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
from itertools import permutations


def count(board, first_square):
    cnt = 0
    n = len(board)
    same = str(first_square)
    inverted = str(1 - first_square)

    for i in range(n):
        for j in range(n):
            if (i + j) % 2 == 0:
                c = same
            else:
                c = inverted
            cnt += board[i][j] != c
    return cnt


def main():
    n = int(input())

    m = n * n * 4

    pieces = []
    for _ in range(4):
        piece = []
        for i in range(n):
            piece.append(input())
        pieces.append(piece)
        try:
            input()
        except:
            pass

    for color in range(2):
        for p in permutations(range(4)):
            changed = (count(pieces[p[0]], color) + count(pieces[p[1]], 1 - color) +
                       count(pieces[p[2]], 1 - color) + count(pieces[p[3]], color))
            if changed < m:
                m = changed

    print(m)


if __name__ == '__main__':
    main()
