P[20(0,P[20(0,48384)(1,-11520)(2,-198528)(3,-155712)(4,14560)(5,66160)(6,49236)(7,15600)(8,640)(9,-2544)(10,-2347)(11,-422)(12,-639)(13,-344)(14,-38)(15,84)(16,30)(17,-8)(18,-3)(19,2)(20,1)])(1,P[17(0,19584)(1,-287232)(2,-233120)(3,-430208)(4,-108328)(5,314832)(6,172676)(7,38608)(8,-9036)(9,-19640)(10,-18004)(11,-11416)(12,-1068)(13,-240)(14,-544)(15,-264)(16,48)(17,40)])(2,P[18(0,-313536)(1,-182784)(2,-406096)(3,22368)(4,61348)(5,232208)(6,568496)(7,112672)(8,-72639)(9,-30814)(10,-10946)(11,-13008)(12,-9986)(13,-308)(14,552)(15,-64)(16,-51)(17,18)(18,10)])(3,P[15(0,-277504)(1,372032)(2,-466688)(3,137312)(4,492940)(5,397744)(6,170320)(7,361568)(8,16892)(9,-91448)(10,-18152)(11,1952)(12,-1888)(13,-2360)(14,336)(15,320)])(4,P[16(0,451696)(1,-424464)(2,772028)(3,-845776)(4,211584)(5,491008)(6,127634)(7,-63420)(8,80039)(9,-1768)(10,-39230)(11,-2876)(12,3008)(13,-224)(14,-300)(15,72)(16,45)])(5,P[13(0,454888)(1,-634608)(2,13772)(3,114032)(4,-700040)(5,156784)(6,272504)(7,-94832)(8,-63348)(9,15280)(10,-1312)(11,-8616)(12,1008)(13,1120)])(6,P[14(0,-280852)(1,622096)(2,-1247888)(3,439776)(4,-50046)(5,-299900)(6,122052)(7,66976)(8,-60362)(9,-6820)(10,8136)(11,-448)(12,-924)(13,168)(14,120)])(7,P[11(0,-257852)(1,442000)(2,22736)(3,-529184)(4,280632)(5,31248)(6,-90928)(7,36800)(8,2720)(9,-16920)(10,1680)(11,2240)])(8,P[12(0,135456)(1,-226832)(2,485417)(3,-227582)(4,-22465)(5,86616)(6,-47538)(7,-7620)(8,12780)(9,-560)(10,-1722)(11,252)(12,210)])(9,P[9(0,70644)(1,-75384)(2,32412)(3,38280)(4,-58196)(5,41840)(6,5280)(7,-19480)(8,1680)(9,2800)])(10,P[10(0,-53043)(1,39290)(2,-40034)(3,28208)(4,-23750)(5,-4316)(6,12280)(7,-448)(8,-2058)(9,252)(10,252)])(11,P[7(0,-10612)(1,-7768)(2,-12648)(3,23200)(4,3296)(5,-13224)(6,1008)(7,2240)])(12,P[8(0,14137)(1,-2328)(2,-9834)(3,-1108)(4,7152)(5,-224)(6,-1596)(7,168)(8,210)])(13,P[5(0,884)(1,5072)(2,672)(3,-4920)(4,336)(5,1120)])(14,P[6(0,-2542)(1,-76)(2,2328)(3,-64)(4,-780)(5,72)(6,120)])(15,P[3(0,-32)(1,-776)(2,48)(3,320)])(16,P[4(0,326)(1,-8)(2,-219)(3,18)(4,45)])(17,P[1(1,40)])(18,P[2(0,-27)(1,2)(2,10)])(20,P[0(0,1)])]

randomCircle:=proc(gw,gh,mr)
local a,b,r;
a:=rand(-gw+1..gw)();
b:=rand(-gh+1..gh)();
r:=rand(1..mr)();
return (x-a)^2+(y-b)^2-r;
end proc:

P:=1;
for i from 1 to 10 do
  P:=P*randomCircle(3,3,3);
od:
expand(P):
y^20 + (10*x^2 + 2*x + (-27))*y^18 + (40*x)*y^17 + (45*x^4 + 18*x^3 + (-219)*x^2 + (-8)*x + 326)*y^16 + (320*x^3 + 48*x^2 + (-776)*x + (-32))*y^15 + (120*x^6 + 72*x^5 + (-780)*x^4 + (-64)*x^3 + 2328*x^2 + (-76)*x + (-2542))*y^14 + (1120*x^5 + 336*x^4 + (-4920)*x^3 + 672*x^2 + 5072*x + 884)*y^13 + (210*x^8 + 168*x^7 + (-1596)*x^6 + (-224)*x^5 + 7152*x^4 + (-1108)*x^3 + (-9834)*x^2 + (-2328)*x + 14137)*y^12 + (2240*x^7 + 1008*x^6 + (-13224)*x^5 + 3296*x^4 + 23200*x^3 + (-12648)*x^2 + (-7768)*x + (-10612))*y^11 + (252*x^10 + 252*x^9 + (-2058)*x^8 + (-448)*x^7 + 12280*x^6 + (-4316)*x^5 + (-23750)*x^4 + 28208*x^3 + (-40034)*x^2 + 39290*x + (-53043))*y^10 + (2800*x^9 + 1680*x^8 + (-19480)*x^7 + 5280*x^6 + 41840*x^5 + (-58196)*x^4 + 38280*x^3 + 32412*x^2 + (-75384)*x + 70644)*y^9 + (210*x^12 + 252*x^11 + (-1722)*x^10 + (-560)*x^9 + 12780*x^8 + (-7620)*x^7 + (-47538)*x^6 + 86616*x^5 + (-22465)*x^4 + (-227582)*x^3 + 485417*x^2 + (-226832)*x + 135456)*y^8 + (2240*x^11 + 1680*x^10 + (-16920)*x^9 + 2720*x^8 + 36800*x^7 + (-90928)*x^6 + 31248*x^5 + 280632*x^4 + (-529184)*x^3 + 22736*x^2 + 442000*x + (-257852))*y^7 + (120*x^14 + 168*x^13 + (-924)*x^12 + (-448)*x^11 + 8136*x^10 + (-6820)*x^9 + (-60362)*x^8 + 66976*x^7 + 122052*x^6 + (-299900)*x^5 + (-50046)*x^4 + 439776*x^3 + (-1247888)*x^2 + 622096*x + (-280852))*y^6 + (1120*x^13 + 1008*x^12 + (-8616)*x^11 + (-1312)*x^10 + 15280*x^9 + (-63348)*x^8 + (-94832)*x^7 + 272504*x^6 + 156784*x^5 + (-700040)*x^4 + 114032*x^3 + 13772*x^2 + (-634608)*x + 454888)*y^5 + (45*x^16 + 72*x^15 + (-300)*x^14 + (-224)*x^13 + 3008*x^12 + (-2876)*x^11 + (-39230)*x^10 + (-1768)*x^9 + 80039*x^8 + (-63420)*x^7 + 127634*x^6 + 491008*x^5 + 211584*x^4 + (-845776)*x^3 + 772028*x^2 + (-424464)*x + 451696)*y^4 + (320*x^15 + 336*x^14 + (-2360)*x^13 + (-1888)*x^12 + 1952*x^11 + (-18152)*x^10 + (-91448)*x^9 + 16892*x^8 + 361568*x^7 + 170320*x^6 + 397744*x^5 + 492940*x^4 + 137312*x^3 + (-466688)*x^2 + 372032*x + (-277504))*y^3 + (10*x^18 + 18*x^17 + (-51)*x^16 + (-64)*x^15 + 552*x^14 + (-308)*x^13 + (-9986)*x^12 + (-13008)*x^11 + (-10946)*x^10 + (-30814)*x^9 + (-72639)*x^8 + 112672*x^7 + 568496*x^6 + 232208*x^5 + 61348*x^4 + 22368*x^3 + (-406096)*x^2 + (-182784)*x + (-313536))*y^2 + (40*x^17 + 48*x^16 + (-264)*x^15 + (-544)*x^14 + (-240)*x^13 + (-1068)*x^12 + (-11416)*x^11 + (-18004)*x^10 + (-19640)*x^9 + (-9036)*x^8 + 38608*x^7 + 172676*x^6 + 314832*x^5 + (-108328)*x^4 + (-430208)*x^3 + (-233120)*x^2 + (-287232)*x + 19584)*y + (x^20 + 2*x^19 + (-3)*x^18 + (-8)*x^17 + 30*x^16 + 84*x^15 + (-38)*x^14 + (-344)*x^13 + (-639)*x^12 + (-422)*x^11 + (-2347)*x^10 + (-2544)*x^9 + 640*x^8 + 15600*x^7 + 49236*x^6 + 66160*x^5 + 14560*x^4 + (-155712)*x^3 + (-198528)*x^2 + (-11520)*x + 48384)
