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())
chess = []
for w in range(3):
    chess.append([input() for i in range(n)])
    input()
chess.append([input() for i in range(n)])

issue = {0:0, 1:0, 2:0, 3:0}
reversed_issue = {0:0, 1:0, 3:0}

for w in range(4):
    chessdesk = [chess[0] + chess[3]] + [chess[1] + chess[2]]
    for s in range(2 * n):
        chessdesk[0][s] += chessdesk[1][s]
    chessdesk.pop(1)
    chessdesk = chessdesk[0]
    colour = chessdesk[0][0]

    for i in range(2 * n):
        for j in range(2 * n):
            if (i + j) % 2 == 0:
                if chessdesk[i][j] != colour:
                    issue[w] += 1
            else:
                if chessdesk[i][j] == colour:
                    issue[w] += 1

    reversed_issue[w] = 4 * n**2 - issue[w]              
    if w == 0:
        chess[0], chess[3] = chess[3], chess[0]
    elif w == 1:
        chess[1], chess[3] = chess[3], chess[1]
    elif w == 2:
        chess[1], chess[2] = chess[2], chess[1]

print(min(min(issue.values()), min(reversed_issue.values())))