python3 << "EOF"
C=[]
for n in range(4096):
 c6=n//1024
 c2=(n//256)%4
 c4=(n//64)%4
 c1=(n//16)%4
 c5=(n//4)%4
 c3=n%4
 c=[c1,c2,c3,c4,c5,c6]
 if any((c[i]+2*c[i+1])%5==1 for i in range(5)):continue
 if (c[0]+2*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)
print(len(C))
print(C)
EOF