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 generate_board(size, color):
    board = []
    for _ in range(size):
        row = []
        for _ in range(size):
            row.append(color)
            color = 0 if color == 1 else 1
        board.append(row)
    return board

def distance_from(have, need):
    paint = 0
    for have_row, need_row in zip(have, need):
        for h, n in zip(have_row, need_row):
            if h != n:
                paint += 1
    return paint

def solution(n, pieces):
    white = generate_board(n, 0)
    black = generate_board(n, 1)
    grid = [
        (distance_from(p, white), distance_from(p, black))
        for p in pieces
    ]
    combinations = [
        [0,0,1,1],
        [0,1,0,1],
        [1,0,0,1],
        [0,1,1,0],
        [1,0,1,0],
        [1,1,0,0]
    ]

    return min(sum(
            grid[i][c]
            for i, c in enumerate(combo)
        )
        for combo in combinations
    )

if __name__ == "__main__":
    n = int(input())
    pieces = []
    for _ in range(4):
        pieces.append(list(
            list(map(int, input()))
            for _ in range(n)
        ))
        if _ < 3:
            input()
    print(solution(n, pieces))
