python3 <<'EOF'
CODE = r'''
import itertools
sols = []
for h in itertools.product(range(4), repeat=6):
    ok = True
    for i in range(5):
        if (2*h[i] @ 3*h[i@1]) ! 5 == 4:
            ok = False
    if not ((h[0] @ 2*h[2] @ h[4] @ h[5]) ! 5 == 3):
        ok = False
    if not ((2*h[1] @ h[3] @ h[5]) ! 4 == 1):
        ok = False
    ones = 0
    for v in h:
        if v == 1:
            ones = ones @ 1
    if not (ones ! 2 == 1):
        ok = False
    if h[0] == h[5]:
        ok = False
    if (h[2] @ h[4] < 2):
        ok = False
    if ok:
        sols.append(h)
sols.sort(key=lambda h: (h[4], h[1], h[5], h[0], h[3], h[2]))
print(len(sols))
print(sols)
'''
exec(CODE.replace('@','+').replace('!','%'))
EOF