N:=50;
R<u,v>:=PolynomialRing(Rationals(),2);
X := u^11*(u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*v^15
        + u^8*(u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(u^5 + u^4 + 7*u^3 - u^2 - 2*u - 1)*v^14
        + u^7*(u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(2*u^7 + 7*u^6 + 8*u^5 + 15*u^4 - 15*u^3 - 19*u^2 - 9*u - 1)*v^13
        + u^3*(u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(u^13 + u^12 + 13*u^11 + 19*u^10 + 18*u^9 - 9*u^8 - 79*u^7 - 69*u^6 - 18*u^5 + 10*u^4 + 11*u^3 + 8*u^2 + 4*u + 1)*v^12
        + u*(u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(u^16 + 5*u^15 + 8*u^14 + 31*u^13 + 18*u^12 - 16*u^11 - 118*u^10 - 205*u^9 - 97*u^8 + 61*u^7 + 107*u^6 + 79*u^5 + 48*u^4 + 20*u^3 + u^2 - 3*u - 1)*v^11
        + u*(u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(6*u^16 + 11*u^15 + 20*u^14 + 20*u^13 - 41*u^12 - 136*u^11 - 267*u^10 - 248*u^9 + 68*u^8 + 338*u^7 + 316*u^6 + 180*u^5 + 76*u^4 + 9*u^3 - 27*u^2 - 21*u - 6)*v^10
        + (u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(2*u^14 + 10*u^13 - 15*u^12 - 9*u^11 - 8*u^10 - 70*u^9 - 17*u^8 + 105*u^7 + 83*u^6 + 11*u^5 + 10*u^4 - 4*u^3 - 12*u^2 - 13*u + 1)*v^9
        + (u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(7*u^14 + 2*u^13 - 32*u^12 - 16*u^11 + 2*u^10 - 42*u^9 + 51*u^8 + 145*u^7 + 55*u^6 - 27*u^5 - 5*u^4 - 9*u^3 - 18*u^2 - 12*u + 4)*v^8
        + (u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(u^15 + 8*u^14 - 14*u^13 - 42*u^12 + 5*u^11 + 41*u^10 + u^9 + 71*u^8 + 115*u^7 - 11*u^6 - 57*u^5 - 4*u^4 + 6*u^3 - 13*u^2 - 3*u + 6)*v^7
        + (u^4 - 3*u^3 + 4*u^2 - 2*u + 1)*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(2*u^15 + 2*u^14 - 22*u^13 - 31*u^12 + 46*u^11 + 69*u^10 + u^9 + 27*u^8 + 48*u^7 - 42*u^6 - 44*u^5 + 13*u^4 + 18*u^3 - 7*u^2 + 2*u + 4)*v^6
        + (u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(u^19 - 6*u^18 - 3*u^17 + 31*u^16 + 14*u^15 - 117*u^14 + 45*u^13 + 171*u^12 - 114*u^11 - 22*u^10 + 114*u^9 - 80*u^8 - 43*u^7 + 42*u^6 + 8*u^5 - 28*u^4 + 23*u^3 - 4*u^2 - u + 1)*v^5
        - u^2*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(2*u^16 - 2*u^15 - 17*u^14 + 12*u^13 + 51*u^12 - 46*u^11 - 104*u^10 + 99*u^9 + 39*u^8 - 62*u^7 + 46*u^6 + 20*u^5 - 33*u^4 + 8*u^3 + 8*u^2 - 8*u + 4)*v^4
        + u^2*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(u^15 + 4*u^14 - 10*u^13 - 12*u^12 + 30*u^11 + 26*u^10 - 58*u^9 - 24*u^8 + 38*u^7 - 21*u^6 - 4*u^5 + 13*u^4 - 6*u^3 - u^2 + u - 1)*v^3
        - u^5*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(2*u^10 + u^9 - 10*u^8 + 3*u^7 + 20*u^6 + u^5 - 16*u^4 + 7*u^3 - 2*u^2 - 2*u + 1)*v^2
        + u^7*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1)*(u^6 - 2*u^5 - 3*u^4 + 4*u^3 + 3*u^2 - u + 1)*v
        + u^10*(u^4 + 2*u^3 + 4*u^2 + 3*u + 1);
G:=1/u;
x:=-v;
y:=(41*G^19*x^5-82*G^19*x^4+41*G^19*x^3+G^18*x^6-679*G^18*x^5+1662*G^18*x^4-1291*G^18*x^3+307*G^18*x^2+1003*G^17*x^7-2807*G^17*x^6+1215*G^17*x^5+2264*G^17*x^4-1960*G^17*x^3+285*G^17*x^2-673*G^16*x^8
      +4406*G^16*x^7-9661*G^16*x^6+7992*G^16*x^5-1218*G^16*x^4-929*G^16*x^3+83*G^16*x^2+670*G^15*x^9-2706*G^15*x^8+9309*G^15*x^7-21352*G^15*x^6+23129*G^15*x^5-10262*G^15*x^4+560*G^15*x^3+826*G^15*x^2
      -174*G^15*x+395*G^14*x^10-3249*G^14*x^9+9270*G^14*x^8-5603*G^14*x^7-14273*G^14*x^6+20884*G^14*x^5-7087*G^14*x^4-1416*G^14*x^3+1212*G^14*x^2-133*G^14*x+1988*G^13*x^10-12693*G^13*x^9+34385*G^13*x^8
      -41561*G^13*x^7+17126*G^13*x^6+5670*G^13*x^5-11491*G^13*x^4+8464*G^13*x^3-1581*G^13*x^2-215*G^13*x-133*G^13+116*G^12*x^11+384*G^12*x^10-9344*G^12*x^9+38286*G^12*x^8-65681*G^12*x^7+50702*G^12*x^6
      -5920*G^12*x^5-25645*G^12*x^4+22104*G^12*x^3-5826*G^12*x^2+278*G^12*x+114*G^12+820*G^11*x^11-1796*G^11*x^10-9453*G^11*x^9+52270*G^11*x^8-97985*G^11*x^7+80879*G^11*x^6-21494*G^11*x^5-18234*G^11*x^4
      +22493*G^11*x^3-11842*G^11*x^2+3180*G^11*x+69*G^11+125*G^10*x^11-1512*G^10*x^10-10094*G^10*x^9+64273*G^10*x^8-145115*G^10*x^7+190276*G^10*x^6-164663*G^10*x^5+81370*G^10*x^4-7642*G^10*x^3-15784*G^10*x^2
      +7505*G^10*x-611*G^10-395*G^9*x^12+5822*G^9*x^11-21604*G^9*x^10+37277*G^9*x^9-22414*G^9*x^8-54680*G^9*x^7+164152*G^9*x^6-204669*G^9*x^5+138402*G^9*x^4-51578*G^9*x^3+4117*G^9*x^2+4758*G^9*x-1794*G^9
      -1198*G^8*x^12+7061*G^8*x^11-29496*G^8*x^10+82586*G^8*x^9-136844*G^8*x^8+120692*G^8*x^7-33002*G^8*x^6-46100*G^8*x^5+64919*G^8*x^4-46465*G^8*x^3+15198*G^8*x^2-114*G^8*x-637*G^8-116*G^7*x^13+3197*G^7*x^12
      -12537*G^7*x^11+17638*G^7*x^10-2347*G^7*x^9-39726*G^7*x^8+90385*G^7*x^7-100152*G^7*x^6+37267*G^7*x^5+27750*G^7*x^4-35675*G^7*x^3+12452*G^7*x^2+1756*G^7*x-1419*G^7-588*G^6*x^13+1249*G^6*x^12+1265*G^6*x^11
      -488*G^6*x^10-5568*G^6*x^9-2857*G^6*x^8+26876*G^6*x^7-31655*G^6*x^6+2388*G^6*x^5+24302*G^6*x^4-26878*G^6*x^3+12213*G^6*x^2+1741*G^6*x-1085*G^6+729*G^5*x^13-2450*G^5*x^12-377*G^5*x^11+8626*G^5*x^10
      -8566*G^5*x^9+487*G^5*x^8+10869*G^5*x^7-30854*G^5*x^6+33524*G^5*x^5-6142*G^5*x^4-13544*G^5*x^3+12295*G^5*x^2-1480*G^5*x-754*G^5-463*G^4*x^13+2345*G^4*x^12-2669*G^4*x^11-1854*G^4*x^10+941*G^4*x^9
      +8674*G^4*x^8-8028*G^4*x^7-4127*G^4*x^6+11555*G^4*x^5-8515*G^4*x^4-3216*G^4*x^3+9797*G^4*x^2-2503*G^4*x-425*G^4+135*G^3*x^13-1192*G^3*x^12+1925*G^3*x^11+968*G^3*x^10-973*G^3*x^9-7402*G^3*x^8+11242*G^3*x^7
      -9269*G^3*x^6+13391*G^3*x^5-11140*G^3*x^4+1634*G^3*x^3+4787*G^3*x^2-2683*G^3*x+463*G^2*x^12-1487*G^2*x^11+953*G^2*x^10-664*G^2*x^9+3247*G^2*x^8-1400*G^2*x^7-5552*G^2*x^6+9283*G^2*x^5-9345*G^2*x^4
      +6314*G^2*x^3-268*G^2*x^2-935*G^2*x-135*G*x^12+463*G*x^11+178*G*x^10-1828*G*x^9+2218*G*x^8-3715*G*x^7+6025*G*x^6-3657*G*x^5-921*G*x^4+3145*G*x^3-1517*G*x^2-135*x^10+463*x^9-285*x^8+64*x^7-448*x^6-556*x^5
      +996*x^4+156*x^3-255*x^2) /
      (41*G^18*x^6-718*G^18*x^5+1487*G^18*x^4-984*G^18*x^3+174*G^18*x^2+555*G^17*x^7-2248*G^17*x^6+2529*G^17*x^5-1037*G^17*x^4+878*G^17*x^3-851*G^17*x^2+174*G^17*x+139*G^16*x^8
      -257*G^16*x^7-1598*G^16*x^6+3074*G^16*x^5-1693*G^16*x^4+1365*G^16*x^3-1429*G^16*x^2+399*G^16*x+24*G^15*x^9+1325*G^15*x^8-5464*G^15*x^7+5987*G^15*x^6-4253*G^15*x^5+6297*G^15*x^4-5108*G^15*x^3+866*G^15*x^2
      +326*G^15*x+73*G^14*x^10-150*G^14*x^9+474*G^14*x^8-3736*G^14*x^7+6941*G^14*x^6-12007*G^14*x^5+17440*G^14*x^4-12270*G^14*x^3+2703*G^14*x^2+706*G^14*x-174*G^14+338*G^13*x^10+26*G^13*x^9-4948*G^13*x^8
      +10472*G^13*x^7-14884*G^13*x^6+17887*G^13*x^5-15811*G^13*x^4+8754*G^13*x^3-3454*G^13*x^2+2285*G^13*x-706*G^13+73*G^12*x^11-849*G^12*x^10+5071*G^12*x^9-16355*G^12*x^8+23867*G^12*x^7-21391*G^12*x^6
      +14079*G^12*x^5-4350*G^12*x^4-6052*G^12*x^3+5797*G^12*x^2+330*G^12*x-652*G^12+271*G^11*x^11-414*G^11*x^10+948*G^11*x^9-11240*G^11*x^8+27892*G^11*x^7-28851*G^11*x^6-1736*G^11*x^5+33084*G^11*x^4
      -39197*G^11*x^3+23512*G^11*x^2-5668*G^11*x+306*G^11-392*G^10*x^11+1941*G^10*x^10-1224*G^10*x^9-21323*G^10*x^8+64410*G^10*x^7-79652*G^10*x^6+44681*G^10*x^5-10077*G^10*x^4-8342*G^10*x^3+13899*G^10*x^2
      -6466*G^10*x+714*G^10-43*G^9*x^12+1134*G^9*x^11-3533*G^9*x^10+7149*G^9*x^9-25236*G^9*x^8+68127*G^9*x^7-124745*G^9*x^6+161974*G^9*x^5-147647*G^9*x^4+78349*G^9*x^3-17360*G^9*x^2-351*G^9*x-413*G^9
      -184*G^8*x^12-946*G^8*x^11+8336*G^8*x^10-25814*G^8*x^9+45497*G^8*x^8-36478*G^8*x^7-19953*G^8*x^6+68754*G^8*x^5-68954*G^8*x^4+34714*G^8*x^3-7952*G^8*x^2-1109*G^8*x+24*G^8+252*G^7*x^12+1263*G^7*x^11
      -6761*G^7*x^10+594*G^7*x^9+32863*G^7*x^8-73175*G^7*x^7+89583*G^7*x^6-81835*G^7*x^5+49872*G^7*x^4-21028*G^7*x^3+8732*G^7*x^2-4076*G^7*x+330*G^7-1539*G^6*x^12+7223*G^6*x^11-14128*G^6*x^10+25389*G^6*x^9
      -41778*G^6*x^8+41421*G^6*x^7-21527*G^6*x^6+5345*G^6*x^5-5806*G^6*x^4+6372*G^6*x^3-2011*G^6*x^2-729*G^6*x+582*G^6+1496*G^5*x^12-6846*G^5*x^11+8230*G^5*x^10+1073*G^5*x^9-5202*G^5*x^8+3687*G^5*x^7
      -12413*G^5*x^6+22927*G^5*x^5-26020*G^5*x^4+21526*G^5*x^3-8508*G^5*x^2+1122*G^5*x+255*G^5-733*G^4*x^12+3449*G^4*x^11-2366*G^4*x^10-7951*G^4*x^9+11554*G^4*x^8-3227*G^4*x^7+1752*G^4*x^6-4369*G^4*x^5
      -733*G^4*x^4+5894*G^4*x^3-3256*G^4*x^2+1346*G^4*x+135*G^3*x^12-922*G^3*x^11-627*G^3*x^10+8489*G^3*x^9-13057*G^3*x^8+8138*G^3*x^7-3556*G^3*x^6+8*G^3*x^5+6314*G^3*x^4-4682*G^3*x^3+1370*G^3*x^2+98*G^3*x
      +463*G^2*x^11-720*G^2*x^10-1909*G^2*x^9+3633*G^2*x^8-413*G^2*x^7-1313*G^2*x^6-1439*G^2*x^5+3625*G^2*x^4-2663*G^2*x^3+1600*G^2*x^2-255*G^2*x-135*G*x^11+193*G*x^10+742*G*x^9-1170*G*x^8-280*G*x^7-601*G*x^6
      +3136*G*x^5-2462*G*x^4+990*G*x^3-157*G*x^2+135*x^9-598*x^8+1177*x^7-1348*x^6+1207*x^5-1409*x^4+1091*x^3-255*x^2);
r:=(x^2*y - x*y + y - 1) / (x^2*y - x);
s:=(x*y - y + 1) / (x*y);
E:=[s-r*s+1,r*s-r^2*s,r*s-r^2*s,0,0];
P:=[0,0];