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
def zero_dis(board, n):

    dis = 0

    for r in range(0, n):
        for c in range(0, n):
            if (r+c)%2 != int(board[r][c]): dis+=1

    return dis

def one_dis(board, n):

    dis = 0

    for r in range(0, n):
        for c in range(0, n):
            if (r+c)%2 == int(board[r][c]): dis+=1

    return dis

while True:
    n = int(input())

    bs = []

    for board in range(0, 4):

        boardy = []
        
        for row in range(0, n):

            R=input()
            boardy.append(R)

        bs.append(boardy)

        if board!=3: input()

    zero_disses = []

    for b in bs:
        zero_disses.append(zero_dis(b, n))

    zero_disses.sort()

    c = zero_disses[0] + zero_disses[1] + 2*(n**2) - zero_disses[2] - zero_disses[3]

    print(c)

    break

