Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. 

Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them.

Input

The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. 

Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line.

Output

Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard.

Examples

Input

1
0

0

1

0


Output

1


Input

3
101
010
101

101
000
101

010
101
011

010
101
010


Output

2
n = int(input())
s = [["" for _ in range(n)] for __ in range(4)]
for i in range(3):
    for j in range(n):
        s[i][j] = input()
    input()
for j in range(n):
    s[3][j] = input()
res = int(1e13)
for i in range(24):
    perm = [0, 1, 2, 3]
    L = [0]*4
    tmp = i
    for j in range(4):
        L[j] = tmp % (4-j)
        tmp //= (4-j)
    LL = [0]*4
    for j in range(4):
        LL[j] = perm[L[j]]
        for k in range(L[j], 3-j):
            perm[k] = perm[k+1]
    lu, ru, ld, rd = LL[0], LL[1], LL[2], LL[3]
    Map = [s[lu][_][:]+s[ru][_][:] for _ in range(n)] + [s[ld][_][:]+s[rd][_][:] for _ in range(n)]
    cnt0, cnt1 = 0, 0
    for j in range(2*n):
        for k in range(2*n):
            if (j+k) % 2:
                if Map[j][k] == '0':
                    cnt0 += 1
                else:
                    cnt1 += 1
            else:
                if Map[j][k] == '1':
                    cnt0 += 1
                else:
                    cnt1 += 1
    res = min(res, cnt0, cnt1)
print(res)