python3 << "EOF"
import itertools
C=[]
for c in itertools.product(range(4),repeat=6):
 if any((c[i]+2*c[i+1])%5==1 for i in range(5)):continue
 if (2*c[0]+c[2]+c[4]+c[5])%5!=4:continue
 if (c[1]+2*c[3]+c[5])%4!=1:continue
 if sum(x==0 for x in c)%2!=0:continue
 if c[0]==c[4]:continue
 if c[2]+c[5]<2:continue
 C.append(c)
C.sort(key=lambda c:(c[5],c[1],c[3],c[0],c[4],c[2]))
print(len(C))
print([list(c) for c in C])
EOF