#Prob 2
MetaZKP3:=proc(n,E,C,K)  local B1,B2,i,j,c,sig,B1iV, B1iC, B1jV, B1jC, B1v,B1c,S,k:
sig:=randperm(3*n):
B1:=[seq(seq([c,i],c=1..3),i=1..n)]:
B1:=[seq(B1[sig[i]],i=1..nops(B1))]:
for i from 1 to 3*n do
 for j from 1 to 3*n do
  B1iC:=B1[i][1]:
  B1iV:=B1[i][2]:
  B1jC:=B1[j][1]:
  B1jV:=B1[j][2]:
  if C[B1iV]=B1iC and C[B1jV]=B1jC and member({B1iV,B1jV},E) then
    B2[i,j]:=1:
   else
   B2[i,j]:=0:
 fi:
od:
od:
B2:=[seq([seq(B2[i,j],j=1..3*n)],i=1..3*n)]:


for k from 1 to K do
if rand(0..1)()=1 then
 B1v:=[seq(B1[i][2],i=1..3*n)]:
  if Verify1(n,E,B1v,B2) = false then
    RETURN(false):
  fi:
else
 B1c:=[seq(B1[i][1],i=1..3*n)]:
 S:={}:
 for i from 1 to 3*n do
 #for j from 1 to 3*n do
 for j from i+1 to 3*n do
   if B1[i][1]=B1[j][1] then
    S:=S union {[[i,j],B2[i][j]]}:
   fi:
 od:
 od:
 if Verify2(B1c,S) = false then
  RETURN(false):
 fi:
fi:
od:
RETURN(true):
end:
#Test run
n, E, C := RGC3(100);
MetaZKP3(n,E,C,20);
                              true


n, E, C := RGC3(50):
MetaZKP3(n,E,C,20);
                              true


n, E, C := RGC3(59):
MetaZKP3(n,E,C,20);
                              true


n, E, C := RGC3(77):
MetaZKP3(n,E,C,20);
                              true


n, E, C := RGC3(89):
MetaZKP3(n,E,C,20);
                              true


#Changing color randomly
n, E, C := RGC3(10):
MetaZKP3(n,E,C,20);
                              true
C[rand(1..nops(C))()]:=1:
MetaZKP3(n,E,C,20);
                             false


n, E, C := RGC3(50):
C[rand(1..nops(C))()]:=1:
MetaZKP3(n,E,C,20);
                             false


n, E, C := RGC3(37):
MetaZKP3(n,E,C,20);
                              true
C[rand(1..nops(C))()]:=1: MetaZKP3(n,E,C,20);
                              true
C[rand(1..nops(C))()]:=1: MetaZKP3(n,E,C,20);
                              true
C[rand(1..nops(C))()]:=1: MetaZKP3(n,E,C,20);
                             false


n, E, C := RGC3(77): MetaZKP3(n,E,C,20);
                              true
C[rand(1..nops(C))()]:=1: MetaZKP3(n,E,C,20);
                             false


n, E, C := RGC3(87): MetaZKP3(n,E,C,20);
                              true
C[rand(1..nops(C))()]:=1: MetaZKP3(n,E,C,20);
                             false
C[rand(1..nops(C))()]:=1: MetaZKP3(n,E,C,20);
                             false
C[rand(1..nops(C))()]:=1: MetaZKP3(n,E,C,20);
                             false