 0.00302294*i38*i70 + 0.0049377*i38*i71 + 
     0.00553496*i38*i72 + 0.00229972*i38*i73 + 0.00318332*i38*i74 + 0.00325074*
     i38*i75 + 0.001803886*i38*i76 + 0.000902562*i38*i77 + 0.001651326*i38*i78
      + 0.0039935*i38*i79 + 0.00233242*i38*i80 + 0.00546644*i38*i81 + 
     0.00223454*i38*i82 - 0.001681894*i38*i83 + 0.0025273*i38*i84 + 0.0032781*
     i38*i85 + 0.001557044*i38*i86 + 0.00327138*i38*i87 + 0.00674346*i38*i88 + 
     0.0020784*i38*i89 + 0.00343958*i38*i90 + 0.00324954*i38*i91 + 0.00206404*
     i38*i92 + 0.00161462*i38*i93 + 0.00247166*i38*i94 + 0.00341238*i38*i95 + 
     0.00585902*i38*i96 + 0.00423638*i38*i97 + 0.00566634*i38*i98 + 0.00315378*
     i38*i99 + 0.00449598*i38*i100 + 0.0491892*i39*i40 + 0.0262408*i39*i41 + 
     0.0205234*i39*i42 + 0.01409356*i39*i43 + 0.0195666*i39*i44 + 0.00525174*
     i39*i45 + 0.01076856*i39*i46 + 0.0216478*i39*i47 + 0.01097136*i39*i48 + 
     0.0178672*i39*i49 + 0.0324104*i39*i50 + 0.0147971*i39*i51 + 0.01855664*i39
     *i52 + 0.0250992*i39*i53 + 0.0213078*i39*i54 + 0.01575182*i39*i55 + 
     0.01438592*i39*i56 + 0.0105253*i39*i57 + 0.01177712*i39*i58 + 0.0207946*
     i39*i59 + 0.00650454*i39*i60 + 0.036126*i39*i61 + 0.0278076*i39*i62 + 
     0.0206546*i39*i63 + 0.01499036*i39*i64 + 0.01276412*i39*i65 + 0.0125414*
     i39*i66 + 0.01617824*i39*i67 + 0.010394*i39*i68 + 0.0290228*i39*i69 + 
     0.01190924*i39*i70 + 0.01824964*i39*i71 + 0.014012*i39*i72 + 0.01408568*
     i39*i73 + 0.0192582*i39*i74 + 0.01283914*i39*i75 + 0.00757714*i39*i76 + 
     0.0157748*i39*i77 + 0.00886562*i39*i78 + 0.0226622*i39*i79 + 0.01506442*
     i39*i80 + 0.01868878*i39*i81 + 0.00371016*i39*i82 + 0.01245306*i39*i83 + 
     0.01693888*i39*i84 + 0.0145704*i39*i85 + 0.0207926*i39*i86 + 0.01487822*
     i39*i87 + 0.0465058*i39*i88 + 0.01052428*i39*i89 + 0.0220072*i39*i90 + 
     0.01887928*i39*i91 + 0.01597714*i39*i92 + 0.00531126*i39*i93 + 0.00658506*
     i39*i94 + 0.01713092*i39*i95 + 0.0328166*i39*i96 + 0.0213542*i39*i97 + 
     0.0210286*i39*i98 + 0.0255336*i39*i99 + 0.0274274*i39*i100 + 0.0504412*i40
     *i41 + 0.0336102*i40*i42 + 0.0294804*i40*i43 + 0.0424704*i40*i44 + 
     0.0030095*i40*i45 + 0.01146224*i40*i46 + 0.0507426*i40*i47 + 0.01585054*
     i40*i48 + 0.0217164*i40*i49 + 0.0491478*i40*i50 + 0.0317926*i40*i51 + 
     0.0284682*i40*i52 + 0.0468934*i40*i53 + 0.0309254*i40*i54 + 0.028626*i40*
     i55 + 0.0309698*i40*i56 + 0.01062184*i40*i57 + 0.01987174*i40*i58 + 
     0.0429952*i40*i59 + 0.00300922*i40*i60 + 0.0574936*i40*i61 + 0.0496304*i40
     *i62 + 0.01678646*i40*i63 + 0.0153295*i40*i64 + 0.0230176*i40*i65 + 
     0.0200972*i40*i66 + 0.0274442*i40*i67 - 0.00465404*i40*i68 + 0.0404524*i40
     *i69 + 0.01243058*i40*i70 + 0.0333654*i40*i71 + 0.01847532*i40*i72 + 
     0.01863464*i40*i73 + 0.01865328*i40*i74 + 0.0086314*i40*i75 + 0.0107773*
     i40*i76 + 0.0203618*i40*i77 + 0.01445046*i40*i78 + 0.0410886*i40*i79 + 
     0.01194082*i40*i80 + 0.044529*i40*i81 + 0.00528742*i40*i82 + 0.0445722*i40
     *i83 + 0.0229102*i40*i84 + 0.0241064*i40*i85 + 0.0368384*i40*i86 + 
     0.0327072*i40*i87 + 0.0612044*i40*i88 + 0.0029601*i40*i89 + 0.0534994*i40*
     i90 + 0.0258428*i40*i91 + 0.0317582*i40*i92 + 0.00965728*i40*i93 + 
     0.01437522*i40*i94 + 0.0249652*i40*i95 + 0.0605768*i40*i96 + 0.0345084*i40
     *i97 + 0.0313726*i40*i98 + 0.064674*i40*i99 + 0.0504464*i40*i100 + 
     0.0211266*i41*i42 + 0.0280268*i41*i43 + 0.0396958*i41*i44 + 0.00245084*i41
     *i45 + 0.00955952*i41*i46 + 0.0396834*i41*i47 + 0.0061862*i41*i48 + 
     0.02227*i41*i49 + 0.0217142*i41*i50 + 0.00978418*i41*i51 + 0.01479238*i41*
     i52 + 0.016171*i41*i53 + 0.0243916*i41*i54 + 0.01422356*i41*i55 + 
     0.0283342*i41*i56 + 0.00801394*i41*i57 + 0.01783044*i41*i58 + 0.01283818*
     i41*i59 + 0.00500652*i41*i60 + 0.0289002*i41*i61 + 0.0313062*i41*i62 + 
     0.0372108*i41*i63 + 0.0192516*i41*i64 + 0.0152555*i41*i65 + 0.01848886*i41
     *i66 + 0.01396382*i41*i67 + 0.01323774*i41*i68 + 0.0319484*i41*i69 + 
     0.01505338*i41*i70 + 0.0464724*i41*i71 + 0.0275962*i41*i72 + 0.01531976*
     i41*i73 + 0.0159052*i41*i74 + 0.00897454*i41*i75 + 0.00931212*i41*i76 + 
     0.01958562*i41*i77 + 0.00344582*i41*i78 + 0.00874906*i41*i79 + 0.01063594*
     i41*i80 + 0.02994*i41*i81 + 0.000668906*i41*i82 + 0.0436128*i41*i83 + 
     0.0233408*i41*i84 + 0.00754018*i41*i85 + 0.01805636*i41*i86 + 0.01281402*
     i41*i87 + 0.0523726*i41*i88 + 0.00844562*i41*i89 + 0.01302218*i41*i90 + 
     0.01396562*i41*i91 + 0.01458222*i41*i92 + 0.0072903*i41*i93 + 0.00709746*
     i41*i94 + 0.01473562*i41*i95 + 0.01085782*i41*i96 + 0.021406*i41*i97 + 
     0.0295828*i41*i98 + 0.01994264*i41*i99 + 0.0263314*i41*i100 + 0.01525376*
     i42*i43 + 0.01763084*i42*i44 + 0.00749008*i42*i45 + 0.00916454*i42*i46 + 
     0.0235102*i42*i47 + 0.00921988*i42*i48 + 0.01347394*i42*i49 + 0.0247352*
     i42*i50 + 0.01120346*i42*i51 + 0.01858118*i42*i52 + 0.01723882*i42*i53 + 
     0.0208142*i42*i54 + 0.01360838*i42*i55 + 0.0118194*i42*i56 + 0.00860676*
     i42*i57 + 0.00935934*i42*i58 + 0.01516418*i42*i59 + 0.0068076*i42*i60 + 
     0.028779*i42*i61 + 0.0258494*i42*i62 + 0.0233604*i42*i63 + 0.01573382*i42*
     i64 + 0.01049188*i42*i65 + 0.00740748*i42*i66 + 0.01082116*i42*i67 + 
     0.00777482*i42*i68 + 0.0240088*i42*i69 + 0.01102072*i42*i70 + 0.01820862*
     i42*i71 + 0.01298112*i42*i72 + 0.01234456*i42*i73 + 0.0141652*i42*i74 + 
     0.00934936*i42*i75 + 0.00505832*i42*i76 + 0.01458566*i42*i77 + 0.00728638*
     i42*i78 + 0.0099359*i42*i79 + 0.01486474*i42*i80 + 0.01668502*i42*i81 + 
     0.00373442*i42*i82 + 0.01190258*i42*i83 + 0.01201006*i42*i84 + 0.0151776*
     i42*i85 + 0.0145938*i42*i86 + 0.00824462*i42*i87 + 0.0160982*i42*i88 + 
     0.006593*i42*i89 + 0.01418496*i42*i90 + 0.01803698*i42*i91 + 0.0159653*i42
     *i92 + 0.00291508*i42*i93 + 0.00538746*i42*i94 + 0.01644022*i42*i95 + 
     0.0250208*i42*i96 + 0.018306*i42*i97 + 0.01797718*i42*i98 + 0.01649756*i42
     *i99 + 0.025412*i42*i100 + 0.01762524*i43*i44 + 0.0026577*i43*i45 + 
     0.00500594*i43*i46 + 0.01987672*i43*i47 + 0.00486026*i43*i48 + 0.01054502*
     i43*i49 + 0.00887754*i43*i50 + 0.00693606*i43*i51 + 0.01006578*i43*i52 + 
     0.01002454*i43*i53 + 0.0138188*i43*i54 + 0.00975298*i43*i55 + 0.01686962*
     i43*i56 + 0.00490722*i43*i57 + 0.00949952*i43*i58 + 0.01032096*i43*i59 + 
     0.00313858*i43*i60 + 0.01509816*i43*i61 + 0.0162044*i43*i62 + 0.01875628*
     i43*i63 + 0.01240346*i43*i64 + 0.0085184*i43*i65 + 0.0097536*i43*i66 + 
     0.00601436*i43*i67 + 0.0069333*i43*i68 + 0.01534648*i43*i69 + 0.00585324*
     i43*i70 + 0.01833662*i43*i71 + 0.01219044*i43*i72 + 0.00997222*i43*i73 + 
     0.00950324*i43*i74 + 0.00395808*i43*i75 + 0.00230734*i43*i76 + 0.01177946*
     i43*i77 + 0.00120913*i43*i78 + 0.00451336*i43*i79 + 0.0087064*i43*i80 + 
     0.01415418*i43*i81 + 0.00158382*i43*i82 + 0.01934448*i43*i83 + 0.01332798*
     i43*i84 + 0.0073079*i43*i85 + 0.01024086*i43*i86 + 0.00333288*i43*i87 + 
     0.01697646*i43*i88 + 0.00457426*i43*i89 + 0.00557218*i43*i90 + 0.0103559*
     i43*i91 + 0.00897022*i43*i92 + 0.00315402*i43*i93 + 0.00504118*i43*i94 + 
     0.01075858*i43*i95 + 0.00678594*i43*i96 + 0.01260626*i43*i97 + 0.0163881*
     i43*i98 + 0.01009846*i43*i99 + 0.01154306*i43*i100 + 0.00483446*i44*i45 + 
     0.00652268*i44*i46 + 0.0242272*i44*i47 + 0.00478826*i44*i48 + 0.01685648*
     i44*i49 + 0.020425*i44*i50 + 0.00923526*i44*i51 + 0.01214276*i44*i52 + 
     0.01807778*i44*i53 + 0.01714928*i44*i54 + 0.0117815*i44*i55 + 0.01675568*
     i44*i56 + 0.0065756*i44*i57 + 0.01226174*i44*i58 + 0.0107529*i44*i59 + 
     0.00316098*i44*i60 + 0.0237412*i44*i61 + 0.023095*i44*i62 + 0.0261176*i44*
     i63 + 0.01217274*i44*i64 + 0.01008618*i44*i65 + 0.0100818*i44*i66 + 
     0.01058518*i44*i67 + 0.00547734*i44*i68 + 0.0242058*i44*i69 + 0.01131642*
     i44*i70 + 0.0238346*i44*i71 + 0.01469328*i44*i72 + 0.01153818*i44*i73 + 
     0.0107527*i44*i74 + 0.00664436*i44*i75 + 0.00643936*i44*i76 + 0.01819866*
     i44*i77 + 0.00401038*i44*i78 + 0.00860378*i44*i79 + 0.01052694*i44*i80 + 
     0.01791956*i44*i81 + 0.001302356*i44*i82 + 0.024415*i44*i83 + 0.01318656*
     i44*i84 + 0.00691488*i44*i85 + 0.0134211*i44*i86 + 0.01005166*i44*i87 + 
     0.036692*i44*i88 + 0.00614716*i44*i89 + 0.0120958*i44*i90 + 0.00884752*i44
     *i91 + 0.01296164*i44*i92 + 0.00513894*i44*i93 + 0.00596534*i44*i94 + 
     0.01196692*i44*i95 + 0.01664976*i44*i96 + 0.01462126*i44*i97 + 0.0157382*
     i44*i98 + 0.01533824*i44*i99 + 0.0188597*i44*i100 + 0.00317774*i45*i46 + 
     0.00420624*i45*i47 + 0.00199361*i45*i48 + 0.0050265*i45*i49 + 0.00894044*
     i45*i50 + 0.00284776*i45*i51 + 0.00547162*i45*i52 + 0.00269966*i45*i53 + 
     0.0064379*i45*i54 + 0.00472118*i45*i55 + 0.0042126*i45*i56 + 0.00394074*
     i45*i57 + 0.00265196*i45*i58 + 0.00448504*i45*i59 + 0.001797504*i45*i60 + 
     0.00867806*i45*i61 + 0.00322858*i45*i62 + 0.00607352*i45*i63 + 0.00436738*
     i45*i64 + 0.00237578*i45*i65 + 0.0044976*i45*i66 + 0.00181419*i45*i67 + 
     0.00495262*i45*i68 + 0.00570214*i45*i69 + 0.00422674*i45*i70 + 0.001748284
     *i45*i71 + 0.00347868*i45*i72 + 0.00586478*i45*i73 + 0.00333902*i45*i74 + 
     0.0046385*i45*i75 + 0.001228842*i45*i76 + 0.00595824*i45*i77 + 0.0027183*
     i45*i78 + 0.00108409*i45*i79 + 0.00761658*i45*i80 + 0.0005468*i45*i81 + 
     0.001647768*i45*i82 - 0.00572218*i45*i83 + 0.00291394*i45*i84 + 0.00667112
     *i45*i85 + 0.00283124*i45*i86 + 0.00214236*i45*i87 + 0.00913532*i45*i88 + 
     0.0031579*i45*i89 + 0.001671266*i45*i90 + 0.007457*i45*i91 + 0.00539294*
     i45*i92 + 0.001548892*i45*i93 + 0.00325768*i45*i94 + 0.00415906*i45*i95 + 
     0.00472416*i45*i96 + 0.00257908*i45*i97 + 0.00311904*i45*i98 - 0.00028754*
     i45*i99 + 0.00641254*i45*i100 + 0.00936266*i46*i47 + 0.00551424*i46*i48 + 
     0.00665328*i46*i49 + 0.01254298*i46*i50 + 0.00457552*i46*i51 + 0.00723508*
     i46*i52 + 0.01013924*i46*i53 + 0.00835722*i46*i54 + 0.00612552*i46*i55 + 
     0.00568528*i46*i56 + 0.00506602*i46*i57 + 0.00547684*i46*i58 + 0.00630834*
     i46*i59 + 0.0034076*i46*i60 + 0.01269782*i46*i61 + 0.01056202*i46*i62 + 
     0.00905674*i46*i63 + 0.00727642*i46*i64 + 0.0053986*i46*i65 + 0.00499194*
     i46*i66 + 0.00693256*i46*i67 + 0.00384534*i46*i68 + 0.01113952*i46*i69 + 
     0.00571676*i46*i70 + 0.00918194*i46*i71 + 0.00582038*i46*i72 + 0.00587208*
     i46*i73 + 0.00927628*i46*i74 + 0.00540062*i46*i75 + 0.00399822*i46*i76 + 
     0.00599102*i46*i77 + 0.00478388*i46*i78 + 0.0052496*i46*i79 + 0.0080323*
     i46*i80 + 0.00786638*i46*i81 + 0.001854684*i46*i82 + 0.00407872*i46*i83 + 
     0.00621788*i46*i84 + 0.00606418*i46*i85 + 0.00669516*i46*i86 + 0.00483036*
     i46*i87 + 0.00889994*i46*i88 + 0.00341184*i46*i89 + 0.00883678*i46*i90 + 
     0.00699852*i46*i91 + 0.00577214*i46*i92 + 0.00238288*i46*i93 + 0.001681122
     *i46*i94 + 0.00660328*i46*i95 + 0.0125098*i46*i96 + 0.00829924*i46*i97 + 
     0.00843732*i46*i98 + 0.00930502*i46*i99 + 0.01141018*i46*i100 + 0.00622806
     *i47*i48 + 0.01275134*i47*i49 + 0.0219686*i47*i50 + 0.00559252*i47*i51 + 
     0.014742*i47*i52 + 0.01293552*i47*i53 + 0.0202408*i47*i54 + 0.01276622*i47
     *i55 + 0.0211842*i47*i56 + 0.00751862*i47*i57 + 0.01167596*i47*i58 + 
     0.0096102*i47*i59 + 0.00476024*i47*i60 + 0.0291008*i47*i61 + 0.0293252*i47
     *i62 + 0.0218568*i47*i63 + 0.01597818*i47*i64 + 0.01230724*i47*i65 + 
     0.01074494*i47*i66 + 0.01192482*i47*i67 + 0.0072756*i47*i68 + 0.0259978*
     i47*i69 + 0.01196354*i47*i70 + 0.0346772*i47*i71 + 0.01997802*i47*i72 + 
     0.0109755*i47*i73 + 0.01126216*i47*i74 + 0.00543986*i47*i75 + 0.00507998*
     i47*i76 + 0.01031016*i47*i77 + 0.0051788*i47*i78 + 0.001275304*i47*i79 + 
     0.00993436*i47*i80 + 0.0302174*i47*i81 + 0.0025327*i47*i82 + 0.0227778*i47
     *i83 + 0.01358392*i47*i84 + 0.01015524*i47*i85 + 0.01402648*i47*i86 + 
     0.00789154*i47*i87 + 0.0151434*i47*i88 + 0.001278866*i47*i89 + 0.0158996*
     i47*i90 + 0.01154264*i47*i91 + 0.01393698*i47*i92 + 0.00304714*i47*i93 + 
     0.00512466*i47*i94 + 0.01429612*i47*i95 + 0.01681572*i47*i96 + 0.01931984*
     i47*i97 + 0.0267484*i47*i98 + 0.01797768*i47*i99 + 0.0282598*i47*i100 + 
     0.00546656*i48*i49 + 0.01037534*i48*i50 + 0.00353598*i48*i51 + 0.00756044*
     i48*i52 + 0.01216498*i48*i53 + 0.00967664*i48*i54 + 0.00647364*i48*i55 + 
     0.00302706*i48*i56 + 0.0053717*i48*i57 + 0.00577622*i48*i58 + 0.00544272*
     i48*i59 + 0.00352554*i48*i60 + 0.01442968*i48*i61 + 0.0109524*i48*i62 + 
     0.00913756*i48*i63 + 0.00640136*i48*i64 + 0.00303604*i48*i65 + 0.00380586*
     i48*i66 + 0.00547728*i48*i67 + 0.00370642*i48*i68 + 0.00883124*i48*i69 + 
     0.00549652*i48*i70 + 0.00566248*i48*i71 + 0.00467596*i48*i72 + 0.00529964*
     i48*i73 + 0.00953518*i48*i74 + 0.00623786*i48*i75 + 0.00402142*i48*i76 + 
     0.00662892*i48*i77 + 0.004711*i48*i78 + 0.001686804*i48*i79 + 0.00761384*
     i48*i80 + 0.0057658*i48*i81 + 0.00181049*i48*i82 - 0.00054847*i48*i83 + 
     0.0048793*i48*i84 + 0.00598068*i48*i85 + 0.00652398*i48*i86 + 0.0036324*
     i48*i87 + 0.00674584*i48*i88 + 0.00354232*i48*i89 + 0.00923644*i48*i90 + 
     0.01247554*i48*i91 + 0.00613734*i48*i92 + 0.000820814*i48*i93 + 
     0.001893008*i48*i94 + 0.00690274*i48*i95 + 0.01623126*i48*i96 + 0.00810288
     *i48*i97 + 0.00702362*i48*i98 + 0.01027006*i48*i99 + 0.01224198*i48*i100
      + 0.01829412*i49*i50 + 0.0119479*i49*i51 + 0.01038228*i49*i52 + 
     0.01375438*i49*i53 + 0.01480194*i49*i54 + 0.01103368*i49*i55 + 0.01464938*
     i49*i56 + 0.00724638*i49*i57 + 0.00857364*i49*i58 + 0.0149174*i49*i59 + 
     0.00407556*i49*i60 + 0.0214208*i49*i61 + 0.01655784*i49*i62 + 0.01832206*
     i49*i63 + 0.0099515*i49*i64 + 0.01025382*i49*i65 + 0.00862324*i49*i66 + 
     0.00863512*i49*i67 + 0.0076467*i49*i68 + 0.0220404*i49*i69 + 0.0095053*i49
     *i70 + 0.01307838*i49*i71 + 0.01047408*i49*i72 + 0.01294838*i49*i73 + 
     0.01471132*i49*i74 + 0.00851398*i49*i75 + 0.00575748*i49*i76 + 0.0145716*
     i49*i77 + 0.00460678*i49*i78 + 0.01570596*i49*i79 + 0.00985226*i49*i80 + 
     0.01023644*i49*i81 + 0.00369278*i49*i82 + 0.00860988*i49*i83 + 0.01393008*
     i49*i84 + 0.00839504*i49*i85 + 0.01483048*i49*i86 + 0.01071222*i49*i87 + 
     0.0344974*i49*i88 + 0.00962838*i49*i89 + 0.01169418*i49*i90 + 0.01045396*
     i49*i91 + 0.0095482*i49*i92 + 0.00539536*i49*i93 + 0.00663516*i49*i94 + 
     0.01120512*i49*i95 + 0.01484196*i49*i96 + 0.0127009*i49*i97 + 0.01167858*
     i49*i98 + 0.01477446*i49*i99 + 0.01842494*i49*i100 + 0.01663076*i50*i51 + 
     0.021828*i50*i52 + 0.029083*i50*i53 + 0.0230518*i50*i54 + 0.01639088*i50*
     i55 + 0.01308142*i50*i56 + 0.01225642*i50*i57 + 0.0094199*i50*i58 + 
     0.0222192*i50*i59 + 0.00884396*i50*i60 + 0.0415716*i50*i61 + 0.032076*i50*
     i62 + 0.021259*i50*i63 + 0.01432872*i50*i64 + 0.01445944*i50*i65 + 
     0.01098896*i50*i66 + 0.0219658*i50*i67 + 0.01066588*i50*i68 + 0.0354768*
     i50*i69 + 0.01575178*i50*i70 + 0.01775054*i50*i71 + 0.01436852*i50*i72 + 
     0.01353572*i50*i73 + 0.01936092*i50*i74 + 0.01665002*i50*i75 + 0.00971184*
     i50*i76 + 0.01642836*i50*i77 + 0.01382168*i50*i78 + 0.0341934*i50*i79 + 
     0.01843884*i50*i80 + 0.01940942*i50*i81 + 0.00527464*i50*i82 + 0.00829608*
     i50*i83 + 0.0138699*i50*i84 + 0.01840912*i50*i85 + 0.0210266*i50*i86 + 
     0.0205286*i50*i87 + 0.0451728*i50*i88 + 0.01361116*i50*i89 + 0.0277252*i50
     *i90 + 0.01783032*i50*i91 + 0.01982086*i50*i92 + 0.00668064*i50*i93 + 
     0.00765962*i50*i94 + 0.01980832*i50*i95 + 0.043863*i50*i96 + 0.0241266*i50
     *i97 + 0.0216094*i50*i98 + 0.0284306*i50*i99 + 0.0308476*i50*i100 + 
     0.01058872*i51*i52 + 0.01279448*i51*i53 + 0.0112444*i51*i54 + 0.00990216*
     i51*i55 + 0.00896022*i51*i56 + 0.00513818*i51*i57 + 0.00543454*i51*i58 + 
     0.01870256*i51*i59 + 0.00309084*i51*i60 + 0.01767624*i51*i61 + 0.01208918*
     i51*i62 + 0.01086364*i51*i63 + 0.00670046*i51*i64 + 0.00877154*i51*i65 + 
     0.00557174*i51*i66 + 0.00887856*i51*i67 + 0.00260902*i51*i68 + 0.01536338*
     i51*i69 + 0.00483316*i51*i70 + 0.00448378*i51*i71 + 0.0043601*i51*i72 + 
     0.00929772*i51*i73 + 0.00989476*i51*i74 + 0.00528028*i51*i75 + 0.00446022*
     i51*i76 + 0.00845848*i51*i77 + 0.00509916*i51*i78 + 0.0204202*i51*i79 + 
     0.00800384*i51*i80 + 0.00529538*i51*i81 + 0.0038846*i51*i82 + 0.00772216*
     i51*i83 + 0.009979*i51*i84 + 0.010097*i51*i85 + 0.0139755*i51*i86 + 
     0.01131734*i51*i87 + 0.02533*i51*i88 + 0.00621034*i51*i89 + 0.01160734*i51
     *i90 + 0.00843408*i51*i91 + 0.00995326*i51*i92 + 0.00455616*i51*i93 + 
     0.00533468*i51*i94 + 0.00929878*i51*i95 + 0.0142337*i51*i96 + 0.01066822*
     i51*i97 + 0.00526832*i51*i98 + 0.01737382*i51*i99 + 0.01465192*i51*i100 + 
     0.01484222*i52*i53 + 0.0171371*i52*i54 + 0.01181392*i52*i55 + 0.00600344*
     i52*i56 + 0.00840878*i52*i57 + 0.0071463*i52*i58 + 0.01536778*i52*i59 + 
     0.0071369*i52*i60 + 0.0280962*i52*i61 + 0.0210708*i52*i62 + 0.01590808*i52
     *i63 + 0.01317442*i52*i64 + 0.0091774*i52*i65 + 0.0068045*i52*i66 + 
     0.01047574*i52*i67 + 0.00882116*i52*i68 + 0.01759098*i52*i69 + 0.00927774*
     i52*i70 + 0.01307496*i52*i71 + 0.0115876*i52*i72 + 0.01090888*i52*i73 + 
     0.0112976*i52*i74 + 0.00919952*i52*i75 + 0.00611904*i52*i76 + 0.0126521*
     i52*i77 + 0.0063454*i52*i78 + 0.01337936*i52*i79 + 0.01210696*i52*i80 + 
     0.01264942*i52*i81 + 0.00476554*i52*i82 + 0.01346924*i52*i83 + 0.01007318*
     i52*i84 + 0.0127267*i52*i85 + 0.01394736*i52*i86 + 0.0099746*i52*i87 + 
     0.0311922*i52*i88 + 0.0079236*i52*i89 + 0.01182038*i52*i90 + 0.01651678*
     i52*i91 + 0.01241554*i52*i92 + 0.0030009*i52*i93 + 0.00533038*i52*i94 + 
     0.0132025*i52*i95 + 0.0243106*i52*i96 + 0.01594256*i52*i97 + 0.01260958*
     i52*i98 + 0.0156343*i52*i99 + 0.01771086*i52*i100 + 0.0153737*i53*i54 + 
     0.01383672*i53*i55 + 0.00715324*i53*i56 + 0.00943676*i53*i57 + 0.00990018*
     i53*i58 + 0.01573366*i53*i59 + 0.00657884*i53*i60 + 0.0319944*i53*i61 + 
     0.029398*i53*i62 + 0.01378922*i53*i63 + 0.01107682*i53*i64 + 0.01095454*
     i53*i65 + 0.00681218*i53*i66 + 0.01767184*i53*i67 + 0.00360916*i53*i68 + 
     0.0271974*i53*i69 + 0.01108326*i53*i70 + 0.00659666*i53*i71 + 0.00877032*
     i53*i72 + 0.01135242*i53*i73 + 0.01814298*i53*i74 + 0.01264072*i53*i75 + 
     0.00851402*i53*i76 + 0.01433306*i53*i77 + 0.00973382*i53*i78 + 0.025286*
     i53*i79 + 0.01345344*i53*i80 + 0.01259382*i53*i81 + 0.0027805*i53*i82 + 
     0.000307752*i53*i83 + 0.0107134*i53*i84 + 0.01054482*i53*i85 + 0.0158905*
     i53*i86 + 0.01354224*i53*i87 + 0.0304602*i53*i88 + 0.0090225*i53*i89 + 
     0.0279162*i53*i90 + 0.01259072*i53*i91 + 0.01154418*i53*i92 + 0.00696904*
     i53*i93 + 0.0036836*i53*i94 + 0.01605638*i53*i95 + 0.0430698*i53*i96 + 
     0.01780592*i53*i97 + 0.01137144*i53*i98 + 0.0256234*i53*i99 + 0.0212362*
     i53*i100 + 0.01304758*i54*i55 + 0.01398616*i54*i56 + 0.00915664*i54*i57 + 
     0.01070596*i54*i58 + 0.01499*i54*i59 + 0.0070249*i54*i60 + 0.0302542*i54*
     i61 + 0.0244214*i54*i62 + 0.0228504*i54*i63 + 0.01378888*i54*i64 + 
     0.00915648*i54*i65 + 0.0089268*i54*i66 + 0.010488*i54*i67 + 0.00997224*i54
     *i68 + 0.0229576*i54*i69 + 0.01077794*i54*i70 + 0.01825372*i54*i71 + 
     0.01517784*i54*i72 + 0.01258444*i54*i73 + 0.01361126*i54*i74 + 0.01029832*
     i54*i75 + 0.00657472*i54*i76 + 0.01463254*i54*i77 + 0.00613474*i54*i78 + 
     0.01201368*i54*i79 + 0.013126*i54*i80 + 0.01505614*i54*i81 + 0.00467872*
     i54*i82 + 0.01050702*i54*i83 + 0.01265914*i54*i84 + 0.01318044*i54*i85 + 
     0.01473222*i54*i86 + 0.01110614*i54*i87 + 0.0261814*i54*i88 + 0.00783796*
     i54*i89 + 0.01294844*i54*i90 + 0.0192808*i54*i91 + 0.0139507*i54*i92 + 
     0.00351228*i54*i93 + 0.0068612*i54*i94 + 0.01527036*i54*i95 + 0.0205052*
     i54*i96 + 0.01688726*i54*i97 + 0.01524852*i54*i98 + 0.0174601*i54*i99 + 
     0.0244266*i54*i100 + 0.00673562*i55*i56 + 0.00707698*i55*i57 + 0.00734322*
     i55*i58 + 0.01405048*i55*i59 + 0.00334038*i55*i60 + 0.0222096*i55*i61 + 
     0.01523028*i55*i62 + 0.0102055*i55*i63 + 0.01002768*i55*i64 + 0.01048288*
     i55*i65 + 0.00635712*i55*i66 + 0.00874464*i55*i67 + 0.00593524*i55*i68 + 
     0.01648812*i55*i69 + 0.0080135*i55*i70 + 0.00887592*i55*i71 + 0.00847214*
     i55*i72 + 0.01055314*i55*i73 + 0.01129422*i55*i74 + 0.00699156*i55*i75 + 
     0.00627446*i55*i76 + 0.01024268*i55*i77 + 0.00531432*i55*i78 + 0.0098513*
     i55*i79 + 0.01065934*i55*i80 + 0.00967318*i55*i81 + 0.00462964*i55*i82 + 
     0.00334858*i55*i83 + 0.01100528*i55*i84 + 0.00975296*i55*i85 + 0.01214742*
     i55*i86 + 0.00846042*i55*i87 + 0.0242638*i55*i88 + 0.0054702*i55*i89 + 
     0.01124098*i55*i90 + 0.0118002*i55*i91 + 0.01077996*i55*i92 + 0.00250778*
     i55*i93 + 0.00555816*i55*i94 + 0.01037364*i55*i95 + 0.0175302*i55*i96 + 
     0.01283314*i55*i97 + 0.01054116*i55*i98 + 0.01565736*i55*i99 + 0.01643682*
     i55*i100 + 0.00563824*i56*i57 + 0.00909602*i56*i58 + 0.0103611*i56*i59 + 
     0.00370386*i56*i60 + 0.01345496*i56*i61 + 0.01240364*i56*i62 + 0.01894134*
     i56*i63 + 0.00842246*i56*i64 + 0.00913306*i56*i65 + 0.0128603*i56*i66 + 
     0.00789202*i56*i67 + 0.0049437*i56*i68 + 0.0172921*i56*i69 + 0.00742364*
     i56*i70 + 0.0201228*i56*i71 + 0.0118952*i56*i72 + 0.01088666*i56*i73 + 
     0.0107701*i56*i74 + 0.00409754*i56*i75 + 0.00366002*i56*i76 + 0.01236854*
     i56*i77 + 0.00300872*i56*i78 + 0.0135613*i56*i79 + 0.00480806*i56*i80 + 
     0.01596128*i56*i81 + 0.00309564*i56*i82 + 0.01777436*i56*i83 + 0.01193038*
     i56*i84 + 0.00565974*i56*i85 + 0.01170688*i56*i86 + 0.01022376*i56*i87 + 
     0.0163427*i56*i88 + 0.00612568*i56*i89 + 0.01115784*i56*i90 + 0.00381802*
     i56*i91 + 0.0089326*i56*i92 + 0.0075443*i56*i93 + 0.00818402*i56*i94 + 
     0.00966992*i56*i95 + 0.00265106*i56*i96 + 0.01019204*i56*i97 + 0.01329902*
     i56*i98 + 0.01411634*i56*i99 + 0.0138779*i56*i100 + 0.00474894*i57*i58 + 
     0.00767974*i57*i59 + 0.0043561*i57*i60 + 0.01478228*i57*i61 + 0.00989558*
     i57*i62 + 0.00895424*i57*i63 + 0.0066828*i57*i64 + 0.00578744*i57*i65 + 
     0.00498864*i57*i66 + 0.00614268*i57*i67 + 0.0054738*i57*i68 + 0.01078148*
     i57*i69 + 0.00688352*i57*i70 + 0.0068114*i57*i71 + 0.00628102*i57*i72 + 
     0.00701898*i57*i73 + 0.00848154*i57*i74 + 0.0066742*i57*i75 + 0.00450208*
     i57*i76 + 0.0074907*i57*i77 + 0.00457588*i57*i78 + 0.00668368*i57*i79 + 
     0.00806954*i57*i80 + 0.00702352*i57*i81 + 0.0038917*i57*i82 + 0.000255196*
     i57*i83 + 0.00565464*i57*i84 + 0.00629044*i57*i85 + 0.00649918*i57*i86 + 
     0.00619514*i57*i87 + 0.01578988*i57*i88 + 0.00523946*i57*i89 + 0.00717944*
     i57*i90 + 0.0080494*i57*i91 + 0.00534064*i57*i92 + 0.00276512*i57*i93 + 
     0.00412012*i57*i94 + 0.00715034*i57*i95 + 0.01300638*i57*i96 + 0.00826382*
     i57*i97 + 0.0068466*i57*i98 + 0.00897648*i57*i99 + 0.01037138*i57*i100 + 
     0.00646004*i58*i59 + 0.00186599*i58*i60 + 0.01246886*i58*i61 + 0.00999352*
     i58*i62 + 0.01381952*i58*i63 + 0.00855014*i58*i64 + 0.00465434*i58*i65 + 
     0.00825376*i58*i66 + 0.00576402*i58*i67 + 0.00273548*i58*i68 + 0.01035762*
     i58*i69 + 0.004824*i58*i70 + 0.01355144*i58*i71 + 0.00700278*i58*i72 + 
     0.00707718*i58*i73 + 0.00851974*i58*i74 + 0.00330912*i58*i75 + 0.00401842*
     i58*i76 + 0.00999942*i58*i77 + 0.00277578*i58*i78 - 0.000989722*i58*i79 + 
     0.00742188*i58*i80 + 0.00901096*i58*i81 + 0.000981242*i58*i82 + 0.01290728
     *i58*i83 + 0.0083181*i58*i84 + 0.00517936*i58*i85 + 0.00723458*i58*i86 + 
     0.0044253*i58*i87 + 0.0137847*i58*i88 + 0.001547694*i58*i89 + 0.00582604*
     i58*i90 + 0.00844516*i58*i91 + 0.00776542*i58*i92 + 0.00182761*i58*i93 + 
     0.0023829*i58*i94 + 0.00628056*i58*i95 + 0.00690478*i58*i96 + 0.00802988*
     i58*i97 + 0.0076502*i58*i98 + 0.01085276*i58*i99 + 0.0112764*i58*i100 + 
     0.00476864*i59*i60 + 0.025812*i59*i61 + 0.01805478*i59*i62 + 0.0109551*i59
     *i63 + 0.00938908*i59*i64 + 0.01178962*i59*i65 + 0.0076335*i59*i66 + 
     0.01177666*i59*i67 + 0.0070214*i59*i68 + 0.0221478*i59*i69 + 0.007972*i59*
     i70 + 0.0074733*i59*i71 + 0.0088486*i59*i72 + 0.01271666*i59*i73 + 
     0.0141508*i59*i74 + 0.00914726*i59*i75 + 0.00537448*i59*i76 + 0.01084216*
     i59*i77 + 0.0073258*i59*i78 + 0.0246694*i59*i79 + 0.01112936*i59*i80 + 
     0.00816652*i59*i81 + 0.00597972*i59*i82 + 0.00662172*i59*i83 + 0.01458364*
     i59*i84 + 0.01429256*i59*i85 + 0.01882618*i59*i86 + 0.01439702*i59*i87 + 
     0.034478*i59*i88 + 0.0080275*i59*i89 + 0.01623632*i59*i90 + 0.01482176*i59
     *i91 + 0.01127396*i59*i92 + 0.00550568*i59*i93 + 0.00798042*i59*i94 + 
     0.01294416*i59*i95 + 0.0212862*i59*i96 + 0.01627426*i59*i97 + 0.0106876*
     i59*i98 + 0.021021*i59*i99 + 0.0210024*i59*i100 + 0.01016558*i60*i61 + 
     0.00950624*i60*i62 + 0.00759926*i60*i63 + 0.00405624*i60*i64 + 0.00408766*
     i60*i65 + 0.001012866*i60*i66 + 0.00434698*i60*i67 + 0.00457798*i60*i68 + 
     0.0080193*i60*i69 + 0.0054101*i60*i70 + 0.0046192*i60*i71 + 0.00570946*i60
     *i72 + 0.00452172*i60*i73 + 0.00634618*i60*i74 + 0.00624388*i60*i75 + 
     0.0033187*i60*i76 + 0.00483228*i60*i77 + 0.00344686*i60*i78 + 0.0083673*
     i60*i79 + 0.00518592*i60*i80 + 0.00542166*i60*i81 + 0.0031059*i60*i82 - 
     0.001025068*i60*i83 + 0.0028835*i60*i84 + 0.00445296*i60*i85 + 0.00423572*
     i60*i86 + 0.0051822*i60*i87 + 0.01112192*i60*i88 + 0.00500464*i60*i89 + 
     0.0062184*i60*i90 + 0.00602*i60*i91 + 0.00246398*i60*i92 + 0.00288384*i60*
     i93 + 0.00278724*i60*i94 + 0.00626372*i60*i95 + 0.01170704*i60*i96 + 
     0.00615192*i60*i97 + 0.00462302*i60*i98 + 0.00471294*i60*i99 + 0.00588256*
     i60*i100 + 0.0418718*i61*i62 + 0.0230598*i61*i63 + 0.01842282*i61*i64 + 
     0.01721234*i61*i65 + 0.00990124*i61*i66 + 0.0216044*i61*i67 + 0.01473812*
     i61*i68 + 0.0394464*i61*i69 + 0.01716988*i61*i70 + 0.0195513*i61*i71 + 
     0.0219932*i61*i72 + 0.01943214*i61*i73 + 0.020134*i61*i74 + 0.0174732*i61*
     i75 + 0.01174406*i61*i76 + 0.01834496*i61*i77 + 0.01109086*i61*i78 + 
     0.0264464*i61*i79 + 0.01965936*i61*i80 + 0.0227546*i61*i81 + 0.00831452*
     i61*i82 + 0.00631004*i61*i83 + 0.01801602*i61*i84 + 0.01882322*i61*i85 + 
     0.026381*i61*i86 + 0.0201168*i61*i87 + 0.0582994*i61*i88 + 0.01420784*i61*
     i89 + 0.0279352*i61*i90 + 0.0260044*i61*i91 + 0.01994278*i61*i92 + 
     0.00558188*i61*i93 + 0.0100806*i61*i94 + 0.0228614*i61*i95 + 0.0472894*i61
     *i96 + 0.0277624*i61*i97 + 0.0233414*i61*i98 + 0.0320998*i61*i99 + 
     0.037788*i61*i100 + 0.0226754*i62*i63 + 0.01497022*i62*i64 + 0.0138219*i62
     *i65 + 0.00559668*i62*i66 + 0.01850946*i62*i67 + 0.01131414*i62*i68 + 
     0.0392412*i62*i69 + 0.01609634*i62*i70 + 0.0216048*i62*i71 + 0.0216526*i62
     *i72 + 0.0150155*i62*i73 + 0.01738604*i62*i74 + 0.01374744*i62*i75 + 
     0.00779326*i62*i76 + 0.01429558*i62*i77 + 0.0081994*i62*i78 + 0.024889*i62
     *i79 + 0.01494124*i62*i80 + 0.0229898*i62*i81 + 0.00445144*i62*i82 + 
     0.01114552*i62*i83 + 0.01793036*i62*i84 + 0.01444614*i62*i85 + 0.01879448*
     i62*i86 + 0.01466504*i62*i87 + 0.0326604*i62*i88 + 0.01169144*i62*i89 + 
     0.0254028*i62*i90 + 0.01965996*i62*i91 + 0.01132102*i62*i92 + 0.0046546*
     i62*i93 + 0.00635342*i62*i94 + 0.0209304*i62*i95 + 0.040751*i62*i96 + 
     0.0251822*i62*i97 + 0.0238578*i62*i98 + 0.0225858*i62*i99 + 0.0313134*i62*
     i100 + 0.01545704*i63*i64 + 0.01086358*i63*i65 + 0.00996396*i63*i66 + 
     0.00982328*i63*i67 + 0.00892944*i63*i68 + 0.024956*i63*i69 + 0.0125295*i63
     *i70 + 0.0274234*i63*i71 + 0.0136346*i63*i72 + 0.0143589*i63*i73 + 
     0.01281966*i63*i74 + 0.009889*i63*i75 + 0.00617316*i63*i76 + 0.0195622*i63
     *i77 + 0.00502572*i63*i78 + 0.00153262*i63*i79 + 0.01706792*i63*i80 + 
     0.01790944*i63*i81 + 0.001490592*i63*i82 + 0.0267338*i63*i83 + 0.01586496*
     i63*i84 + 0.01166282*i63*i85 + 0.01568614*i63*i86 + 0.00753188*i63*i87 + 
     0.0417782*i63*i88 + 0.0112216*i63*i89 + 0.00371206*i63*i90 + 0.01829192*
     i63*i91 + 0.01841964*i63*i92 + 0.00206622*i63*i93 + 0.00505172*i63*i94 + 
     0.01487174*i63*i95 + 0.01414348*i63*i96 + 0.0156802*i63*i97 + 0.01823426*
     i63*i98 + 0.01258764*i63*i99 + 0.01994098*i63*i100 + 0.00854654*i64*i65 + 
     0.01079866*i64*i66 + 0.00602732*i64*i67 + 0.00921276*i64*i68 + 0.01464414*
     i64*i69 + 0.00664932*i64*i70 + 0.0144736*i64*i71 + 0.00978338*i64*i72 + 
     0.00959208*i64*i73 + 0.0112566*i64*i74 + 0.00671142*i64*i75 + 0.00408206*
     i64*i76 + 0.01167568*i64*i77 + 0.00375274*i64*i78 + 0.00404336*i64*i79 + 
     0.00963238*i64*i80 + 0.0122908*i64*i81 + 0.001806772*i64*i82 + 0.01577266*
     i64*i83 + 0.01128074*i64*i84 + 0.0095111*i64*i85 + 0.0097723*i64*i86 + 
     0.00346618*i64*i87 + 0.01289324*i64*i88 + 0.00453186*i64*i89 + 0.0078486*
     i64*i90 + 0.01310134*i64*i91 + 0.00985686*i64*i92 + 0.00257788*i64*i93 + 
     0.00260324*i64*i94 + 0.0108877*i64*i95 + 0.01349616*i64*i96 + 0.01306042*
     i64*i97 + 0.01405114*i64*i98 + 0.0115142*i64*i99 + 0.01728302*i64*i100 + 
     0.0048225*i65*i66 + 0.00871696*i65*i67 + 0.00504014*i65*i68 + 0.01673796*
     i65*i69 + 0.00728674*i65*i70 + 0.00969202*i65*i71 + 0.0082057*i65*i72 + 
     0.0103704*i65*i73 + 0.00998004*i65*i74 + 0.00672722*i65*i75 + 0.00633346*
     i65*i76 + 0.00774852*i65*i77 + 0.00440922*i65*i78 + 0.01343946*i65*i79 + 
     0.00798994*i65*i80 + 0.01225132*i65*i81 + 0.00444398*i65*i82 + 0.00673302*
     i65*i83 + 0.0109598*i65*i84 + 0.00683186*i65*i85 + 0.01183874*i65*i86 + 
     0.0090907*i65*i87 + 0.0283952*i65*i88 + 0.00785096*i65*i89 + 0.01125058*
     i65*i90 + 0.00510526*i65*i91 + 0.00837574*i65*i92 + 0.00385798*i65*i93 + 
     0.00464904*i65*i94 + 0.00896456*i65*i95 + 0.0160694*i65*i96 + 0.0113557*
     i65*i97 + 0.01155766*i65*i98 + 0.01443876*i65*i99 + 0.01238186*i65*i100 + 
     0.00548536*i66*i67 + 0.00630564*i66*i68 + 0.00939978*i66*i69 + 0.00431468*
     i66*i70 + 0.01542742*i66*i71 + 0.0071665*i66*i72 + 0.00755022*i66*i73 + 
     0.00838922*i66*i74 + 0.00386922*i66*i75 + 0.001951058*i66*i76 + 0.01146338
     *i66*i77 + 0.001980078*i66*i78 + 0.00444902*i66*i79 + 0.00356762*i66*i80
      + 0.00956806*i66*i81 - 0.00023183*i66*i82 + 0.01703884*i66*i83 + 
     0.01002452*i66*i84 + 0.0062546*i66*i85 + 0.00563304*i66*i86 + 0.00514984*
     i66*i87 + 0.01908326*i66*i88 + 0.00457928*i66*i89 + 0.003995*i66*i90 + 
     0.0080501*i66*i91 + 0.00810108*i66*i92 + 0.00328186*i66*i93 + 0.00369064*
     i66*i94 + 0.0058103*i66*i95 + 0.00438208*i66*i96 + 0.00867896*i66*i97 + 
     0.0114927*i66*i98 + 0.01103938*i66*i99 + 0.00981454*i66*i100 + 0.00310364*
     i67*i68 + 0.0195756*i67*i69 + 0.00833924*i67*i70 + 0.01122*i67*i71 + 
     0.00862168*i67*i72 + 0.00711248*i67*i73 + 0.00958304*i67*i74 + 0.00671208*
     i67*i75 + 0.00667666*i67*i76 + 0.00639998*i67*i77 + 0.00746068*i67*i78 + 
     0.0164696*i67*i79 + 0.00952472*i67*i80 + 0.01054908*i67*i81 + 0.00295206*
     i67*i82 + 0.00786538*i67*i83 + 0.00812566*i67*i84 + 0.00774908*i67*i85 + 
     0.01084866*i67*i86 + 0.01179554*i67*i87 + 0.022894*i67*i88 + 0.00619526*
     i67*i89 + 0.01517056*i67*i90 + 0.00567344*i67*i91 + 0.00901318*i67*i92 + 
     0.00388018*i67*i93 + 0.0036956*i67*i94 + 0.008896*i67*i95 + 0.021896*i67*
     i96 + 0.01327636*i67*i97 + 0.0109*i67*i98 + 0.0178563*i67*i99 + 0.01328366
     *i67*i100 + 0.01361686*i68*i69 + 0.00764086*i68*i70 + 0.00794036*i68*i71
      + 0.01077146*i68*i72 + 0.00701056*i68*i73 + 0.00764336*i68*i74 + 
     0.01085638*i68*i75 + 0.00267198*i68*i76 + 0.00622086*i68*i77 + 0.0026961*
     i68*i78 + 0.01283914*i68*i79 + 0.00651186*i68*i80 + 0.00444824*i68*i81 + 
     0.00245108*i68*i82 - 0.000724804*i68*i83 + 0.01001432*i68*i84 + 0.00659112
     *i68*i85 + 0.00798872*i68*i86 + 0.00378278*i68*i87 + 0.0249894*i68*i88 + 
     0.00935338*i68*i89 + 0.00406214*i68*i90 + 0.01547864*i68*i91 + 0.0026383*
     i68*i92 + 0.001956366*i68*i93 + 0.00433104*i68*i94 + 0.0086862*i68*i95 + 
     0.00871594*i68*i96 + 0.00917804*i68*i97 + 0.01147728*i68*i98 + 0.000904318
     *i68*i99 + 0.0095902*i68*i100 + 0.01716134*i69*i70 + 0.0210128*i69*i71 + 
     0.01970512*i69*i72 + 0.01824406*i69*i73 + 0.0202038*i69*i74 + 0.0166321*
     i69*i75 + 0.0080034*i69*i76 + 0.01785698*i69*i77 + 0.00956708*i69*i78 + 
     0.0273938*i69*i79 + 0.01578286*i69*i80 + 0.01986548*i69*i81 + 0.00472512*
     i69*i82 + 0.0064477*i69*i83 + 0.0205866*i69*i84 + 0.01485404*i69*i85 + 
     0.0219926*i69*i86 + 0.01726592*i69*i87 + 0.044296*i69*i88 + 0.01519388*i69
     *i89 + 0.0245318*i69*i90 + 0.019668*i69*i91 + 0.01322886*i69*i92 + 
     0.00622812*i69*i93 + 0.00886068*i69*i94 + 0.0207946*i69*i95 + 0.0369544*
     i69*i96 + 0.0252064*i69*i97 + 0.0246794*i69*i98 + 0.0240826*i69*i99 + 
     0.0322226*i69*i100 + 0.01122678*i70*i71 + 0.00985708*i70*i72 + 0.00817346*
     i70*i73 + 0.01042594*i70*i74 + 0.0087512*i70*i75 + 0.00587552*i70*i76 + 
     0.00956692*i70*i77 + 0.00604702*i70*i78 + 0.01012786*i70*i79 + 0.00894572*
     i70*i80 + 0.00937532*i70*i81 + 0.0040741*i70*i82 + 0.001290572*i70*i83 + 
     0.00820512*i70*i84 + 0.00683756*i70*i85 + 0.00768078*i70*i86 + 0.00827048*
     i70*i87 + 0.01990564*i70*i88 + 0.007123*i70*i89 + 0.00998564*i70*i90 + 
     0.00953688*i70*i91 + 0.00558782*i70*i92 + 0.00342686*i70*i93 + 0.00568486*
     i70*i94 + 0.00914938*i70*i95 + 0.01630104*i70*i96 + 0.01110616*i70*i97 + 
     0.010247*i70*i98 + 0.00833958*i70*i99 + 0.01265252*i70*i100 + 0.0220254*
     i71*i72 + 0.0095213*i71*i73 + 0.01209936*i71*i74 + 0.00527094*i71*i75 + 
     0.00557218*i71*i76 + 0.01262004*i71*i77 + 0.0037353*i71*i78 - 0.000223588*
     i71*i79 + 0.00801532*i71*i80 + 0.0286786*i71*i81 + 0.000788336*i71*i82 + 
     0.0387752*i71*i83 + 0.01552284*i71*i84 + 0.00720994*i71*i85 + 0.01148132*
     i71*i86 + 0.00870698*i71*i87 + 0.028675*i71*i88 + 0.00544718*i71*i89 + 
     0.00673884*i71*i90 + 0.01008984*i71*i91 + 0.01241834*i71*i92 + 0.0025495*
     i71*i93 + 0.00280272*i71*i94 + 0.00947552*i71*i95 + 0.0070495*i71*i96 + 
     0.0170916*i71*i97 + 0.0269036*i71*i98 + 0.01506306*i71*i99 + 0.0206782*i71
     *i100 + 0.00925426*i72*i73 + 0.00967792*i72*i74 + 0.00847338*i72*i75 + 
     0.005213*i72*i76 + 0.00908662*i72*i77 + 0.00316872*i72*i78 + 0.00898138*
     i72*i79 + 0.0069179*i72*i80 + 0.0151281*i72*i81 + 0.00348424*i72*i82 + 
     0.01111986*i72*i83 + 0.01165966*i72*i84 + 0.0064802*i72*i85 + 0.00959246*
     i72*i86 + 0.0084611*i72*i87 + 0.0240956*i72*i88 + 0.00687054*i72*i89 + 
     0.0094553*i72*i90 + 0.0110757*i72*i91 + 0.00543508*i72*i92 + 0.0037306*i72
     *i93 + 0.00500972*i72*i94 + 0.01005818*i72*i95 + 0.01294332*i72*i96 + 
     0.01344022*i72*i97 + 0.01593132*i72*i98 + 0.0093216*i72*i99 + 0.01640118*
     i72*i100 + 0.01198598*i73*i74 + 0.00750544*i73*i75 + 0.0050216*i73*i76 + 
     0.01285904*i73*i77 + 0.00339452*i73*i78 + 0.00891788*i73*i79 + 0.00948614*
     i73*i80 + 0.00944098*i73*i81 + 0.00409826*i73*i82 + 0.00488372*i73*i83 + 
     0.01210326*i73*i84 + 0.00827726*i73*i85 + 0.0117403*i73*i86 + 0.00812428*
     i73*i87 + 0.031499*i73*i88 + 0.00909586*i73*i89 + 0.00829156*i73*i90 + 
     0.0112196*i73*i91 + 0.00781298*i73*i92 + 0.00380884*i73*i93 + 0.00624296*
     i73*i94 + 0.01005016*i73*i95 + 0.01437472*i73*i96 + 0.011277*i73*i97 + 
     0.01058622*i73*i98 + 0.0121454*i73*i99 + 0.01373088*i73*i100 + 0.01080198*
     i74*i75 + 0.00656182*i74*i76 + 0.01437682*i74*i77 + 0.00746976*i74*i78 + 
     0.0158128*i74*i79 + 0.01161714*i74*i80 + 0.01098286*i74*i81 + 0.00409892*
     i74*i82 + 0.00263806*i74*i83 + 0.01368742*i74*i84 + 0.00966578*i74*i85 + 
     0.0126469*i74*i86 + 0.0097362*i74*i87 + 0.0236752*i74*i88 + 0.0087263*i74*
     i89 + 0.01653132*i74*i90 + 0.01259886*i74*i91 + 0.0074886*i74*i92 + 
     0.00612882*i74*i93 + 0.00553384*i74*i94 + 0.01256076*i74*i95 + 0.022837*
     i74*i96 + 0.01489052*i74*i97 + 0.0138654*i74*i98 + 0.01608016*i74*i99 + 
     0.0185439*i74*i100 + 0.00483222*i75*i76 + 0.0084646*i75*i77 + 0.00605234*
     i75*i78 + 0.01627408*i75*i79 + 0.00784142*i75*i80 + 0.00564276*i75*i81 + 
     0.00324588*i75*i82 - 0.00767236*i75*i83 + 0.00699372*i75*i84 + 0.00737608*
     i75*i85 + 0.00954642*i75*i86 + 0.00823136*i75*i87 + 0.0262748*i75*i88 + 
     0.00948902*i75*i89 + 0.01252876*i75*i90 + 0.01423104*i75*i91 + 0.00521492*
     i75*i92 + 0.00397698*i75*i93 + 0.00422896*i75*i94 + 0.01025216*i75*i95 + 
     0.021456*i75*i96 + 0.01000128*i75*i97 + 0.00860654*i75*i98 + 0.0079023*i75
     *i99 + 0.01223272*i75*i100 + 0.00508036*i76*i77 + 0.00440326*i76*i78 + 
     0.00722936*i76*i79 + 0.00592748*i76*i80 + 0.00543106*i76*i81 + 0.00352072*
     i76*i82 + 0.00282876*i76*i83 + 0.00421804*i76*i84 + 0.00327576*i76*i85 + 
     0.00605002*i76*i86 + 0.00724932*i76*i87 + 0.01581762*i76*i88 + 0.00366428*
     i76*i89 + 0.00812736*i76*i90 + 0.00388382*i76*i91 + 0.0047062*i76*i92 + 
     0.00287772*i76*i93 + 0.00297876*i76*i94 + 0.00459654*i76*i95 + 0.01070758*
     i76*i96 + 0.0061617*i76*i97 + 0.00324936*i76*i98 + 0.00970994*i76*i99 + 
     0.00690694*i76*i100 + 0.00393188*i77*i78 + 0.00648912*i77*i79 + 0.00880144
     *i77*i80 + 0.00990674*i77*i81 + 0.00277832*i77*i82 + 0.01369158*i77*i83 + 
     0.01108874*i77*i84 + 0.00804488*i77*i85 + 0.0100624*i77*i86 + 0.00868852*
     i77*i87 + 0.0320896*i77*i88 + 0.00865688*i77*i89 + 0.00846622*i77*i90 + 
     0.01262084*i77*i91 + 0.01111726*i77*i92 + 0.00462154*i77*i93 + 0.00718072*
     i77*i94 + 0.01147082*i77*i95 + 0.0176254*i77*i96 + 0.01224072*i77*i97 + 
     0.00939734*i77*i98 + 0.012534*i77*i99 + 0.01295098*i77*i100 + 0.00907912*
     i78*i79 + 0.00720642*i78*i80 + 0.00426806*i78*i81 + 0.0028332*i78*i82 - 
     0.001354666*i78*i83 + 0.00318608*i78*i84 + 0.00627032*i78*i85 + 0.00574778
     *i78*i86 + 0.00663794*i78*i87 + 0.00493084*i78*i88 + 0.00225816*i78*i89 + 
     0.01063042*i78*i90 + 0.0063342*i78*i91 + 0.00541402*i78*i92 + 0.00268782*
     i78*i93 + 0.00290288*i78*i94 + 0.00588184*i78*i95 + 0.01436716*i78*i96 + 
     0.00728756*i78*i97 + 0.00442972*i78*i98 + 0.00924454*i78*i99 + 0.00979098*
     i78*i100 + 0.0060581*i79*i80 + 0.00755126*i79*i81 + 0.00637932*i79*i82 - 
     0.00105651*i79*i83 + 0.01349704*i79*i84 + 0.01178354*i79*i85 + 0.0220208*
     i79*i86 + 0.0245836*i79*i87 + 0.0524002*i79*i88 + 0.0230428*i79*i89 + 
     0.0314514*i79*i90 + 0.00636018*i79*i91 + 0.0061917*i79*i92 + 0.01207768*
     i79*i93 + 0.00753416*i79*i94 + 0.01719794*i79*i95 + 0.0367202*i79*i96 + 
     0.01636496*i79*i97 + 0.01053626*i79*i98 + 0.0223148*i79*i99 + 0.0125583*
     i79*i100 + 0.00731124*i80*i81 + 0.0043053*i80*i82 + 0.00250064*i80*i83 + 
     0.00942746*i80*i84 + 0.01109824*i80*i85 + 0.0094077*i80*i86 + 0.00584688*
     i80*i87 + 0.01773876*i80*i88 + 0.00587054*i80*i89 + 0.0073899*i80*i90 + 
     0.01217556*i80*i91 + 0.0092825*i80*i92 + 0.001672258*i80*i93 + 0.00403362*
     i80*i94 + 0.01001412*i80*i95 + 0.01641906*i80*i96 + 0.01159292*i80*i97 + 
     0.01062798*i80*i98 + 0.00967468*i80*i99 + 0.0140493*i80*i100 + 0.00288116*
     i81*i82 + 0.022981*i81*i83 + 0.01105584*i81*i84 + 0.00722284*i81*i85 + 
     0.01178602*i81*i86 + 0.00945868*i81*i87 + 0.024973*i81*i88 + 0.00575624*
     i81*i89 + 0.01415098*i81*i90 + 0.0066048*i81*i91 + 0.01072344*i81*i92 + 
     0.00322326*i81*i93 + 0.00351188*i81*i94 + 0.01127788*i81*i95 + 0.01956074*
     i81*i96 + 0.01617428*i81*i97 + 0.0227228*i81*i98 + 0.01855842*i81*i99 + 
     0.01991896*i81*i100 - 0.00333172*i82*i83 + 0.00228114*i82*i84 + 0.00336158
     *i82*i85 + 0.00354748*i82*i86 + 0.00514572*i82*i87 + 0.00636398*i82*i88 + 
     0.00276272*i82*i89 + 0.00394504*i82*i90 + 0.00242814*i82*i91 + 0.00151634*
     i82*i92 + 0.00205258*i82*i93 + 0.00416174*i82*i94 + 0.0036601*i82*i95 + 
     0.00573294*i82*i96 + 0.0040347*i82*i97 + 0.001040396*i82*i98 + 0.00519918*
     i82*i99 + 0.00479088*i82*i100 + 0.01497528*i83*i84 + 0.0032291*i83*i85 + 
     0.01011148*i83*i86 + 0.00471364*i83*i87 + 0.0246434*i83*i88 + 0.000996878*
     i83*i89 - 0.00262512*i83*i90 - 0.000789784*i83*i91 + 0.01304756*i83*i92 + 
     0.000531142*i83*i93 - 0.000443948*i83*i94 + 0.00279848*i83*i95 - 0.0065326
     *i83*i96 + 0.01221224*i83*i97 + 0.01799712*i83*i98 + 0.0158385*i83*i99 + 
     0.0071337*i83*i100 + 0.00892568*i84*i85 + 0.01364388*i84*i86 + 0.0072533*
     i84*i87 + 0.0326884*i84*i88 + 0.00896504*i84*i89 + 0.00823562*i84*i90 + 
     0.0125821*i84*i91 + 0.00787816*i84*i92 + 0.00249586*i84*i93 + 0.00519262*
     i84*i94 + 0.01044988*i84*i95 + 0.01107886*i84*i96 + 0.0139867*i84*i97 + 
     0.01596046*i84*i98 + 0.01218826*i84*i99 + 0.01543212*i84*i100 + 0.00990954
     *i85*i86 + 0.00725662*i85*i87 + 0.0133432*i85*i88 + 0.00507396*i85*i89 + 
     0.00930526*i85*i90 + 0.01462284*i85*i91 + 0.01055408*i85*i92 + 0.00190258*
     i85*i93 + 0.00468802*i85*i94 + 0.0107648*i85*i95 + 0.01646608*i85*i96 + 
     0.01215728*i85*i97 + 0.01028698*i85*i98 + 0.01183266*i85*i99 + 0.01660366*
     i85*i100 + 0.0120373*i86*i87 + 0.0422718*i86*i88 + 0.00969238*i86*i89 + 
     0.01765146*i86*i90 + 0.01429788*i86*i91 + 0.0124585*i86*i92 + 0.0040945*
     i86*i93 + 0.0046898*i86*i94 + 0.01232074*i86*i95 + 0.0222548*i86*i96 + 
     0.0145479*i86*i97 + 0.0128277*i86*i98 + 0.0192244*i86*i99 + 0.01947568*i86
     *i100 + 0.032904*i87*i88 + 0.0084843*i87*i89 + 0.01591916*i87*i90 + 
     0.0059879*i87*i91 + 0.00789644*i87*i92 + 0.00607862*i87*i93 + 0.00667478*
     i87*i94 + 0.0088746*i87*i95 + 0.01963916*i87*i96 + 0.01115822*i87*i97 + 
     0.0065973*i87*i98 + 0.01821046*i87*i99 + 0.01269924*i87*i100 + 0.04164*i88
     *i89 + 0.01700894*i88*i90 + 0.0282218*i88*i91 + 0.0247666*i88*i92 + 
     0.00860626*i88*i93 + 0.0146832*i88*i94 + 0.0207292*i88*i95 + 0.0482992*i88
     *i96 + 0.026772*i88*i97 + 0.0300758*i88*i98 + 0.0329128*i88*i99 + 
     0.01375988*i88*i100 + 0.00594302*i89*i90 + 0.00801468*i89*i91 + 0.00437824
     *i89*i92 + 0.00302882*i89*i93 + 0.0041304*i89*i94 + 0.00803522*i89*i95 + 
     0.01620516*i89*i96 + 0.00836644*i89*i97 + 0.01022328*i89*i98 + 0.0069101*
     i89*i99 + 0.00464412*i89*i100 + 0.01014268*i90*i91 + 0.00890216*i90*i92 + 
     0.00857494*i90*i93 + 0.00416286*i90*i94 + 0.01435266*i90*i95 + 0.038709*
     i90*i96 + 0.01593092*i90*i97 + 0.0108455*i90*i98 + 0.0247362*i90*i99 + 
     0.0239224*i90*i100 + 0.01172504*i91*i92 - 3.25928e-5*i91*i93 + 0.00582154*
     i91*i94 + 0.01455814*i91*i95 + 0.0217724*i91*i96 + 0.01520358*i91*i97 + 
     0.01361584*i91*i98 + 0.01107608*i91*i99 + 0.0218082*i91*i100 + 0.000834202
     *i92*i93 + 0.00361846*i92*i94 + 0.00964536*i92*i95 + 0.01621624*i92*i96 + 
     0.01139352*i92*i97 + 0.01032652*i92*i98 + 0.01663626*i92*i99 + 0.01551254*
     i92*i100 + 0.00302326*i93*i94 + 0.0039602*i93*i95 + 0.0070366*i93*i96 + 
     0.0035814*i93*i97 + 0.00156313*i93*i98 + 0.00599576*i93*i99 + 0.00427812*
     i93*i100 + 0.00550244*i94*i95 + 0.00558508*i94*i96 + 0.0059384*i94*i97 + 
     0.00357124*i94*i98 + 0.0064057*i94*i99 + 0.00623724*i94*i100 + 0.0227304*
     i95*i96 + 0.01445112*i95*i97 + 0.01257804*i95*i98 + 0.01368382*i95*i99 + 
     0.01773414*i95*i100 + 0.0257114*i96*i97 + 0.01933344*i96*i98 + 0.0317874*
     i96*i99 + 0.0306278*i96*i100 + 0.01873902*i97*i98 + 0.01912542*i97*i99 + 
     0.0219022*i97*i100 + 0.01388668*i98*i99 + 0.0207524*i98*i100 + 0.0256994*
     i99*i100 - objvar =L= 0;

e2..    0.00411438*i1 - 0.0186628*i2 - 0.0124176*i3 - 0.00587102*i4
      - 0.0137519*i5 - 0.0174501*i6 - 0.0143449*i7 - 0.135908*i8 + 0.0183991*i9
      - 0.00059102*i10 - 0.0458625*i11 + 0.00263166*i12 - 0.00331355*i13
      - 0.0367972*i14 - 0.0139845*i15 - 0.0094868*i16 + 0.0248532*i17
      - 0.0094023*i18 + 0.0023017*i19 - 0.0464684*i20 - 0.00593531*i21
      - 0.00567252*i22 - 0.0053525*i23 - 0.0195131*i24 - 0.00539281*i25
      + 0.00014069*i26 - 0.0192418*i27 - 0.0094094*i28 - 0.00628791*i29
      - 0.0640481*i30 + 0.00479685*i31 - 0.00773524*i32 - 0.0181879*i33
      - 0.0252863*i34 - 0.0138439*i35 - 0.0175713*i36 - 0.0087821*i37
      - 0.0159321*i38 - 0.0116042*i39 + 0.0157787*i40 - 0.0202007*i41
      - 0.0126018*i42 - 0.00304129*i43 - 0.00993*i44 - 0.0128447*i45
      - 0.00181865*i46 - 0.0158853*i47 - 0.00510726*i48 - 0.00213898*i49
      - 0.030707*i50 + 0.00148868*i51 - 0.0125947*i52 - 0.00471196*i53
      - 0.0148213*i54 - 0.00451418*i55 + 0.00107459*i56 - 0.00272748*i57
      + 0.00192127*i58 - 0.00643836*i59 + 0.00659625*i60 - 0.0160773*i61
      - 0.0311089*i62 - 0.0220835*i63 - 0.0123205*i64 - 0.00688571*i65
      - 0.0329356*i66 + 0.00327885*i67 - 0.009863*i68 - 0.0161333*i69
      - 0.00415196*i70 - 0.0234616*i71 - 0.00105996*i72 + 0.00381383*i73
      - 0.00073674*i74 - 0.0169568*i75 - 0.00559808*i76 - 0.0098104*i77
      - 0.00457398*i78 - 0.0417583*i79 + 0.00283802*i80 - 0.0168204*i81
      - 0.00228309*i82 - 0.0197823*i83 - 0.0100875*i84 - 0.0118258*i85
      - 0.00342073*i86 - 0.00803049*i87 + 0.0213439*i88 - 0.0213604*i89
      - 0.0139007*i90 - 0.0183623*i91 - 0.012037*i92 - 0.00197365*i93
      - 0.0102456*i94 - 0.00369496*i95 - 0.00582019*i96 - 0.00227006*i97
      - 0.0248562*i98 - 0.0205847*i99 - 0.0221142*i100 =G= 0;

e3..    52.59*i1 + 28.87*i2 + 29.19*i3 + 46.55*i4 + 24.26*i5 + 42.53*i6
      + 40.53*i7 + 79.56*i8 + 108.9*i9 + 79.06*i10 + 20.15*i11 + 35.64*i12
      + 39.55*i13 + 14.32*i14 + 26.41*i15 + 62.48*i16 + 254.3*i17 + 32.42*i18
      + 24.84*i19 + 10.1*i20 + 21.2*i21 + 40.25*i22 + 17.32*i23 + 60.92*i24
      + 54.73*i25 + 78.62*i26 + 49.24*i27 + 68.19*i28 + 50.3*i29 + 3.83*i30
      + 18.27*i31 + 59.67*i32 + 12.21*i33 + 38.09*i34 + 71.72*i35 + 23.6*i36
      + 70.71*i37 + 56.98*i38 + 34.47*i39 + 10.23*i40 + 59.19*i41 + 58.61*i42
      + 445.29*i43 + 131.69*i44 + 34.24*i45 + 43.11*i46 + 25.18*i47 + 28*i48
      + 19.43*i49 + 14.33*i50 + 28.41*i51 + 74.5*i52 + 36.54*i53 + 38.99*i54
      + 43.15*i55 + 199.55*i56 + 59.07*i57 + 123.55*i58 + 20.55*i59 + 66.72*i60
      + 37.95*i61 + 27.62*i62 + 23.21*i63 + 36.09*i64 + 23.09*i65 + 46.54*i66
      + 67.89*i67 + 34.83*i68 + 11.96*i69 + 45.77*i70 + 32.91*i71 + 77.37*i72
      + 21.46*i73 + 53.11*i74 + 14.29*i75 + 61.13*i76 + 32.79*i77 + 59.84*i78
      + 6.59*i79 + 14.06*i80 + 55.29*i81 + 33.33*i82 + 4.24*i83 + 23.21*i84
      + 47.85*i85 + 48.99*i86 + 57.46*i87 + 28.87*i88 + 24.6*i89 + 22.26*i90
      + 28.31*i91 + 26.67*i92 + 48.1*i93 + 28.01*i94 + 64.85*i95 + 25.54*i96
      + 31.47*i97 + 18.31*i98 + 35.06*i99 + 8.06*i100 =G= 10000;

e4..    52.59*i1 + 28.87*i2 + 29.19*i3 + 46.55*i4 + 24.26*i5 + 42.53*i6
      + 40.53*i7 + 79.56*i8 + 108.9*i9 + 79.06*i10 + 20.15*i11 + 35.64*i12
      + 39.55*i13 + 14.32*i14 + 26.41*i15 + 62.48*i16 + 254.3*i17 + 32.42*i18
      + 24.84*i19 + 10.1*i20 + 21.2*i21 + 40.25*i22 + 17.32*i23 + 60.92*i24
      + 54.73*i25 + 78.62*i26 + 49.24*i27 + 68.19*i28 + 50.3*i29 + 3.83*i30
      + 18.27*i31 + 59.67*i32 + 12.21*i33 + 38.09*i34 + 71.72*i35 + 23.6*i36
      + 70.71*i37 + 56.98*i38 + 34.47*i39 + 10.23*i40 + 59.19*i41 + 58.61*i42
      + 445.29*i43 + 131.69*i44 + 34.24*i45 + 43.11*i46 + 25.18*i47 + 28*i48
      + 19.43*i49 + 14.33*i50 + 28.41*i51 + 74.5*i52 + 36.54*i53 + 38.99*i54
      + 43.15*i55 + 199.55*i56 + 59.07*i57 + 123.55*i58 + 20.55*i59 + 66.72*i60
      + 37.95*i61 + 27.62*i62 + 23.21*i63 + 36.09*i64 + 23.09*i65 + 46.54*i66
      + 67.89*i67 + 34.83*i68 + 11.96*i69 + 45.77*i70 + 32.91*i71 + 77.37*i72
      + 21.46*i73 + 53.11*i74 + 14.29*i75 + 61.13*i76 + 32.79*i77 + 59.84*i78
      + 6.59*i79 + 14.06*i80 + 55.29*i81 + 33.33*i82 + 4.24*i83 + 23.21*i84
      + 47.85*i85 + 48.99*i86 + 57.46*i87 + 28.87*i88 + 24.6*i89 + 22.26*i90
      + 28.31*i91 + 26.67*i92 + 48.1*i93 + 28.01*i94 + 64.85*i95 + 25.54*i96
      + 31.47*i97 + 18.31*i98 + 35.06*i99 + 8.06*i100 =L= 11000;

* set non-default bounds

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2019-11-29 Git hash: 4a97e4ed
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