#
bounds=[12,9,7,6,6]

{tot=0;
for(r1=1,sqrtint(bounds[1]),for(r2=0,min(r1,sqrtint(bounds[1]-r1^2)),for(r3=0,min(r2,sqrtint(bounds[1]-r1^2-r2^2)),for(r4=0,min(r3,sqrtint(bounds[1]-r1^2-r2^2-r3^2)),for(r5=0,min(r4,sqrtint(bounds[1]-r1^2-r2^2-r3^2-r4^2)),
b1=[r1,r2,r3,r4,r5];print(b1);
if(b1[2]==0,q2=0,q2=1);if(b1[3]==0,q3=0,q3=1);if(b1[4]==0,q4=0,q4=1);if(b1[5]==0,q5=0,q5=1);
bs1=b1;
for(s1=-sqrtint(bounds[2]),sqrtint(bounds[2]),for(s2=-q2*sqrtint(bounds[2]-s1^2),sqrtint(bounds[2]-s1^2),for(s3=-q3*sqrtint(bounds[2]-s1^2-s2^2),sqrtint(bounds[2]-s1^2-s2^2),for(s4=-q4*sqrtint(bounds[2]-s1^2-s2^2-s3^2),sqrtint(bounds[2]-s1^2-s2^2-s3^2),for(s5=-q5*sqrtint(bounds[2]-s1^2-s2^2-s3^2-s4^2),sqrtint(bounds[2]-s1^2-s2^2-s3^2-s4^2),
   b2=[s1,s2,s3,s4,s5];
   mu21=(b2*bs1~)/(bs1*bs1~);
   bs2=b2-mu21*bs1;
   check=bs2+mu21*bs1;
   if(abs(mu21)<=1/2,if(check*check~>=3/4*(bs1*bs1~),
   if(bs2*bs2~<=3*2^(5-2-2),
  for(t1=-sqrtint(bounds[3]),sqrtint(bounds[3]),for(t2=-sqrtint(bounds[3]-t1^2),sqrtint(bounds[3]-t1^2),for(t3=-sqrtint(bounds[3]-t1^2-t2^2),sqrtint(bounds[3]-t1^2-t2^2),for(t4=-sqrtint(bounds[3]-t1^2-t2^2-t3^2),sqrtint(bounds[3]-t1^2-t2^2-t3^2),for(t5=-sqrtint(bounds[3]-t1^2-t2^2-t3^2-t4^2),sqrtint(bounds[3]-t1^2-t2^2-t3^2-t4^2),
       b3=[t1,t2,t3,t4,t5];
       mu32=(b3*bs2~)/(bs2*bs2~);mu31=(b3*bs1~)/(bs1*bs1~);bs3=b3-mu31*bs1-mu32*bs2;check=bs3+mu32*bs2;
       if(abs(mu32)<=1/2,if(abs(mu31)<=1/2,if(check*check~>=3/4*(bs2*bs2~),
       if(bs3*bs3~<=3*2^(5-3-2),
      for(u1=-sqrtint(bounds[4]),sqrtint(bounds[4]),for(u2=-sqrtint(bounds[4]-u1^2),sqrtint(bounds[4]-u1^2),for(u3=-sqrtint(bounds[4]-u1^2-u2^2),sqrtint(bounds[4]-u1^2-u2^2),for(u4=-sqrtint(bounds[4]-u1^2-u2^2-u3^2),sqrtint(bounds[4]-u1^2-u2^2-u3^2),for(u5=-sqrtint(bounds[4]-u1^2-u2^2-u3^2-u4^2),sqrtint(bounds[4]-u1^2-u2^2-u3^2-u4^2),
          b4=[u1,u2,u3,u4,u5];
          mu43=(b4*bs3~)/(bs3*bs3~);mu42=(b4*bs2~)/(bs2*bs2~);mu41=(b4*bs1~)/(bs1*bs1~);bs4=b4-mu41*bs1-mu42*bs2-mu43*bs3;check=bs4+mu43*bs3;
          if(abs(mu43)<=1/2,if(abs(mu42)<=1/2,if(abs(mu41)<=1/2,if(check*check~>=3/4*(bs3*bs3~),
          if(bs4*bs4~<=3*2^(5-4-2),
          for(v1=-sqrtint(bounds[5]),sqrtint(bounds[5]),for(v2=-sqrtint(bounds[5]-v1^2),sqrtint(bounds[5]-v1^2),for(v3=-sqrtint(bounds[5]-v1^2-v2^2),sqrtint(bounds[5]-v1^2-v2^2),for(v4=-sqrtint(bounds[5]-v1^2-v2^2-v3^2),sqrtint(bounds[5]-v1^2-v2^2-v3^2),for(v5=-sqrtint(bounds[5]-v1^2-v2^2-v3^2-v4^2),sqrtint(bounds[5]-v1^2-v2^2-v3^2-v4^2),
          b5=[v1,v2,v3,v4,v5];
          mu54=(b5*bs4~)/(bs4*bs4~);mu53=(b5*bs3~)/(bs3*bs3~);mu52=(b5*bs2~)/(bs2*bs2~);mu51=(b5*bs1~)/(bs1*bs1~);bs5=b5-mu51*bs1-mu52*bs2-mu53*bs3-mu54*bs4;check=bs5+mu54*bs4;
          if(abs(mu51)<=1/2,if(abs(mu52)<=1/2,if(abs(mu53)<=1/2,if(abs(mu54)<=1/2,if(check*check~>=3/4*(bs4*bs4~),
          if(bs5*bs5~<=1,
          if(bs4*bs4~<=1/(1-(4/3)*mu54^2),
            M=[b1[1],b1[2],b1[3],b1[4],b1[5];b2[1],b2[2],b2[3],b2[4],b2[5];b3[1],b3[2],b3[3],b3[4],b3[5];b4[1],b4[2],b4[3],b4[4],b4[5];b5[1],b5[2],b5[3],b5[4],b5[5]];
            if(abs(matdet(M))>1,
            tot=tot+1;print(tot,M);
            N=M^(-1);
            P=matrix(5,5,i,j,floor(abs(N[i,j])));
            S=(P[,1]~*P[,1])*(P[,2]~*P[,2])*(P[,3]~*P[,3])*(P[,4]~*P[,4])*(P[,5]~*P[,5]);
            if(S==0,,print("counterexample: ",M)
))))))))))))))))))))))))))))))))))))))))))))));tot
}

print([gettime(),tot])