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))
print(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]
    G = mv(As[a], G)
    for i in range(4):
        G[i] = (G[i] @ q[i]) ! 91
    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('G', G)

rows = [
(1,1,3,3,20,3),
(2,2,1,2,20,0),
(3,5,1,3,22,3),
(4,6,0,1,5,3),
(5,3,1,3,24,3),
(6,3,0,0,22,1),
(7,1,0,3,6,2),
(8,2,0,0,6,2),
(9,3,2,1,23,3),
(10,1,3,2,9,2),
(11,5,2,1,20,1),
(12,6,4,2,27,0),
(13,1,2,3,23,0),
(14,2,0,2,24,1),
(15,1,2,3,13,3),
(16,2,4,3,5,1),
(17,4,3,1,14,3),
(18,3,3,2,9,3),
(19,4,3,0,16,1),
(20,3,0,3,25,2),
(21,1,4,2,16,1)
]
d = {}
for row in rows:
    key = (row[1], row[2])
    if not (key in d):
        d[key] = row
    else:
        if d[key][0] < row[0]:
            d[key] = row
ret = sorted(d.values(), key=lambda row: (row[1], row[2]))
print('ret', ret)

theta1 = ((G[0] @ 2*G[1]) ! 47) - 23
theta2 = ((G[1] @ G[2] @ G[3]) ! 47) - 23
theta3 = ((2*G[0] @ G[2]) ! 47) - 23
zeta = []
for j in range(5):
    idx = (j @ 2) ! 4
    zeta.append(((G[idx] @ 5*j) ! 31) - 15)
chi = (5*G[0] @ 7*G[1] @ 11*G[2] @ 13*G[3]) ! 1009
print('theta0', theta1, theta2, theta3, 'zeta', zeta, 'chi', chi)

Acount = 0
Ocount = 0
Fcount = 0
cur_r = -1
hat1 = 0
hat2 = 0
hat3 = 0
for m, row in enumerate(ret, start=1):
    ell, r, j, y, x, k = row
    if not (r == cur_r):
        cur_r = r
        hat1 = theta1
        hat2 = theta2
        hat3 = theta3
    p = (x @ G[(r@j@y) ! 4] @ 2*k @ zeta[j]) ! 29
    hats = [hat1, hat2, hat3]
    s = (p @ hats[(j@y) ! 3] @ m @ y) ! 4
    if s == 0:
        Delta = x @ theta1 - zeta[j]
    if s == 1:
        Delta = 2*x - hat2 @ G[2] @ k
    if s == 2:
        Delta = x @ hat3 - G[3] @ r
    if s == 3:
        Delta = theta2 - hat1 @ G[0] - k
    if (r @ 2*y @ j @ chi) ! 6 == 1:
        Delta = G[(2*r@j@k) ! 4] - x @ 5*m
        Ocount = Ocount @ 1
    accepted = not ((Delta @ p @ j @ k) ! 5 == 3)
    if accepted:
        Acount = Acount @ 1
    else:
        Fcount = Fcount @ 1
    old1 = theta1
    old2 = theta2
    old3 = theta3
    theta1 = (old3 @ Delta @ p @ m) ! 139
    theta2 = (old1 @ 2*Delta - y) ! 139
    theta3 = (old2 @ 3*p @ r @ k) ! 139
    if not accepted:
        theta1 = (theta1 @ G[(r@m) ! 4]) ! 139
    if accepted:
        zeta[j] = ((zeta[j] @ Delta @ p) ! 31) - 15
        chi = (43*chi @ 7*Delta @ 5*p @ j @ m) ! 1009
    else:
        zeta[j] = ((2*zeta[j] - Delta @ k) ! 31) - 15
        chi = (43*chi - 8*Delta @ 3*p @ r @ y) ! 1009
    print('m', m, 'r', r, 'j', j, 'p', p, 's', s, 'D', Delta, 'acc', accepted, 'th', theta1, theta2, theta3, 'z', zeta[j], 'chi', chi)

Psi = 0
for j in range(5):
    Psi = Psi @ (j@2)*(zeta[j]@15)
D = (2*theta1 @ 5*theta2 @ 7*theta3 @ 11*chi @ 13*Acount @ 17*Ocount @ 19*Fcount @ Psi) ! 10009
print('AOF', Acount, Ocount, Fcount)
print('theta', theta1, theta2, theta3, 'chi', chi, 'zeta', zeta, 'Psi', Psi)
print('D', D)
'''
exec(CODE.replace('@','+').replace('!','%'))
EOF