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
rows = int(input())
boards = []
board = ""
for i in range(4 * rows + 3):
    line = input()
    if not line:
        boards.append(board)
        board = ""
    else:
        board += line
boards.append(board)


def difference(board_in, type=0):
    to_return = 0
    for i in board_in:
        to_return += int(i != str(type))
        type = (type + 1) % 2
    return to_return


zero_board_diff = [difference(i, 0) for i in boards]
one_board_diff = [rows ** 2 - i for i in zero_board_diff]
possibilities = []

for i in range(4):
    for j in range(4):
        if i == j:
            continue
        ones = [0, 1, 2, 3]
        ones.remove(i)
        ones.remove(j)
        possibilities.append(zero_board_diff[i] +
                             zero_board_diff[j] +
                             one_board_diff[ones[0]] +
                             one_board_diff[ones[1]]
                             )

print(sorted(possibilities)[0])
