/*
We give here the PORC formulae for the functions g(r,s;p) giving the
number of p-class two groups of order p^(r+s) on r generators.

This file is a MAGMA program which defines the polynomials.

The functions are given as polynomials in 44 variables Y1,Y2,...,Y44.

These polynomials DON'T all work for p=3,5,7 which are exceptional primes
in Lemma 3.1 from Higman's PORC paper. (And all of the polynomials
are suspect for p=2.)  Specifically, the functions g(r,s;p) for r=1,2,3,4
are valid for all odd primes. The functions g(5,s;p) are valid for p>5,
and the functions g(6,s;p) are valid for p>7.

The polynomial g(r,s;p) is denoted by grs.

We also define the polynomials p2,p3,p4,p5,p6,p7,p8 giving the
number of p-class two groups of order p^2,p^3,...,p^8.
(Note that we EXCLUDE the elementary abelian groups of these orders.)
*/

P<Y1,Y2,Y3,Y4,Y5,Y6,Y7,Y8,Y9,Y10,Y11,Y12,Y13,Y14,Y15,Y16,Y17,Y18,Y19,
Y20,Y21,Y22,Y23,Y24,Y25,Y26,Y27,Y28,Y29,Y30,Y31,Y32,Y33,Y34,Y35,Y36,Y37,
Y38,Y39,Y40,Y41,Y42,Y43,Y44>:=PolynomialRing(Rationals(),44);
//Y1 is the prime p, Y2=GCD(p-1,3), Y3=GCD(p-1,4), Y4=GCD(p-1,5),
//Y5=GCD(p+1,3), Y6=GCD(p+1,5), Y7=GCD(p^2+1,5), Y8=GCD(p-1,7),
//Y9=GCD(p-1,8), Y10=GCD(p-1,9), Y11=GCD(p-1,11), Y12=GCD(p+3,8),
//Y13=GCD(p+5,8), Y14=GCD(p+1,8), Y15=GCD(p+3,5), Y16=GCD(p+2,5),
//Y17=GCD(p+8,11), Y18=GCD(p+7,11), Y19=GCD(p+6,11), Y20=GCD(p+2,11)
//Y21=GCD(p-1,16), Y22=GCD(p-1,13), Y23=GCD(p-1,17), Y24=GCD(p-1,19)
//Y25=GCD(p+7,16), Y26=GCD(p+1,11), Y27=GCD(p+1,7), Y28=GCD(p+1,13)
//Y29=GCD(p+1,9), Y30:=GCD(p+9,16), Y31=GCD(p+3,7), Y32=GCD(p+10,13)
//Y33=GCD(p+4,13), Y34=GCD(p+12,19), Y35=GCD(p+8,19), Y36=GCD(p+5,7),
//Y37=GCD(p+2,9), Y38=GCD(p+5,9), Y39=GCD(p+13,16), Y40=GCD(p+5,16),
//Y41=GCD(p+7,9), Y42=GCD(p+4,9), Y43=GCD(p+4,7), Y44=GCD(p+2,7)

/*
If you choose a prime p and set

vals:=[p,GCD(p-1,3),GCD(p-1,4),GCD(p-1,5),GCD(p+1,3),GCD(p+1,5),
GCD(p^2+1,5),GCD(p-1,7),GCD(p-1,8),GCD(p-1,9),GCD(p-1,11),GCD(p+3,8),
GCD(p+5,8),GCD(p+1,8),GCD(p+3,5),GCD(p+2,5),GCD(p+8,11),GCD(p+7,11),
GCD(p+6,11),GCD(p+2,11),GCD(p-1,16),GCD(p-1,13),GCD(p-1,17),
GCD(p-1,19),GCD(p+7,16),GCD(p+1,11),GCD(p+1,7),GCD(p+1,13),
GCD(p+1,9),GCD(p+9,16),GCD(p+3,7),GCD(p+10,13),GCD(p+4,13), 
GCD(p+12,19),GCD(p+8,19),GCD(p+5,7),GCD(p+2,9),GCD(p+5,9),
GCD(p+13,16),GCD(p+5,16),GCD(p+7,9),GCD(p+4,9),GCD(p+4,7),
GCD(p+2,7)];

then you can get the value of one of these polynomials at p with
the command

Evaluate(g45,vals);

*/

g11:=1;

g21:=3;
g22:=3;
g23:=1;

g31:=4;
g32:=Y1 + 14;
g33:=3*Y1 + 27;
g34:=g32;
g35:=g31;
g36:=1;

g41:=6;
g42:=4*Y1 + 48;
g43:=Y1^5 + 2*Y1^4 + 7*Y1^3 + 25*Y1^2 + Y1*Y2 + 88*Y1 + 9/2*Y2 + Y3 + 1/2*Y5 + 268;
g44:=Y1^8 + 2*Y1^7 + 5*Y1^6 + 10*Y1^5 + 24*Y1^4 + 53*Y1^3 + Y1^2*Y2 + 138*Y1^2 + 6*Y1*Y2 
     + 2*Y1*Y3 + 323*Y1 + 21*Y2 + 6*Y3 + 5/4*Y4 + 2*Y5 + 1/4*Y6 + 1/4*Y7 + 2753/4;
g45:=Y1^9 + 2*Y1^8 + 5*Y1^7 + 10*Y1^6 + 21*Y1^5 + 44*Y1^4 + 94*Y1^3 + 2*Y1^2*Y2 + Y1^2*Y3 
     + 216*Y1^2 + 10*Y1*Y2 + 4*Y1*Y3 + 1/4*Y1*Y4 + 1/4*Y1*Y6 + 1/4*Y1*Y7 + 1889/4*Y1 + 33*Y2 
     + 12*Y3 + 9/4*Y4 + Y5 + 1/4*Y6 + 1/4*Y7 + 3657/4;
g46:=g44;
g47:=g43;
g48:=g42;
g49:=g41;
g410:=1;

g51:=7;
g52:=Y1^2 + 15*Y1 + 1/2*Y2 + 1/2*Y5 + 123;
g53:=Y1^11 + 2*Y1^10 + 5*Y1^9 + 10*Y1^8 + 20*Y1^7 + 38*Y1^6 + 74*Y1^5 + 142*Y1^4 
     + 3/2*Y1^3*Y2 + 1/2*Y1^3*Y5 + 275*Y1^3 + 19/2*Y1^2*Y2 + 2*Y1^2*Y3 + 3/2*Y1^2*Y5 + 552*Y1^2
     + 65/2*Y1*Y2 + 11*Y1*Y3 + Y1*Y4 + 5/2*Y1*Y5 + 1110*Y1 + 73*Y2 + 29*Y3 + 3*Y4 + 6*Y5 
     + 1986;
g54:=Y1^19 + 2*Y1^18 + 5*Y1^17 + 10*Y1^16 + 20*Y1^15 + 35*Y1^14 + 61*Y1^13 + 99*Y1^12 
     + 160*Y1^11 + 249*Y1^10 + 389*Y1^9 + 605*Y1^8 + 939*Y1^7 + Y1^6*Y2 + 1457*Y1^6 
     + 15/2*Y1^5*Y2 + 1/2*Y1^5*Y5 + 2251*Y1^5 + 33*Y1^4*Y2 + 3*Y1^4*Y3 + Y1^4*Y5 + 3476*Y1^4 
     + 111*Y1^3*Y2 + 26*Y1^3*Y3 + 5/4*Y1^3*Y4 + 3*Y1^3*Y5 + 1/4*Y1^3*Y6 + 1/4*Y1^3*Y25 
     + 1/4*Y1^3*Y26 + 5292*Y1^3 + 613/2*Y1^2*Y2 + 106*Y1^2*Y3 + 41/4*Y1^2*Y4 + 15/2*Y1^2*Y5 
     + 1/4*Y1^2*Y6 + 1/4*Y1^2*Y25 + 1/4*Y1^2*Y26 + 7987*Y1^2 + 657*Y1*Y2 + 282*Y1*Y3 
     + 163/4*Y1*Y4 + 12*Y1*Y5 + 3/4*Y1*Y6 + Y1*Y8 + 1/4*Y1*Y25 + 1/4*Y1*Y26 + 11229*Y1 
     + 1995/2*Y2 + 478*Y3 + 367/4*Y4 + 51/2*Y5 + 7/4*Y6 + 11*Y8 + 25/2*Y9 + 1/2*Y22 + 3/4*Y25 
     + 3/4*Y26 + 13635;
g55:=Y1^25 + 2*Y1^24 + 5*Y1^23 + 10*Y1^22 + 20*Y1^21 + 36*Y1^20 + 63*Y1^19 + 104*Y1^18 
     + 169*Y1^17 + 264*Y1^16 + 405*Y1^15 + 604*Y1^14 + 891*Y1^13 + 1292*Y1^12 + 1865*Y1^11 
     + 2673*Y1^10 + 3835*Y1^9 + Y1^8*Y2 + 5490*Y1^8 + 17/2*Y1^7*Y2 + 1/2*Y1^7*Y5 + 7851*Y1^7 
     + 41*Y1^6*Y2 + Y1^6*Y3 + Y1^6*Y5 + 11187*Y1^6 + 145*Y1^5*Y2 + 13*Y1^5*Y3 + 1/4*Y1^5*Y4 
     + 3*Y1^5*Y5 + 1/4*Y1^5*Y6 + 1/4*Y1^5*Y25 + 1/4*Y1^5*Y26 + 15841*Y1^5 + 417*Y1^4*Y2 
     + 80*Y1^4*Y3 + 5/2*Y1^4*Y4 + 5*Y1^4*Y5 + 1/2*Y1^4*Y6 + 1/2*Y1^4*Y25 + 1/2*Y1^4*Y26 
     + 22173*Y1^4 + 1034*Y1^3*Y2 + 320*Y1^3*Y3 + 97/4*Y1^3*Y4 + 11*Y1^3*Y5 + 5/4*Y1^3*Y6 
     + 3/4*Y1^3*Y25 + 3/4*Y1^3*Y26 + 30384*Y1^3 + 4477/2*Y1^2*Y2 + 906*Y1^2*Y3 + 447/4*Y1^2*Y4 
     + 41/2*Y1^2*Y5 + 7/4*Y1^2*Y6 + 2*Y1^2*Y8 + 3/4*Y1^2*Y25 + 3/4*Y1^2*Y26 + 40150*Y1^2 
     + 3963*Y1*Y2 + 1874*Y1*Y3 + 324*Y1*Y4 + 31*Y1*Y5 + 3*Y1*Y6 + 23*Y1*Y8 + 27/2*Y1*Y9 
     + 1/2*Y1*Y22 + 3/2*Y1*Y25 + 3/2*Y1*Y26 + 48362*Y1 + 10251/2*Y2 + 2570*Y3 + 2461/4*Y4 
     + 107/2*Y5 + 21/4*Y6 + 105*Y8 + 235/2*Y9 + 18*Y20 + 6/5*Y21 + 5/2*Y22 + 3/2*Y23 + 3/2*Y24 
     + 7/4*Y25 + 7/4*Y26 + 1/5*Y27 + 1/5*Y28 + 1/5*Y29 + 1/5*Y30 + 49410;
g56:=Y1^29 + 2*Y1^28 + 5*Y1^27 + 10*Y1^26 + 20*Y1^25 + 36*Y1^24 + 64*Y1^23 + 106*Y1^22 
     + 174*Y1^21 + 274*Y1^20 + 424*Y1^19 + 637*Y1^18 + 944*Y1^17 + 1367*Y1^16 + 1957*Y1^15 
     + 2759*Y1^14 + 3861*Y1^13 + 5357*Y1^12 + 7415*Y1^11 + 10234*Y1^10 + 5/2*Y1^9*Y2 
     + 1/2*Y1^9*Y5 + 14119*Y1^9 + 16*Y1^8*Y2 + Y1^8*Y5 + 19449*Y1^8 + 72*Y1^7*Y2 + Y1^7*Y3 
     + 3*Y1^7*Y5 + 26715*Y1^7 + 244*Y1^6*Y2 + 13*Y1^6*Y3 + 5*Y1^6*Y5 + 36519*Y1^6 + 691*Y1^5*Y2
     + 91*Y1^5*Y3 + 5/4*Y1^5*Y4 + 10*Y1^5*Y5 + 1/4*Y1^5*Y6 + 1/4*Y1^5*Y25 + 1/4*Y1^5*Y26 
     + 49423*Y1^5 + 1689*Y1^4*Y2 + 396*Y1^4*Y3 + 37/2*Y1^4*Y4 + 16*Y1^4*Y5 + 1/2*Y1^4*Y6 
     + 1/2*Y1^4*Y25 + 1/2*Y1^4*Y26 + 65863*Y1^4 + 3684*Y1^3*Y2 + 1262*Y1^3*Y3 + 455/4*Y1^3*Y4 
     + 29*Y1^3*Y5 + 7/4*Y1^3*Y6 + Y1^3*Y8 + 3/4*Y1^3*Y25 + 3/4*Y1^3*Y26 + 85291*Y1^3 
     + 7129*Y1^2*Y2 + 3073*Y1^2*Y3 + 1701/4*Y1^2*Y4 + 48*Y1^2*Y5 + 9/4*Y1^2*Y6 + 17*Y1^2*Y8 
     + 9/2*Y1^2*Y9 + 1/2*Y1^2*Y22 + 3/4*Y1^2*Y25 + 3/4*Y1^2*Y26 + 105337*Y1^2 + 11530*Y1*Y2 
     + 5654*Y1*Y3 + 2157/2*Y1*Y4 + 66*Y1*Y5 + 9/2*Y1*Y6 + 111*Y1*Y8 + 159/2*Y1*Y9 + 6*Y1*Y20 
     + 5/2*Y1*Y22 + 3/2*Y1*Y25 + 3/2*Y1*Y26 + 117234*Y1 + 27467/2*Y2 + 6956*Y3 + 7419/4*Y4 
     + 205/2*Y5 + 35/4*Y6 + 357*Y8 + 402*Y9 + 84*Y20 + 6*Y21 + 6*Y22 + 3/2*Y23 + 3/2*Y24 
     + 7/4*Y25 + 7/4*Y26 + 109913;
g57:=Y1^31 + 2*Y1^30 + 5*Y1^29 + 10*Y1^28 + 20*Y1^27 + 36*Y1^26 + 64*Y1^25 + 107*Y1^24 
     + 176*Y1^23 + 278*Y1^22 + 432*Y1^21 + 652*Y1^20 + 970*Y1^19 + 1410*Y1^18 + 2023*Y1^17 
     + 2854*Y1^16 + 3986*Y1^15 + 5501*Y1^14 + 7548*Y1^13 + 10293*Y1^12 + 14013*Y1^11 + Y1^10*Y2
     + 19033*Y1^10 + 19/2*Y1^9*Y2 + 1/2*Y1^9*Y5 + 25835*Y1^9 + 47*Y1^8*Y2 + Y1^8*Y5 
     + 35003*Y1^8 + 353/2*Y1^7*Y2 + 3*Y1^7*Y3 + 7/2*Y1^7*Y5 + 47269*Y1^7 + 536*Y1^6*Y2 
     + 35*Y1^6*Y3 + 6*Y1^6*Y5 + 63448*Y1^6 + 2793/2*Y1^5*Y2 + 204*Y1^5*Y3 + 9/2*Y1^5*Y4 
     + 25/2*Y1^5*Y5 + 1/2*Y1^5*Y6 + 84228*Y1^5 + 3205*Y1^4*Y2 + 796*Y1^4*Y3 + 43*Y1^4*Y4 
     + 20*Y1^4*Y5 + Y1^4*Y6 + 109818*Y1^4 + 13267/2*Y1^3*Y2 + 2348*Y1^3*Y3 + 915/4*Y1^3*Y4 
     + 73/2*Y1^3*Y5 + 11/4*Y1^3*Y6 + 4*Y1^3*Y8 + 1/2*Y1^3*Y9 + 1/2*Y1^3*Y22 + 1/4*Y1^3*Y25 
     + 1/4*Y1^3*Y26 + 138753*Y1^3 + 24503/2*Y1^2*Y2 + 5386*Y1^2*Y3 + 3139/4*Y1^2*Y4 
     + 119/2*Y1^2*Y5 + 15/4*Y1^2*Y6 + 41*Y1^2*Y8 + 29/2*Y1^2*Y9 + 5/2*Y1^2*Y22 + 1/2*Y1^2*Y23 
     + 1/2*Y1^2*Y24 + 1/4*Y1^2*Y25 + 1/4*Y1^2*Y26 + 166286*Y1^2 + 38167/2*Y1*Y2 + 9457*Y1*Y3 
     + 7571/4*Y1*Y4 + 165/2*Y1*Y5 + 27/4*Y1*Y6 + 222*Y1*Y8 + 339/2*Y1*Y9 + 18*Y1*Y20 
     + 13/2*Y1*Y22 + 1/4*Y1*Y25 + 1/4*Y1*Y26 + 178883*Y1 + 21909*Y2 + 11108*Y3 + 12417/4*Y4 
     + 125*Y5 + 49/4*Y6 + 625*Y8 + 704*Y9 + 162*Y20 + 12*Y21 + 11*Y22 + 5/2*Y23 + 5/2*Y24 
     + 3/4*Y25 + 3/4*Y26 + 161486;
g58:=g57;
g59:=g56;
g510:=g55;
g511:=g54;
g512:=g53;
g513:=g52;
g514:=g51;
g515:=1;

g61:=9;
g62:= Y1^3 + 7*Y1^2 + 53*Y1 + 2*Y2 + 316;

g63:= Y1^18 + 2*Y1^17 + 5*Y1^16 + 10*Y1^15 + 19*Y1^14 + 34*Y1^13 + 60*Y1^12 + 
    100*Y1^11 + 166*Y1^10 + 267*Y1^9 + 429*Y1^8 + 677*Y1^7 + 1/2*Y1^6*Y2 + 
    1/2*Y1^6*Y5 + 1079*Y1^6 + 3*Y1^5*Y2 + Y1^5*Y5 + 1697*Y1^5 + 18*Y1^4*Y2 + 
    2*Y1^4*Y3 + 3*Y1^4*Y5 + 2693*Y1^4 + 69*Y1^3*Y2 + 17*Y1^3*Y3 + 6*Y1^3*Y5 + 
    4210*Y1^3 + 447/2*Y1^2*Y2 + 76*Y1^2*Y3 + 4*Y1^2*Y4 + 27/2*Y1^2*Y5 + 6596*Y1^2 
    + 1027/2*Y1*Y2 + 224*Y1*Y3 + 26*Y1*Y4 + 35/2*Y1*Y5 + Y1*Y8 + 9862*Y1 + 
    804*Y2 + 385*Y3 + 67*Y4 + 31*Y5 + Y6 + 19/3*Y8 + 9/2*Y9 - 1/2*Y14 + 1/3*Y31 + 
    1/3*Y36 + 12838;

g64:= Y1^32 + 2*Y1^31 + 5*Y1^30 + 10*Y1^29 + 20*Y1^28 + 35*Y1^27 + 62*Y1^26 + 
    101*Y1^25 + 164*Y1^24 + 254*Y1^23 + 390*Y1^22 + 579*Y1^21 + 854*Y1^20 + 
    1229*Y1^19 + 1754*Y1^18 + 2461*Y1^17 + 3432*Y1^16 + 4728*Y1^15 + 6489*Y1^14 + 
    8840*Y1^13 + 12020*Y1^12 + 16280*Y1^11 + 5/2*Y1^10*Y2 + 1/2*Y1^10*Y5 + 
    22035*Y1^10 + 17*Y1^9*Y2 + Y1^9*Y5 + 29759*Y1^9 + 151/2*Y1^8*Y2 + Y1^8*Y3 + 
    7/2*Y1^8*Y5 + 40150*Y1^8 + 499/2*Y1^7*Y2 + 13*Y1^7*Y3 + 11/2*Y1^7*Y5 + 
    53984*Y1^7 + 1411/2*Y1^6*Y2 + 81*Y1^6*Y3 + 27/2*Y1^6*Y5 + 72238*Y1^6 + 
    3489/2*Y1^5*Y2 + 341*Y1^5*Y3 + 6*Y1^5*Y4 + 43/2*Y1^5*Y5 + 95704*Y1^5 + 
    7851/2*Y1^4*Y2 + 1123*Y1^4*Y3 + 237/4*Y1^4*Y4 + 87/2*Y1^4*Y5 + 1/4*Y1^4*Y6 + 
    1/4*Y1^4*Y15 + 1/4*Y1^4*Y16 + 124689*Y1^4 + 16105/2*Y1^3*Y2 + 3035*Y1^3*Y3 + 
    589/2*Y1^3*Y4 + 137/2*Y1^3*Y5 + 1/2*Y1^3*Y6 + 7*Y1^3*Y8 + 3*Y1^3*Y9 + 
    1/2*Y1^3*Y15 + 1/2*Y1^3*Y16 + 157829*Y1^3 + 14858*Y1^2*Y2 + 6733*Y1^2*Y3 + 
    3929/4*Y1^2*Y4 + 118*Y1^2*Y5 + 9/4*Y1^2*Y6 + 371/6*Y1^2*Y8 + 37*Y1^2*Y9 + 
    Y1^2*Y10 + 3/4*Y1^2*Y15 + 3/4*Y1^2*Y16 + 1/2*Y1^2*Y27 + 1/3*Y1^2*Y31 + 
    1/3*Y1^2*Y36 + 190813*Y1^2 + 22800*Y1*Y2 + 11587*Y1*Y3 + 9187/4*Y1*Y4 + 
    146*Y1*Y5 + 15/4*Y1*Y6 + 808/3*Y1*Y8 + 218*Y1*Y9 + 18*Y1*Y10 + 3/4*Y1*Y15 + 
    3/4*Y1*Y16 + 1/3*Y1*Y31 + 1/3*Y1*Y36 + 209950*Y1 + 7*Y2*Y3 + 49891/2*Y2 + 
    13204*Y3 + 14089/4*Y4 + 405/2*Y5 + 33/4*Y6 + 1347/2*Y8 + 721*Y9 + 152*Y10 + 
    15*Y11 - Y14 + 5/4*Y15 + 5/4*Y16 + 3/2*Y27 + Y29 + Y31 + Y36 + 191635;

g65:= Y1^44 + 2*Y1^43 + 5*Y1^42 + 10*Y1^41 + 20*Y1^40 + 36*Y1^39 + 64*Y1^38 + 
    106*Y1^37 + 174*Y1^36 + 274*Y1^35 + 425*Y1^34 + 640*Y1^33 + 952*Y1^32 + 
    1384*Y1^31 + 1989*Y1^30 + 2811*Y1^29 + 3930*Y1^28 + 5419*Y1^27 + 7405*Y1^26 + 
    10005*Y1^25 + 13410*Y1^24 + 17807*Y1^23 + 23481*Y1^22 + 30725*Y1^21 + 39976*Y1^20 
    + 51692*Y1^19 + 66551*Y1^18 + 85299*Y1^17 + 109012*Y1^16 + 138904*Y1^15 + 
    7/2*Y1^14*Y2 + 1/2*Y1^14*Y5 + 176708*Y1^14 + 22*Y1^13*Y2 + Y1^13*Y5 + 
    224392*Y1^13 + 201/2*Y1^12*Y2 + 7/2*Y1^12*Y5 + 284696*Y1^12 + 345*Y1^11*Y2 + 
    Y1^11*Y3 + 6*Y1^11*Y5 + 360696*Y1^11 + 1014*Y1^10*Y2 + 15*Y1^10*Y3 + 
    14*Y1^10*Y5 + 456431*Y1^10 + 2616*Y1^9*Y2 + 106*Y1^9*Y3 + 22*Y1^9*Y5 + 
    576092*Y1^9 + 12279/2*Y1^8*Y2 + 499*Y1^8*Y3 + 9/4*Y1^8*Y4 + 83/2*Y1^8*Y5 + 
    1/4*Y1^8*Y6 + 1/4*Y1^8*Y15 + 1/4*Y1^8*Y16 + 724451*Y1^8 + 26517/2*Y1^7*Y2 + 
    1818*Y1^7*Y3 + 57/2*Y1^7*Y4 + 125/2*Y1^7*Y5 + 1/2*Y1^7*Y6 + 1/2*Y1^7*Y15 + 
    1/2*Y1^7*Y16 + 904857*Y1^7 + 26736*Y1^6*Y2 + 5485*Y1^6*Y3 + 199*Y1^6*Y4 + 
    108*Y1^6*Y5 + 2*Y1^6*Y6 + Y1^6*Y15 + Y1^6*Y16 + 1118362*Y1^6 + 
    101317/2*Y1^5*Y2 + 14306*Y1^5*Y3 + 1899/2*Y1^5*Y4 + 323/2*Y1^5*Y5 + 
    7/2*Y1^5*Y6 + 6*Y1^5*Y8 + Y1^5*Y9 + 2*Y1^5*Y15 + 2*Y1^5*Y16 + 1358306*Y1^5 + 
    90671*Y1^4*Y2 + 32844*Y1^4*Y3 + 6829/2*Y1^4*Y4 + 266*Y1^4*Y5 + 17/2*Y1^4*Y6 + 
    177/2*Y1^4*Y8 + 28*Y1^4*Y9 + 2*Y1^4*Y10 + 1/5*Y1^4*Y11 + 1/2*Y1^4*Y13 + 
    1/2*Y1^4*Y14 + 7/2*Y1^4*Y15 + 7/2*Y1^4*Y16 + 1/5*Y1^4*Y17 + 1/5*Y1^4*Y18 + 
    1/5*Y1^4*Y19 + 1/5*Y1^4*Y20 + 1/2*Y1^4*Y27 + 1606240*Y1^4 + 304113/2*Y1^3*Y2 + 
    66285*Y1^3*Y3 + 9746*Y1^3*Y4 + 749/2*Y1^3*Y5 + 12*Y1^3*Y6 + 1163/2*Y1^3*Y8 + 
    300*Y1^3*Y9 + 31*Y1^3*Y10 + 6/5*Y1^3*Y11 + Y1^3*Y13 + Y1^3*Y14 + 
    9/2*Y1^3*Y15 + 9/2*Y1^3*Y16 + 1/5*Y1^3*Y17 + 1/5*Y1^3*Y18 + 1/5*Y1^3*Y19 + 
    1/5*Y1^3*Y20 + 1/2*Y1^3*Y27 + 1821734*Y1^3 + 232301*Y1^2*Y2 + 114565*Y1^2*Y3 + 
    89065/4*Y1^2*Y4 + 565*Y1^2*Y5 + 93/4*Y1^2*Y6 + 14261/6*Y1^2*Y8 + 1672*Y1^2*Y9 
    + 232*Y1^2*Y10 + 41/5*Y1^2*Y11 + 7/2*Y1^2*Y13 + 5/2*Y1^2*Y14 + 19/4*Y1^2*Y15 +
    19/4*Y1^2*Y16 + 1/5*Y1^2*Y17 + 1/5*Y1^2*Y18 + 1/5*Y1^2*Y19 + 1/5*Y1^2*Y20 + 
    5/2*Y1^2*Y27 + Y1^2*Y29 + 1/3*Y1^2*Y31 + 1/3*Y1^2*Y36 + 1936385*Y1^2 + 
    55/2*Y1*Y2*Y3 + 602483/2*Y1*Y2 + 1/2*Y1*Y3*Y5 + 158788*Y1*Y3 + 39783*Y1*Y4 +
    1273/2*Y1*Y5 + 28*Y1*Y6 + 19918/3*Y1*Y8 + 11971/2*Y1*Y9 + 1231*Y1*Y10 + 
    431/5*Y1*Y11 + 11/2*Y1*Y13 + 5*Y1*Y14 + 6*Y1*Y15 + 6*Y1*Y16 + 1/5*Y1*Y17 + 
    1/5*Y1*Y18 + 1/5*Y1*Y19 + 1/5*Y1*Y20 + Y1*Y22 + 2*Y1*Y27 + Y1*Y29 + 
    1/3*Y1*Y31 + 1/3*Y1*Y36 + 1834825*Y1 + 2073/2*Y2*Y3 + 35/2*Y2*Y4 + 1/2*Y2*Y6 
    + 557103/2*Y2 + 15/2*Y3*Y5 + 147225*Y3 + 49629*Y4 + 1543/2*Y5 + 47*Y6 + 
    23647/2*Y8 + 13083*Y9 + 3975*Y10 + 3403/5*Y11 + 12*Y13 + 6*Y14 + 13/2*Y15 + 
    13/2*Y16 + 3/5*Y17 + 3/5*Y18 + 3/5*Y19 + 3/5*Y20 + 21/2*Y21 + 116*Y22 + 5/2*Y25 
    + 7/2*Y27 + Y29 + Y31 + Y36 + 1416783;

g66:= Y1^54 + 2*Y1^53 + 5*Y1^52 + 10*Y1^51 + 20*Y1^50 + 36*Y1^49 + 65*Y1^48 + 
    108*Y1^47 + 179*Y1^46 + 284*Y1^45 + 445*Y1^44 + 676*Y1^43 + 1017*Y1^42 + 
    1492*Y1^41 + 2168*Y1^40 + 3094*Y1^39 + 4371*Y1^38 + 6085*Y1^37 + 8398*Y1^36 + 
    11444*Y1^35 + 15472*Y1^34 + 20700*Y1^33 + 27488*Y1^32 + 36176*Y1^31 + 47297*Y1^30 
    + 61350*Y1^29 + 79103*Y1^28 + 101302*Y1^27 + 129029*Y1^26 + 163379*Y1^25 + 
    205900*Y1^24 + 258178*Y1^23 + 322447*Y1^22 + 401077*Y1^21 + 497309*Y1^20 + 
    614729*Y1^19 + 1/2*Y1^18*Y2 + 1/2*Y1^18*Y5 + 758175*Y1^18 + 7*Y1^17*Y2 + 
    Y1^17*Y5 + 933104*Y1^17 + 85/2*Y1^16*Y2 + 7/2*Y1^16*Y5 + 1146745*Y1^16 + 
    176*Y1^15*Y2 + 6*Y1^15*Y5 + 1407405*Y1^15 + 599*Y1^14*Y2 + 14*Y1^14*Y5 + 
    1725676*Y1^14 + 1740*Y1^13*Y2 + 4*Y1^13*Y3 + 22*Y1^13*Y5 + 2113685*Y1^13 + 
    9041/2*Y1^12*Y2 + 45*Y1^12*Y3 + 87/2*Y1^12*Y5 + 2586135*Y1^12 + 10681*Y1^11*Y2 
    + 271*Y1^11*Y3 + 63*Y1^11*Y5 + 3158888*Y1^11 + 23404*Y1^10*Y2 + 1194*Y1^10*Y3 +
    9/4*Y1^10*Y4 + 110*Y1^10*Y5 + 1/4*Y1^10*Y6 + 1/4*Y1^10*Y15 + 1/4*Y1^10*Y16 + 
    3848908*Y1^10 + 95957/2*Y1^9*Y2 + 4228*Y1^9*Y3 + 73/2*Y1^9*Y4 + 305/2*Y1^9*Y5 +
    1/2*Y1^9*Y6 + 1/2*Y1^9*Y15 + 1/2*Y1^9*Y16 + 4670734*Y1^9 + 185779/2*Y1^8*Y2 + 
    12709*Y1^8*Y3 + 1093/4*Y1^8*Y4 + 495/2*Y1^8*Y5 + 9/4*Y1^8*Y6 + 5/4*Y1^8*Y15 + 
    5/4*Y1^8*Y16 + 5632472*Y1^8 + 170649*Y1^7*Y2 + 33474*Y1^7*Y3 + 2733/2*Y1^7*Y4 +
    338*Y1^7*Y5 + 7/2*Y1^7*Y6 + Y1^7*Y8 + 2*Y1^7*Y15 + 2*Y1^7*Y16 + 6726154*Y1^7 
    + 299040*Y1^6*Y2 + 78891*Y1^6*Y3 + 10565/2*Y1^6*Y4 + 522*Y1^6*Y5 + 
    21/2*Y1^6*Y6 + 199/6*Y1^6*Y8 + 4*Y1^6*Y9 + 4*Y1^6*Y15 + 4*Y1^6*Y16 + 
    1/6*Y1^6*Y27 + 1/6*Y1^6*Y31 + 1/6*Y1^6*Y36 + 1/6*Y1^6*Y43 + 1/6*Y1^6*Y44 + 
    7913761*Y1^6 + 1002005/2*Y1^5*Y2 + 168426*Y1^5*Y3 + 66915/4*Y1^5*Y4 + 
    1429/2*Y1^5*Y5 + 59/4*Y1^5*Y6 + 349*Y1^5*Y8 + 87*Y1^5*Y9 + 5*Y1^5*Y10 + 
    1/2*Y1^5*Y13 + 1/2*Y1^5*Y14 + 25/4*Y1^5*Y15 + 25/4*Y1^5*Y16 + 9104992*Y1^5 + 
    801419*Y1^4*Y2 + 326149*Y1^4*Y3 + 44690*Y1^4*Y4 + 1048*Y1^4*Y5 + 33*Y1^4*Y6 + 
    2112*Y1^4*Y8 + 875*Y1^4*Y9 + 87*Y1^4*Y10 + 11/5*Y1^4*Y11 + 2*Y1^4*Y13 + 
    2*Y1^4*Y14 + 9*Y1^4*Y15 + 9*Y1^4*Y16 + 1/5*Y1^4*Y17 + 1/5*Y1^4*Y18 + 
    1/5*Y1^4*Y19 + 1/5*Y1^4*Y20 + 2*Y1^4*Y27 + 10132625*Y1^4 + Y1^3*Y2*Y3 + 
    2418867/2*Y1^3*Y2 + 566287*Y1^3*Y3 + 406295/4*Y1^3*Y4 + 2759/2*Y1^3*Y5 + 
    171/4*Y1^3*Y6 + 8765*Y1^3*Y8 + 5187*Y1^3*Y9 + 743*Y1^3*Y10 + 121/5*Y1^3*Y11 + 
    11/2*Y1^3*Y13 + 11/2*Y1^3*Y14 + 41/4*Y1^3*Y15 + 41/4*Y1^3*Y16 + 1/5*Y1^3*Y17 +
    1/5*Y1^3*Y18 + 1/5*Y1^3*Y19 + 1/5*Y1^3*Y20 + Y1^3*Y27 + Y1^3*Y31 + Y1^3*Y36 
    + 10730505*Y1^3 + 47*Y1^2*Y2*Y3 + 3337879/2*Y1^2*Y2 + Y1^2*Y3*Y5 + 
    854224*Y1^2*Y3 + 388577/2*Y1^2*Y4 + 3665/2*Y1^2*Y5 + 151/2*Y1^2*Y6 + 
    26609*Y1^2*Y8 + 40861/2*Y1^2*Y9 + 7965/2*Y1^2*Y10 + 1071/5*Y1^2*Y11 + 
    25/2*Y1^2*Y13 + 11*Y1^2*Y14 + 11*Y1^2*Y15 + 11*Y1^2*Y16 + 1/5*Y1^2*Y17 + 
    1/5*Y1^2*Y18 + 1/5*Y1^2*Y19 + 1/5*Y1^2*Y20 + 3*Y1^2*Y22 + 8*Y1^2*Y27 + 
    5/2*Y1^2*Y29 + 10532252*Y1^2 + 3199/2*Y1*Y2*Y3 + 7*Y1*Y2*Y4 + 1964288*Y1*Y2 +
    13/2*Y1*Y3*Y5 + 1044626*Y1*Y3 + 1209565/4*Y1*Y4 + 2036*Y1*Y5 + 385/4*Y1*Y6 + 
    59733*Y1*Y8 + 113697/2*Y1*Y9 + 15045*Y1*Y10 + 8346/5*Y1*Y11 + 20*Y1*Y13 + 
    39/2*Y1*Y14 + 59/4*Y1*Y15 + 59/4*Y1*Y16 + 1/5*Y1*Y17 + 1/5*Y1*Y18 + 
    1/5*Y1*Y19 + 1/5*Y1*Y20 + 147*Y1*Y22 + 17/3*Y1*Y27 + Y1*Y29 + 1/2*Y1*Y31 + 
    1/2*Y1*Y36 + 1/6*Y1*Y43 + 1/6*Y1*Y44 + 9114742*Y1 + 24267/2*Y2*Y3 + 
    2443/4*Y2*Y4 + 9/4*Y2*Y6 + 1636313*Y2 + 7/2*Y3*Y4 + 35/2*Y3*Y5 + 1/2*Y3*Y6 + 
    853445*Y3 + 3/2*Y4*Y5 + 1330947/4*Y4 + 1/4*Y5*Y15 + 1/4*Y5*Y16 + 2068*Y5 + 
    523/4*Y6 + 265465/3*Y8 + 98550*Y9 + 103877/3*Y10 + 71911/10*Y11 + 39*Y13 + 26*Y14
    + 51/4*Y15 + 51/4*Y16 + 3/5*Y17 + 3/5*Y18 + 3/5*Y19 + 3/5*Y20 + 1197/4*Y21 + 
    3443/2*Y22 + 56*Y23 + 28/3*Y24 + 63/4*Y25 + 3/2*Y26 + 46/3*Y27 + 1/2*Y28 + 
    23/3*Y29 + 1/2*Y30 + 17/6*Y31 + Y32 + Y33 + 1/3*Y34 + 1/3*Y35 + 17/6*Y36 + 
    1/6*Y37 + 1/6*Y38 + 1/4*Y39 + 1/4*Y40 + 1/6*Y41 + 1/6*Y42 - 1/6*Y43 - 1/6*Y44 + 
    6369159;

g67:= Y1^62 + 2*Y1^61 + 5*Y1^60 + 10*Y1^59 + 20*Y1^58 + 36*Y1^57 + 65*Y1^56 + 
    109*Y1^55 + 181*Y1^54 + 289*Y1^53 + 455*Y1^52 + 696*Y1^51 + 1053*Y1^50 + 
    1557*Y1^49 + 2277*Y1^48 + 3274*Y1^47 + 4658*Y1^46 + 6535*Y1^45 + 9084*Y1^44 + 
    12477*Y1^43 + 16992*Y1^42 + 22908*Y1^41 + 30642*Y1^40 + 40625*Y1^39 + 53480*Y1^38 
    + 69850*Y1^37 + 90638*Y1^36 + 116795*Y1^35 + 149606*Y1^34 + 190439*Y1^33 + 
    241106*Y1^32 + 303541*Y1^31 + 380258*Y1^30 + 473974*Y1^29 + 588149*Y1^28 + 
    726561*Y1^27 + 893999*Y1^26 + 1095731*Y1^25 + 1338421*Y1^24 + 1629530*Y1^23 + 
    1978472*Y1^22 + 2395957*Y1^21 + 7/2*Y1^20*Y2 + 1/2*Y1^20*Y5 + 2895512*Y1^20 + 
    24*Y1^19*Y2 + Y1^19*Y5 + 3492679*Y1^19 + 118*Y1^18*Y2 + 4*Y1^18*Y5 + 
    4206997*Y1^18 + 873/2*Y1^17*Y2 + 15/2*Y1^17*Y5 + 5061002*Y1^17 + 2753/2*Y1^16*Y2
    + 37/2*Y1^16*Y5 + 6082568*Y1^16 + 7611/2*Y1^15*Y2 + 4*Y1^15*Y3 + 61/2*Y1^15*Y5 
    + 7303483*Y1^15 + 9548*Y1^14*Y2 + 46*Y1^14*Y3 + 60*Y1^14*Y5 + 8761815*Y1^14 + 
    44071/2*Y1^13*Y2 + 289*Y1^13*Y3 + 183/2*Y1^13*Y5 + 10499196*Y1^13 + 
    94969/2*Y1^12*Y2 + 1326*Y1^12*Y3 + 315/2*Y1^12*Y5 + 12561804*Y1^12 + 
    96295*Y1^11*Y2 + 4904*Y1^11*Y3 + 15*Y1^11*Y4 + 225*Y1^11*Y5 + 14993708*Y1^11 + 
    185257*Y1^10*Y2 + 15431*Y1^10*Y3 + 611/4*Y1^10*Y4 + 355*Y1^10*Y5 + 
    3/4*Y1^10*Y6 + 1/4*Y1^10*Y15 + 1/4*Y1^10*Y16 + 17832399*Y1^10 + 
    679359/2*Y1^9*Y2 + 42652*Y1^9*Y3 + 1845/2*Y1^9*Y4 + 977/2*Y1^9*Y5 + 
    3/2*Y1^9*Y6 + 1/2*Y1^9*Y15 + 1/2*Y1^9*Y16 + 21091904*Y1^9 + 1192443/2*Y1^8*Y2 +
    105708*Y1^8*Y3 + 16327/4*Y1^8*Y4 + 1463/2*Y1^8*Y5 + 27/4*Y1^8*Y6 + 
    13/6*Y1^8*Y8 + 5/4*Y1^8*Y15 + 5/4*Y1^8*Y16 + 1/6*Y1^8*Y27 + 1/6*Y1^8*Y31 + 
    1/6*Y1^8*Y36 + 1/6*Y1^8*Y43 + 1/6*Y1^8*Y44 + 24743899*Y1^8 + 1004624*Y1^7*Y2 + 
    238415*Y1^7*Y3 + 29167/2*Y1^7*Y4 + 992*Y1^7*Y5 + 21/2*Y1^7*Y6 + 355/6*Y1^7*Y8 
    + 5*Y1^7*Y9 + 2*Y1^7*Y15 + 2*Y1^7*Y16 + 1/6*Y1^7*Y27 + 1/6*Y1^7*Y31 + 
    1/6*Y1^7*Y36 + 1/6*Y1^7*Y43 + 1/6*Y1^7*Y44 + 28677555*Y1^7 + 3258469/2*Y1^6*Y2 
    + 493964*Y1^6*Y3 + 44046*Y1^6*Y4 + 2885/2*Y1^6*Y5 + 28*Y1^6*Y6 + 
    3697/6*Y1^6*Y8 + 113*Y1^6*Y9 + 3*Y1^6*Y10 + 1/2*Y1^6*Y13 + 1/2*Y1^6*Y14 + 
    4*Y1^6*Y15 + 4*Y1^6*Y16 + 7/6*Y1^6*Y27 + 1/6*Y1^6*Y31 + 1/6*Y1^6*Y36 + 
    1/6*Y1^6*Y43 + 1/6*Y1^6*Y44 + 32652612*Y1^6 + 2543809*Y1^5*Y2 + 943670*Y1^5*Y3 
    + 461075/4*Y1^5*Y4 + 1923*Y1^5*Y5 + 163/4*Y1^5*Y6 + 11477/3*Y1^5*Y8 + 
    1222*Y1^5*Y9 + 86*Y1^5*Y10 + 3/2*Y1^5*Y13 + 3/2*Y1^5*Y14 + 25/4*Y1^5*Y15 + 
    25/4*Y1^5*Y16 + Y1^5*Y27 + 2/3*Y1^5*Y31 + 2/3*Y1^5*Y36 + 36229077*Y1^5 + 
    Y1^4*Y2*Y3 + 7617563/2*Y1^4*Y2 + 1655280*Y1^4*Y3 + 528503/2*Y1^4*Y4 + 
    5371/2*Y1^4*Y5 + 167/2*Y1^4*Y6 + 50456/3*Y1^4*Y8 + 16033/2*Y1^4*Y9 + 
    1935/2*Y1^4*Y10 + 21*Y1^4*Y11 + 7*Y1^4*Y13 + 13/2*Y1^4*Y14 + 9*Y1^4*Y15 + 
    9*Y1^4*Y16 + 6*Y1^4*Y27 + 3/2*Y1^4*Y29 + 2/3*Y1^4*Y31 + 2/3*Y1^4*Y36 + 
    38717058*Y1^4 + 42*Y1^3*Y2*Y3 + 10785661/2*Y1^3*Y2 + Y1^3*Y3*Y5 + 
    2625581*Y1^3*Y3 + 2120025/4*Y1^3*Y4 + 6773/2*Y1^3*Y5 + 437/4*Y1^3*Y6 + 
    335993/6*Y1^3*Y8 + 71977/2*Y1^3*Y9 + 12377/2*Y1^3*Y10 + 248*Y1^3*Y11 + 
    14*Y1^3*Y13 + 27/2*Y1^3*Y14 + 41/4*Y1^3*Y15 + 41/4*Y1^3*Y16 + 3*Y1^3*Y22 + 
    31/6*Y1^3*Y27 + 3/2*Y1^3*Y29 + 5/6*Y1^3*Y31 + 5/6*Y1^3*Y36 + 1/6*Y1^3*Y43 + 
    1/6*Y1^3*Y44 + 39162060*Y1^3 + 1153*Y1^2*Y2*Y3 + 6989315*Y1^2*Y2 + 
    10*Y1^2*Y3*Y5 + 3641228*Y1^2*Y3 + 915611*Y1^2*Y4 + 4318*Y1^2*Y5 + 184*Y1^2*Y6
    + 144471*Y1^2*Y8 + 117085*Y1^2*Y9 + 53747/2*Y1^2*Y10 + 3977/2*Y1^2*Y11 + 
    131/4*Y1^2*Y13 + 107/4*Y1^2*Y14 + 11*Y1^2*Y15 + 11*Y1^2*Y16 + 177/2*Y1^2*Y22 +
    3/2*Y1^2*Y26 + 17*Y1^2*Y27 + 1/2*Y1^2*Y28 + 49/6*Y1^2*Y29 + 2*Y1^2*Y31 + 
    2*Y1^2*Y36 + 1/2*Y1^2*Y37 + 1/2*Y1^2*Y38 + 1/6*Y1^2*Y41 + 1/6*Y1^2*Y42 + 
    36458706*Y1^2 + 13738*Y1*Y2*Y3 + 287*Y1*Y2*Y4 + 15459969/2*Y1*Y2 + 
    31*Y1*Y3*Y5 + 4112160*Y1*Y3 + 3*Y1*Y4*Y5 + 5241541/4*Y1*Y4 + 9025/2*Y1*Y5 + 
    829/4*Y1*Y6 + 570509/2*Y1*Y8 + 279701*Y1*Y9 + 83539*Y1*Y10 + 23045/2*Y1*Y11 + 
    89/2*Y1*Y13 + 81/2*Y1*Y14 + 59/4*Y1*Y15 + 59/4*Y1*Y16 + 77*Y1*Y21 + 
    3149/2*Y1*Y22 + 14*Y1*Y23 + 3/2*Y1*Y25 + 3/2*Y1*Y26 + 29/2*Y1*Y27 + 
    1/2*Y1*Y28 + 20/3*Y1*Y29 + 1/2*Y1*Y30 + 2*Y1*Y31 + 2*Y1*Y36 + 1/2*Y1*Y37 + 
    1/2*Y1*Y38 + 1/6*Y1*Y41 + 1/6*Y1*Y42 + 29719590*Y1 + 127247/2*Y2*Y3 + 
    18011/4*Y2*Y4 + 17/4*Y2*Y6 + 6004789*Y2 + 63/2*Y3*Y4 + 127/2*Y3*Y5 + 
    1/2*Y3*Y6 + 3091387*Y3 + 9/2*Y4*Y5 + 5305703/4*Y4 + 1/4*Y5*Y15 + 1/4*Y5*Y16 + 
    4363*Y5 + 1099/4*Y6 + 376226*Y8 + 838597/2*Y9 + 159099*Y10 + 72943/2*Y11 + 
    345/4*Y13 + 219/4*Y14 + 51/4*Y15 + 51/4*Y16 + 8617/4*Y21 + 20149/2*Y22 + 490*Y23 
    + 84*Y24 + 169/4*Y25 + 3/2*Y26 + 70/3*Y27 + 1/2*Y28 + 23/3*Y29 + Y30 + 9/2*Y31 +
    9/2*Y36 + 1/2*Y37 + 1/2*Y38 + 1/4*Y39 + 1/4*Y40 + 1/6*Y41 + 1/6*Y42 - 1/6*Y43 - 
    1/6*Y44 + 19467019;

g68:= Y1^68 + 2*Y1^67 + 5*Y1^66 + 10*Y1^65 + 20*Y1^64 + 36*Y1^63 + 65*Y1^62 + 
    109*Y1^61 + 182*Y1^60 + 291*Y1^59 + 460*Y1^58 + 706*Y1^57 + 1073*Y1^56 + 
    1593*Y1^55 + 2341*Y1^54 + 3381*Y1^53 + 4835*Y1^52 + 6816*Y1^51 + 9524*Y1^50 + 
    13147*Y1^49 + 18000*Y1^48 + 24392*Y1^47 + 32802*Y1^46 + 43717*Y1^45 + 57859*Y1^44 
    + 75965*Y1^43 + 99094*Y1^42 + 128347*Y1^41 + 165243*Y1^40 + 211379*Y1^39 + 
    268909*Y1^38 + 340102*Y1^37 + 427955*Y1^36 + 535651*Y1^35 + 667299*Y1^34 + 
    827292*Y1^33 + 1021220*Y1^32 + 1255073*Y1^31 + 1536385*Y1^30 + 1873305*Y1^29 + 
    2275975*Y1^28 + 2755478*Y1^27 + 3325574*Y1^26 + 4001483*Y1^25 + 4802090*Y1^24 + 
    5748630*Y1^23 + 7/2*Y1^22*Y2 + 1/2*Y1^22*Y5 + 6867397*Y1^22 + 25*Y1^21*Y2 + 
    Y1^21*Y5 + 8188391*Y1^21 + 122*Y1^20*Y2 + 4*Y1^20*Y5 + 9748612*Y1^20 + 
    456*Y1^19*Y2 + 7*Y1^19*Y5 + 11590574*Y1^19 + 2921/2*Y1^18*Y2 + 37/2*Y1^18*Y5 + 
    13766127*Y1^18 + 4114*Y1^17*Y2 + Y1^17*Y3 + 30*Y1^17*Y5 + 16334666*Y1^17 + 
    10523*Y1^16*Y2 + 17*Y1^16*Y3 + 62*Y1^16*Y5 + 19366917*Y1^16 + 24774*Y1^15*Y2 + 
    130*Y1^15*Y3 + 94*Y1^15*Y5 + 22942116*Y1^15 + 54457*Y1^14*Y2 + 685*Y1^14*Y3 + 
    169*Y1^14*Y5 + 27150170*Y1^14 + 225307/2*Y1^13*Y2 + 2834*Y1^13*Y3 + Y1^13*Y4 + 
    483/2*Y1^13*Y5 + 32085180*Y1^13 + 221073*Y1^12*Y2 + 9838*Y1^12*Y3 + 
    59/2*Y1^12*Y4 + 393*Y1^12*Y5 + 1/2*Y1^12*Y6 + 37841303*Y1^12 + 
    827223/2*Y1^11*Y2 + 29698*Y1^11*Y3 + 261*Y1^11*Y4 + 1073/2*Y1^11*Y5 + Y1^11*Y6
    + 44495608*Y1^11 + 741266*Y1^10*Y2 + 79891*Y1^10*Y3 + 1479*Y1^10*Y4 + 
    816*Y1^10*Y5 + 5*Y1^10*Y6 + 52086760*Y1^10 + 1276424*Y1^9*Y2 + 194717*Y1^9*Y3 +
    6375*Y1^9*Y4 + 1084*Y1^9*Y5 + 8*Y1^9*Y6 + Y1^9*Y8 + 60572511*Y1^9 + 
    4235493/2*Y1^8*Y2 + 435189*Y1^8*Y3 + 22540*Y1^8*Y4 + 3157/2*Y1^8*Y5 + 
    23*Y1^8*Y6 + 253/6*Y1^8*Y8 + 2*Y1^8*Y9 + 1/2*Y1^8*Y15 + 1/2*Y1^8*Y16 + 
    1/6*Y1^8*Y27 + 1/6*Y1^8*Y31 + 1/6*Y1^8*Y36 + 1/6*Y1^8*Y43 + 1/6*Y1^8*Y44 + 
    69770699*Y1^8 + 6783989/2*Y1^7*Y2 + 899744*Y1^7*Y3 + 272737/4*Y1^7*Y4 + 
    4155/2*Y1^7*Y5 + 129/4*Y1^7*Y6 + 3157/6*Y1^7*Y8 + 64*Y1^7*Y9 + 1/2*Y1^7*Y13 + 
    1/2*Y1^7*Y14 + 3/4*Y1^7*Y15 + 3/4*Y1^7*Y16 + 1/6*Y1^7*Y27 + 1/6*Y1^7*Y31 + 
    1/6*Y1^7*Y36 + 1/6*Y1^7*Y43 + 1/6*Y1^7*Y44 + 79267094*Y1^7 + 10505023/2*Y1^6*Y2
    + 1729306*Y1^6*Y3 + 361491/2*Y1^6*Y4 + 5859/2*Y1^6*Y5 + 145/2*Y1^6*Y6 + 
    22201/6*Y1^6*Y8 + 852*Y1^6*Y9 + 29*Y1^6*Y10 + 2*Y1^6*Y13 + 2*Y1^6*Y14 + 
    3/2*Y1^6*Y15 + 3/2*Y1^6*Y16 + 13/6*Y1^6*Y27 + 1/6*Y1^6*Y31 + 1/6*Y1^6*Y36 + 
    1/6*Y1^6*Y43 + 1/6*Y1^6*Y44 + 88299493*Y1^6 + 7857230*Y1^5*Y2 + 3090583*Y1^5*Y3
    + 425366*Y1^5*Y4 + 3804*Y1^5*Y5 + 96*Y1^5*Y6 + 108625/6*Y1^5*Y8 + 6603*Y1^5*Y9
    + 556*Y1^5*Y10 + 3*Y1^5*Y11 + 7*Y1^5*Y13 + 7*Y1^5*Y14 + 5/2*Y1^5*Y15 + 
    5/2*Y1^5*Y16 + 3/2*Y1^5*Y27 + 2/3*Y1^5*Y31 + 2/3*Y1^5*Y36 + 95628118*Y1^5 + 
    18*Y1^4*Y2*Y3 + 11293930*Y1^4*Y2 + Y1^4*Y3*Y5 + 5101696*Y1^4*Y3 + 
    3570847/4*Y1^4*Y4 + 5117*Y1^4*Y5 + 719/4*Y1^4*Y6 + 404407/6*Y1^4*Y8 + 
    69669/2*Y1^4*Y9 + 9575/2*Y1^4*Y10 + 124*Y1^4*Y11 + 19*Y1^4*Y13 + 35/2*Y1^4*Y14
    + 19/4*Y1^4*Y15 + 19/4*Y1^4*Y16 + Y1^4*Y22 + 23/2*Y1^4*Y27 + 13/6*Y1^4*Y29 + 
    2/3*Y1^4*Y31 + 2/3*Y1^4*Y36 + 1/2*Y1^4*Y37 + 1/2*Y1^4*Y38 + 1/6*Y1^4*Y41 + 
    1/6*Y1^4*Y42 + 99465352*Y1^4 + 927/2*Y1^3*Y2*Y3 + 30729535/2*Y1^3*Y2 + 
    11/2*Y1^3*Y3*Y5 + 7647756*Y1^3*Y3 + 3325173/2*Y1^3*Y4 + 12671/2*Y1^3*Y5 + 
    457/2*Y1^3*Y6 + 594619/3*Y1^3*Y8 + 268167/2*Y1^3*Y9 + 51479/2*Y1^3*Y10 + 
    1281*Y1^3*Y11 + 75/2*Y1^3*Y13 + 36*Y1^3*Y14 + 13/2*Y1^3*Y15 + 13/2*Y1^3*Y16 + 
    32*Y1^3*Y22 + 23/3*Y1^3*Y27 + 3/2*Y1^3*Y29 + 5/6*Y1^3*Y31 + 5/6*Y1^3*Y36 + 
    Y1^3*Y37 + Y1^3*Y38 + 1/6*Y1^3*Y43 + 1/6*Y1^3*Y44 + 97572806*Y1^3 + 
    6834*Y1^2*Y2*Y3 + 63/2*Y1^2*Y2*Y4 + 38270053/2*Y1^2*Y2 + 30*Y1^2*Y3*Y5 + 
    10055854*Y1^2*Y3 + 3/2*Y1^2*Y4*Y5 + 10799513/4*Y1^2*Y4 + 15383/2*Y1^2*Y5 + 
    1401/4*Y1^2*Y6 + 928121/2*Y1^2*Y8 + 388887*Y1^2*Y9 + 195531/2*Y1^2*Y10 + 
    8764*Y1^2*Y11 + 289/4*Y1^2*Y13 + 249/4*Y1^2*Y14 + 29/4*Y1^2*Y15 + 
    29/4*Y1^2*Y16 + 35/4*Y1^2*Y21 + 1229/2*Y1^2*Y22 + 3/4*Y1^2*Y25 + 2*Y1^2*Y26 + 
    63/2*Y1^2*Y27 + 1/2*Y1^2*Y28 + 77/6*Y1^2*Y29 + 2*Y1^2*Y31 + 2*Y1^2*Y36 + 
    2*Y1^2*Y37 + 2*Y1^2*Y38 + 1/4*Y1^2*Y39 + 1/4*Y1^2*Y40 + 1/3*Y1^2*Y41 + 
    1/3*Y1^2*Y42 + 87689867*Y1^2 + 54575*Y1*Y2*Y3 + 1757*Y1*Y2*Y4 + 
    40641011/2*Y1*Y2 + 75*Y1*Y3*Y5 + 10786563*Y1*Y3 + 9*Y1*Y4*Y5 + 3664068*Y1*Y4
    + 15989/2*Y1*Y5 + 397*Y1*Y6 + 846208*Y1*Y8 + 844050*Y1*Y9 + 269680*Y1*Y10 + 
    83833/2*Y1*Y11 + 181/2*Y1*Y13 + 169/2*Y1*Y14 + 17/2*Y1*Y15 + 17/2*Y1*Y16 + 
    1043/2*Y1*Y21 + 13931/2*Y1*Y22 + 98*Y1*Y23 + 3*Y1*Y25 + 3/2*Y1*Y26 + 
    26*Y1*Y27 + 1/2*Y1*Y28 + 20/3*Y1*Y29 + 1/2*Y1*Y30 + 2*Y1*Y31 + 2*Y1*Y36 + 
    3/2*Y1*Y37 + 3/2*Y1*Y38 + 1/6*Y1*Y41 + 1/6*Y1*Y42 + 68701893*Y1 + 
    196299*Y2*Y3 + 16408*Y2*Y4 + 19/2*Y2*Y6 + 30132293/2*Y2 + 126*Y3*Y4 + 
    106*Y3*Y5 + 2*Y3*Y6 + 7678229*Y3 + 27/2*Y4*Y5 + 7017141/2*Y4 + 14433/2*Y5 + 
    959/2*Y6 + 1035284*Y8 + 2305405/2*Y9 + 915031/2*Y10 + 221861/2*Y11 + 651/4*Y13 + 
    453/4*Y14 + 19/2*Y15 + 19/2*Y16 + 31269/4*Y21 + 33024*Y22 + 1918*Y23 + 336*Y24 + 
    331/4*Y25 + 11/2*Y26 + 148/3*Y27 + 2*Y28 + 125/6*Y29 + 5/2*Y30 + 9/2*Y31 + 
    9/2*Y36 + Y37 + Y38 + 1/4*Y39 + 1/4*Y40 + 1/3*Y41 + 1/3*Y42 - 1/6*Y43 - 1/6*Y44
    + 43139214;

g69:= Y1^72 + 2*Y1^71 + 5*Y1^70 + 10*Y1^69 + 20*Y1^68 + 36*Y1^67 + 65*Y1^66 + 
    109*Y1^65 + 182*Y1^64 + 292*Y1^63 + 462*Y1^62 + 711*Y1^61 + 1083*Y1^60 + 
    1612*Y1^59 + 2375*Y1^58 + 3441*Y1^57 + 4934*Y1^56 + 6978*Y1^55 + 9780*Y1^54 + 
    13544*Y1^53 + 18602*Y1^52 + 25293*Y1^51 + 34123*Y1^50 + 45632*Y1^49 + 60594*Y1^48 
    + 79826*Y1^47 + 104479*Y1^46 + 135785*Y1^45 + 175401*Y1^44 + 225131*Y1^43 + 
    287347*Y1^42 + 364612*Y1^41 + 460256*Y1^40 + 577892*Y1^39 + 722092*Y1^38 + 
    897860*Y1^37 + 1111435*Y1^36 + 1369611*Y1^35 + 1680794*Y1^34 + 2054164*Y1^33 + 
    2500907*Y1^32 + 3033324*Y1^31 + 3666308*Y1^30 + 4416268*Y1^29 + 5303072*Y1^28 + 
    6348809*Y1^27 + 7580167*Y1^26 + 9027221*Y1^25 + 1/2*Y1^24*Y2 + 1/2*Y1^24*Y5 + 
    10726418*Y1^24 + 7*Y1^23*Y2 + Y1^23*Y5 + 12719212*Y1^23 + 91/2*Y1^22*Y2 + 
    7/2*Y1^22*Y5 + 15055999*Y1^22 + 393/2*Y1^21*Y2 + 13/2*Y1^21*Y5 + 17794604*Y1^21 
    + 1409/2*Y1^20*Y2 + 31/2*Y1^20*Y5 + 21004965*Y1^20 + 2165*Y1^19*Y2 + 
    26*Y1^19*Y5 + 24767472*Y1^19 + 11931/2*Y1^18*Y2 + 2*Y1^18*Y3 + 105/2*Y1^18*Y5 +
    29178206*Y1^18 + 29945/2*Y1^17*Y2 + 20*Y1^17*Y3 + 163/2*Y1^17*Y5 + 
    34346227*Y1^17 + 34850*Y1^16*Y2 + 143*Y1^16*Y3 + 145*Y1^16*Y5 + 40398501*Y1^16 +
    151803/2*Y1^15*Y2 + 731*Y1^15*Y3 + 425/2*Y1^15*Y5 + 47474345*Y1^15 + 
    156148*Y1^14*Y2 + 3018*Y1^14*Y3 + Y1^14*Y4 + 346*Y1^14*Y5 + 55726333*Y1^14 + 
    305172*Y1^13*Y2 + 10535*Y1^13*Y3 + 22*Y1^13*Y4 + 483*Y1^13*Y5 + 65306555*Y1^13 
    + 1139643/2*Y1^12*Y2 + 32185*Y1^12*Y3 + 807/4*Y1^12*Y4 + 1471/2*Y1^12*Y5 + 
    3/4*Y1^12*Y6 + 1/4*Y1^12*Y15 + 1/4*Y1^12*Y16 + 76354664*Y1^12 + 
    1020378*Y1^11*Y2 + 87909*Y1^11*Y3 + 2405/2*Y1^11*Y4 + 989*Y1^11*Y5 + 
    3/2*Y1^11*Y6 + 1/2*Y1^11*Y15 + 1/2*Y1^11*Y16 + 88962362*Y1^11 + 
    3516857/2*Y1^10*Y2 + 218061*Y1^10*Y3 + 10857/2*Y1^10*Y4 + 2871/2*Y1^10*Y5 + 
    15/2*Y1^10*Y6 + Y1^10*Y15 + Y1^10*Y16 + 103129870*Y1^10 + 5846251/2*Y1^9*Y2 + 
    496928*Y1^9*Y3 + 20079*Y1^9*Y4 + 3777/2*Y1^9*Y5 + 12*Y1^9*Y6 + 10*Y1^9*Y8 + 
    3/2*Y1^9*Y15 + 3/2*Y1^9*Y16 + 118683234*Y1^9 + 4697477*Y1^8*Y2 + 
    1049346*Y1^8*Y3 + 253803/4*Y1^8*Y4 + 2655*Y1^8*Y5 + 135/4*Y1^8*Y6 + 
    409/2*Y1^8*Y8 + 13*Y1^8*Y9 + 11/4*Y1^8*Y15 + 11/4*Y1^8*Y16 + 1/2*Y1^8*Y27 + 
    135166998*Y1^8 + 14617307/2*Y1^7*Y2 + 2066038*Y1^7*Y3 + 703447/4*Y1^7*Y4 + 
    6909/2*Y1^7*Y5 + 191/4*Y1^7*Y6 + 3709/2*Y1^7*Y8 + 277*Y1^7*Y9 + Y1^7*Y10 + 
    1/2*Y1^7*Y13 + 1/2*Y1^7*Y14 + 15/4*Y1^7*Y15 + 15/4*Y1^7*Y16 + 1/2*Y1^7*Y27 + 
    151680100*Y1^7 + 22038147/2*Y1^6*Y2 + 3803801*Y1^6*Y3 + 434229*Y1^6*Y4 + 
    9461/2*Y1^6*Y5 + 104*Y1^6*Y6 + 65183/6*Y1^6*Y8 + 2819*Y1^6*Y9 + 365/3*Y1^6*Y10
    + 3*Y1^6*Y13 + 3*Y1^6*Y14 + 11/2*Y1^6*Y15 + 11/2*Y1^6*Y16 + 25/6*Y1^6*Y27 + 
    2/3*Y1^6*Y29 + 5/6*Y1^6*Y31 + 5/6*Y1^6*Y36 + 1/6*Y1^6*Y37 + 1/6*Y1^6*Y38 + 
    1/6*Y1^6*Y41 + 1/6*Y1^6*Y42 + 1/6*Y1^6*Y43 + 1/6*Y1^6*Y44 + 166689419*Y1^6 + 
    7/2*Y1^5*Y2*Y3 + 32152151/2*Y1^5*Y2 + 1/2*Y1^5*Y3*Y5 + 6539453*Y1^5*Y3 + 
    963172*Y1^5*Y4 + 12079/2*Y1^5*Y5 + 140*Y1^5*Y6 + 94041/2*Y1^5*Y8 + 
    18463*Y1^5*Y9 + 1736*Y1^5*Y10 + 16*Y1^5*Y11 + 9*Y1^5*Y13 + 9*Y1^5*Y14 + 
    8*Y1^5*Y15 + 8*Y1^5*Y16 + 7/2*Y1^5*Y27 + 2/3*Y1^5*Y29 + 1/2*Y1^5*Y37 + 
    1/2*Y1^5*Y38 + 1/6*Y1^5*Y41 + 1/6*Y1^5*Y42 + 177836043*Y1^5 + 105*Y1^4*Y2*Y3 +
    45116101/2*Y1^4*Y2 + 4*Y1^4*Y3*Y5 + 10415655*Y1^4*Y3 + 7690371/4*Y1^4*Y4 + 
    15889/2*Y1^4*Y5 + 1039/4*Y1^4*Y6 + 159982*Y1^4*Y8 + 173317/2*Y1^4*Y9 + 
    12877*Y1^4*Y10 + 785/2*Y1^4*Y11 + 55/2*Y1^4*Y13 + 25*Y1^4*Y14 + 51/4*Y1^4*Y15 
    + 51/4*Y1^4*Y16 + 6*Y1^4*Y22 + 1/2*Y1^4*Y26 + 18*Y1^4*Y27 + 16/3*Y1^4*Y29 + 
    2*Y1^4*Y37 + 2*Y1^4*Y38 + 1/3*Y1^4*Y41 + 1/3*Y1^4*Y42 + 181896300*Y1^4 + 
    1750*Y1^3*Y2*Y3 + 29967833*Y1^3*Y2 + 17*Y1^3*Y3*Y5 + 15098429*Y1^3*Y3 + 
    3431137*Y1^3*Y4 + 9595*Y1^3*Y5 + 328*Y1^3*Y6 + 2631923/6*Y1^3*Y8 + 
    611893/2*Y1^3*Y9 + 187613/3*Y1^3*Y10 + 7163/2*Y1^3*Y11 + 103/2*Y1^3*Y13 + 
    49*Y1^3*Y14 + 16*Y1^3*Y15 + 16*Y1^3*Y16 + 376/3*Y1^3*Y22 + 1/2*Y1^3*Y26 + 
    29/2*Y1^3*Y27 + 14/3*Y1^3*Y29 + 10/3*Y1^3*Y31 + 1/3*Y1^3*Y32 + 1/3*Y1^3*Y33 + 
    10/3*Y1^3*Y36 + 19/6*Y1^3*Y37 + 19/6*Y1^3*Y38 + 1/6*Y1^3*Y41 + 1/6*Y1^3*Y42 + 
    175075602*Y1^3 + 19391*Y1^2*Y2*Y3 + 315/2*Y1^2*Y2*Y4 + 36437460*Y1^2*Y2 + 
    68*Y1^2*Y3*Y5 + 19228287*Y1^2*Y3 + 9/2*Y1^2*Y4*Y5 + 5374101*Y1^2*Y4 + 
    11415*Y1^2*Y5 + 500*Y1^2*Y6 + 1941867/2*Y1^2*Y8 + 1659773/2*Y1^2*Y9 + 
    219467*Y1^2*Y10 + 43853/2*Y1^2*Y11 + 409/4*Y1^2*Y13 + 343/4*Y1^2*Y14 + 
    17*Y1^2*Y15 + 17*Y1^2*Y16 + 175/4*Y1^2*Y21 + 3801/2*Y1^2*Y22 + 3/4*Y1^2*Y25 + 
    9/2*Y1^2*Y26 + 87/2*Y1^2*Y27 + 3/2*Y1^2*Y28 + 61/3*Y1^2*Y29 + 4*Y1^2*Y37 + 
    4*Y1^2*Y38 + 1/4*Y1^2*Y39 + 1/4*Y1^2*Y40 + 1/3*Y1^2*Y41 + 1/3*Y1^2*Y42 + 
    153944392*Y1^2 + 127042*Y1*Y2*Y3 + 4977*Y1*Y2*Y4 + 37745354*Y1*Y2 + 
    143*Y1*Y3*Y5 + 19991479*Y1*Y3 + 21*Y1*Y4*Y5 + 28255955/4*Y1*Y4 + 11506*Y1*Y5
    + 2179/4*Y1*Y6 + 1688774*Y1*Y8 + 1700608*Y1*Y9 + 1128375/2*Y1*Y10 + 
    93630*Y1*Y11 + 123*Y1*Y13 + 112*Y1*Y14 + 73/4*Y1*Y15 + 73/4*Y1*Y16 + 
    3059/2*Y1*Y21 + 34309/2*Y1*Y22 + 294*Y1*Y23 + 6*Y1*Y25 + 4*Y1*Y26 + 
    113/3*Y1*Y27 + 3/2*Y1*Y28 + 85/6*Y1*Y29 + 3/2*Y1*Y30 + 3/2*Y1*Y31 + 
    3/2*Y1*Y36 + 5/2*Y1*Y37 + 5/2*Y1*Y38 + 1/6*Y1*Y41 + 1/6*Y1*Y42 + 1/6*Y1*Y43 
    + 1/6*Y1*Y44 + 117687956*Y1 + 398572*Y2*Y3 + 72723/2*Y2*Y4 + 12*Y2*Y6 + 
    54380669/2*Y2 + 294*Y3*Y4 + 182*Y3*Y5 + 2*Y3*Y6 + 13763290*Y3 + 45/2*Y4*Y5 + 
    6536487*Y4 + 20317/2*Y5 + 656*Y6 + 5922026/3*Y8 + 2195571*Y9 + 5365099/6*Y10 + 
    447455/2*Y11 + 885/4*Y13 + 597/4*Y14 + 33/2*Y15 + 33/2*Y16 + 69307/4*Y21 + 
    208040/3*Y22 + 4410*Y23 + 784*Y24 + 513/4*Y25 + 11/2*Y26 + 178/3*Y27 + 2*Y28 + 
    125/6*Y29 + 7/2*Y30 + 37/6*Y31 + 8/3*Y32 + 8/3*Y33 + Y34 + Y35 + 37/6*Y36 + 
    5/3*Y37 + 5/3*Y38 + 1/4*Y39 + 1/4*Y40 + 1/3*Y41 + 1/3*Y42 - 1/6*Y43 - 1/6*Y44 + 
    72019201;

g610:= Y1^74 + 2*Y1^73 + 5*Y1^72 + 10*Y1^71 + 20*Y1^70 + 36*Y1^69 + 65*Y1^68 + 
    109*Y1^67 + 182*Y1^66 + 292*Y1^65 + 463*Y1^64 + 713*Y1^63 + 1087*Y1^62 + 
    1620*Y1^61 + 2390*Y1^60 + 3467*Y1^59 + 4979*Y1^58 + 7051*Y1^57 + 9897*Y1^56 + 
    13727*Y1^55 + 18883*Y1^54 + 25714*Y1^53 + 34748*Y1^52 + 46541*Y1^51 + 61901*Y1^50 
    + 81681*Y1^49 + 107083*Y1^48 + 139395*Y1^47 + 180364*Y1^46 + 231879*Y1^45 + 
    296446*Y1^44 + 376770*Y1^43 + 476372*Y1^42 + 599073*Y1^41 + 749735*Y1^40 + 
    933652*Y1^39 + 1157463*Y1^38 + 1428389*Y1^37 + 1755368*Y1^36 + 2148149*Y1^35 + 
    2618639*Y1^34 + 3179850*Y1^33 + 3847556*Y1^32 + 4639031*Y1^31 + 5575109*Y1^30 + 
    6678761*Y1^29 + 7977609*Y1^28 + 9502407*Y1^27 + 11290205*Y1^26 + 13382693*Y1^25 + 
    7/2*Y1^24*Y2 + 1/2*Y1^24*Y5 + 15830226*Y1^24 + 25*Y1^23*Y2 + Y1^23*Y5 + 
    18690137*Y1^23 + 124*Y1^22*Y2 + 4*Y1^22*Y5 + 22031670*Y1^22 + 943/2*Y1^21*Y2 + 
    15/2*Y1^21*Y5 + 25934250*Y1^21 + 3065/2*Y1^20*Y2 + 39/2*Y1^20*Y5 + 
    30493336*Y1^20 + 8771/2*Y1^19*Y2 + 65/2*Y1^19*Y5 + 35818271*Y1^19 + 
    11407*Y1^18*Y2 + 6*Y1^18*Y3 + 67*Y1^18*Y5 + 42038603*Y1^18 + 27329*Y1^17*Y2 + 
    57*Y1^17*Y3 + 104*Y1^17*Y5 + 49300673*Y1^17 + 61164*Y1^16*Y2 + 343*Y1^16*Y3 + 
    187*Y1^16*Y5 + 57772580*Y1^16 + 128870*Y1^15*Y2 + 1566*Y1^15*Y3 + 272*Y1^15*Y5 
    + 67636866*Y1^15 + 515241/2*Y1^14*Y2 + 5931*Y1^14*Y3 + 21/4*Y1^14*Y4 + 
    887/2*Y1^14*Y5 + 1/4*Y1^14*Y6 + 1/4*Y1^14*Y15 + 1/4*Y1^14*Y16 + 79089165*Y1^14 
    + 982145/2*Y1^13*Y2 + 19382*Y1^13*Y3 + 129/2*Y1^13*Y4 + 1229/2*Y1^13*Y5 + 
    1/2*Y1^13*Y6 + 1/2*Y1^13*Y15 + 1/2*Y1^13*Y16 + 92319190*Y1^13 + 896913*Y1^12*Y2
    + 56188*Y1^12*Y3 + 1855/4*Y1^12*Y4 + 934*Y1^12*Y5 + 11/4*Y1^12*Y6 + 
    5/4*Y1^12*Y15 + 5/4*Y1^12*Y16 + 107490765*Y1^12 + 3149655/2*Y1^11*Y2 + 
    147061*Y1^11*Y3 + 4809/2*Y1^11*Y4 + 2493/2*Y1^11*Y5 + 9/2*Y1^11*Y6 + 
    2*Y1^11*Y15 + 2*Y1^11*Y16 + 124693343*Y1^11 + 5332531/2*Y1^10*Y2 + 
    352107*Y1^10*Y3 + 39725/4*Y1^10*Y4 + 3607/2*Y1^10*Y5 + 57/4*Y1^10*Y6 + 
    15/4*Y1^10*Y15 + 15/4*Y1^10*Y16 + 143878454*Y1^10 + 8723575/2*Y1^9*Y2 + 
    778804*Y1^9*Y3 + 137877/4*Y1^9*Y4 + 4715/2*Y1^9*Y5 + 85/4*Y1^9*Y6 + 27*Y1^9*Y8
    + 21/4*Y1^9*Y15 + 21/4*Y1^9*Y16 + 164749496*Y1^9 + 6907822*Y1^8*Y2 + 
    1603087*Y1^8*Y3 + 415129/4*Y1^8*Y4 + 3304*Y1^8*Y5 + 205/4*Y1^8*Y6 + 
    2507/6*Y1^8*Y8 + 32*Y1^8*Y9 + 33/4*Y1^8*Y15 + 33/4*Y1^8*Y16 + 1/2*Y1^8*Y27 + 
    1/3*Y1^8*Y31 + 1/3*Y1^8*Y36 + 186614658*Y1^8 + 10605138*Y1^7*Y2 + 
    3086807*Y1^7*Y3 + 1107045/4*Y1^7*Y4 + 4274*Y1^7*Y5 + 277/4*Y1^7*Y6 + 
    20021/6*Y1^7*Y8 + 547*Y1^7*Y9 + 5*Y1^7*Y10 + Y1^7*Y13 + Y1^7*Y14 + 
    43/4*Y1^7*Y15 + 43/4*Y1^7*Y16 + 1/2*Y1^7*Y27 + 1/3*Y1^7*Y31 + 1/3*Y1^7*Y36 + 
    208176435*Y1^7 + 15792877*Y1^6*Y2 + 5571792*Y1^6*Y3 + 2647833/4*Y1^6*Y4 + 
    5818*Y1^6*Y5 + 565/4*Y1^6*Y6 + 54289/3*Y1^6*Y8 + 9919/2*Y1^6*Y9 + 237*Y1^6*Y10
    + 9/2*Y1^6*Y13 + 4*Y1^6*Y14 + 65/4*Y1^6*Y15 + 65/4*Y1^6*Y16 + 5*Y1^6*Y27 + 
    2/3*Y1^6*Y29 + 1/3*Y1^6*Y31 + 1/3*Y1^6*Y36 + 1/2*Y1^6*Y37 + 1/2*Y1^6*Y38 + 
    1/6*Y1^6*Y41 + 1/6*Y1^6*Y42 + 227292385*Y1^6 + 19/2*Y1^5*Y2*Y3 + 
    45548653/2*Y1^5*Y2 + 1/2*Y1^5*Y3*Y5 + 9408151*Y1^5*Y3 + 5717599/4*Y1^5*Y4 + 
    14783/2*Y1^5*Y5 + 747/4*Y1^5*Y6 + 222745/3*Y1^5*Y8 + 60333/2*Y1^5*Y9 + 
    2988*Y1^5*Y10 + 33*Y1^5*Y11 + 14*Y1^5*Y13 + 27/2*Y1^5*Y14 + 89/4*Y1^5*Y15 + 
    89/4*Y1^5*Y16 + 4*Y1^5*Y27 + 2/3*Y1^5*Y29 + 4/3*Y1^5*Y31 + 4/3*Y1^5*Y36 + 
    3/2*Y1^5*Y37 + 3/2*Y1^5*Y38 + 1/6*Y1^5*Y41 + 1/6*Y1^5*Y42 + 240752160*Y1^5 + 
    225*Y1^4*Y2*Y3 + 31599811*Y1^4*Y2 + 5*Y1^4*Y3*Y5 + 14736783*Y1^4*Y3 + 
    11154263/4*Y1^4*Y4 + 9637*Y1^4*Y5 + 1335/4*Y1^4*Y6 + 727918/3*Y1^4*Y8 + 
    134365*Y1^4*Y9 + 20698*Y1^4*Y10 + 6869/10*Y1^4*Y11 + 38*Y1^4*Y13 + 34*Y1^4*Y14
    + 123/4*Y1^4*Y15 + 123/4*Y1^4*Y16 + 2/5*Y1^4*Y17 + 2/5*Y1^4*Y18 + 2/5*Y1^4*Y19
    + 2/5*Y1^4*Y20 + 13*Y1^4*Y22 + 1/2*Y1^4*Y26 + 22*Y1^4*Y27 + 6*Y1^4*Y29 + 
    4/3*Y1^4*Y31 + 4/3*Y1^4*Y36 + 7/2*Y1^4*Y37 + 7/2*Y1^4*Y38 + 1/2*Y1^4*Y41 + 
    1/2*Y1^4*Y42 + 244273286*Y1^4 + 6409/2*Y1^3*Y2*Y3 + 41513557*Y1^3*Y2 + 
    43/2*Y1^3*Y3*Y5 + 21028651*Y1^3*Y3 + 19518993/4*Y1^3*Y4 + 11597*Y1^3*Y5 + 
    1657/4*Y1^3*Y6 + 3866137/6*Y1^3*Y8 + 911911/2*Y1^3*Y9 + 95900*Y1^3*Y10 + 
    58709/10*Y1^3*Y11 + 141/2*Y1^3*Y13 + 67*Y1^3*Y14 + 141/4*Y1^3*Y15 + 
    141/4*Y1^3*Y16 + 2/5*Y1^3*Y17 + 2/5*Y1^3*Y18 + 2/5*Y1^3*Y19 + 2/5*Y1^3*Y20 + 
    237*Y1^3*Y22 + 1/2*Y1^3*Y26 + 33/2*Y1^3*Y27 + 14/3*Y1^3*Y29 + 5/3*Y1^3*Y31 + 
    5/3*Y1^3*Y36 + 9/2*Y1^3*Y37 + 9/2*Y1^3*Y38 + 1/6*Y1^3*Y41 + 1/6*Y1^3*Y42 + 
    232976939*Y1^3 + 31643*Y1^2*Y2*Y3 + 315*Y1^2*Y2*Y4 + 99815031/2*Y1^2*Y2 + 
    87*Y1^2*Y3*Y5 + 26380451*Y1^2*Y3 + 6*Y1^2*Y4*Y5 + 30063089/4*Y1^2*Y4 + 
    27233/2*Y1^2*Y5 + 2449/4*Y1^2*Y6 + 4168948/3*Y1^2*Y8 + 2397679/2*Y1^2*Y9 + 
    648757/2*Y1^2*Y10 + 170207/5*Y1^2*Y11 + 531/4*Y1^2*Y13 + 453/4*Y1^2*Y14 + 
    145/4*Y1^2*Y15 + 145/4*Y1^2*Y16 + 2/5*Y1^2*Y17 + 2/5*Y1^2*Y18 + 2/5*Y1^2*Y19 +
    2/5*Y1^2*Y20 + 175/2*Y1^2*Y21 + 6443/2*Y1^2*Y22 + 3/2*Y1^2*Y25 + 5*Y1^2*Y26 + 
    53*Y1^2*Y27 + 3/2*Y1^2*Y28 + 47/2*Y1^2*Y29 + 10/3*Y1^2*Y31 + 10/3*Y1^2*Y36 + 
    11/2*Y1^2*Y37 + 11/2*Y1^2*Y38 + 1/2*Y1^2*Y41 + 1/2*Y1^2*Y42 + 202719247*Y1^2 + 
    190326*Y1*Y2*Y3 + 8092*Y1*Y2*Y4 + 51089785*Y1*Y2 + 181*Y1*Y3*Y5 + 
    27024039*Y1*Y3 + 27*Y1*Y4*Y5 + 9730935*Y1*Y4 + 13709*Y1*Y5 + 669*Y1*Y6 + 
    14184041/6*Y1*Y8 + 2390911*Y1*Y9 + 1613685/2*Y1*Y10 + 689452/5*Y1*Y11 + 
    309/2*Y1*Y13 + 285/2*Y1*Y14 + 81/2*Y1*Y15 + 81/2*Y1*Y16 + 2/5*Y1*Y17 + 
    2/5*Y1*Y18 + 2/5*Y1*Y19 + 2/5*Y1*Y20 + 2520*Y1*Y21 + 52691/2*Y1*Y22 + 
    490*Y1*Y23 + 15/2*Y1*Y25 + 4*Y1*Y26 + 91/2*Y1*Y27 + 3/2*Y1*Y28 + 85/6*Y1*Y29
    + 3/2*Y1*Y30 + 10/3*Y1*Y31 + 10/3*Y1*Y36 + 7/2*Y1*Y37 + 7/2*Y1*Y38 + 
    1/6*Y1*Y41 + 1/6*Y1*Y42 + 153163065*Y1 + 1123395/2*Y2*Y3 + 106519/2*Y2*Y4 + 
    31/2*Y2*Y6 + 72597539/2*Y2 + 441*Y3*Y4 + 429/2*Y3*Y5 + 3*Y3*Y6 + 18311775*Y3 +
    30*Y4*Y5 + 35432387/4*Y4 + 1/2*Y5*Y15 + 1/2*Y5*Y16 + 23769/2*Y5 + 3139/4*Y6 + 
    2704191*Y8 + 6011849/2*Y9 + 1238779*Y10 + 1572011/5*Y11 + 1083/4*Y13 + 749/4*Y14 +
    119/4*Y15 + 119/4*Y16 + 6/5*Y17 + 6/5*Y18 + 6/5*Y19 + 6/5*Y20 + 25396*Y21 + 
    99224*Y22 + 6566*Y23 + 1176*Y24 + 311/2*Y25 + 8*Y26 + 75*Y27 + 3*Y28 + 85/3*Y29 
    + 9/2*Y30 + 7*Y31 + 7*Y36 + 2*Y37 + 2*Y38 + 1/2*Y39 + 1/2*Y40 + 1/3*Y41 + 
    1/3*Y42 + 92586185;

g611:=g610;
g612:=g69;
g613:=g68;
g614:=g67;
g615:=g66;
g616:=g65;
g617:=g64;
g618:=g63;
g619:=g62;
g620:=g61;
g621:=1;

g71:=10;

p2:=1;
p3:=3;
p4:=7;
p5:=Y1 + 21;
p6:=7*Y1 + 82;
p7:=Y1^5 + 2*Y1^4 + 7*Y1^3 + 26*Y1^2 + Y1*Y2 + 104*Y1 + 5*Y2 + Y3 + Y5 + 414;
p8:=Y1^11 + 2*Y1^10 + 5*Y1^9 + 11*Y1^8 + 22*Y1^7 + 43*Y1^6 + 84*Y1^5 + 166*Y1^4 + 3/2*Y1^3*Y2 + 1/2*Y1^3*Y5 + 
    329*Y1^3 + 21/2*Y1^2*Y2 + 2*Y1^2*Y3 + 3/2*Y1^2*Y5 + 697*Y1^2 + 77/2*Y1*Y2 + 13*Y1*Y3 + Y1*Y4 + 5/2*Y1*Y5 
    + 1486*Y1 + 96*Y2 + 35*Y3 + 17/4*Y4 + 8*Y5 + 1/4*Y6 + 1/4*Y7 + 12017/4;

p3 eq g21;
p4 eq g31+g22;
p5 eq g41+g32+g23;
p6 eq g51+g42+g33;
p7 eq g61+g52+g43+g34;
p8 eq g71+g62+g53+g44+g35;