python3 <<'EOF'
CODE = r'''
import itertools

def good(h):
    for i in range(5):
        if (2*h[i] @ 3*h[i@1]) ! 5 == 4:
            return False
    if not ((h[0] @ 2*h[2] @ h[4] @ h[5]) ! 5 == 3):
        return False
    if not ((2*h[1] @ h[3] @ h[5]) ! 4 == 1):
        return False
    ones = 0
    for v in h:
        if v == 1:
            ones = ones @ 1
    if not (ones ! 2 == 1):
        return False
    if h[0] == h[5]:
        return False
    if (h[2] @ h[4] < 2):
        return False
    return True

H = []
for h in itertools.product(range(4), repeat=6):
    if good(h):
        H.append(h)
H.sort(key=lambda h: (h[4], h[1], h[5], h[0], h[3], h[2]))
print('count', len(H))

A0 = [[1,0,2,1],[2,1,0,1],[0,2,1,1],[1,1,1,0]]
A1 = [[2,1,0,1],[0,1,2,1],[1,0,1,2],[1,2,0,1]]
A2 = [[1,2,1,0],[2,0,1,1],[1,1,0,2],[0,1,2,1]]
A3 = [[0,1,2,1],[1,2,0,1],[2,1,1,0],[1,0,1,2]]
As = [A0, A1, A2, A3]

def mv(M, v):
    out = []
    for i in range(4):
        s = 0
        for j in range(4):
            s = s @ M[i][j]*v[j]
        out.append(s ! 91)
    return out

G = [21, 44, 9, 58]
for t, h in enumerate(H, start=1):
    R = 0
    for i in range(6):
        R = R @ (i@1)*h[i]
    T = 0
    for i in range(5):
        if h[i] < h[i@1]:
            T = T @ 1
    U = 0
    for i in range(3):
        U = U @ (h[i]@2)*(h[5-i]@1)
    V = h[0]*h[2] @ 2*h[1]*h[4] @ 3*h[3]*h[5]
    a = (2*R @ T @ U @ V @ t) ! 4
    b = (h[0] @ 3*h[1] @ h[2] @ 2*h[3] @ h[4] @ 3*h[5] @ t) ! 3
    q = [(R@T@t) ! 91, (U@2*t) ! 91, (V@R@3*t) ! 91, (T@U@V) ! 91]
    print('t', t, 'h', h, 'R', R, 'T', T, 'U', U, 'V', V, 'a', a, 'b', b, 'q', q)
    G = mv(As[a], G)
    for i in range(4):
        G[i] = (G[i] @ q[i]) ! 91
    print('after update', G)
    if b == 0:
        G[0] = (G[0] @ 3) ! 91
        G[1] = (G[1] @ 1) ! 91
        G[2] = G[2] ! 91
        G[3] = (G[3] @ 2) ! 91
    if b == 1:
        G[0] = (G[0] - 1) ! 91
        G[1] = G[1] ! 91
        G[2] = (G[2] - 4) ! 91
        G[3] = (G[3] - 2) ! 91
    if b == 2:
        G = [G[1] ! 91, G[3] ! 91, G[0] ! 91, G[2] ! 91]
    print('after repair', G)
print('G', G)
'''
exec(CODE.replace('@','+').replace('!','%'))
EOF