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
import itertools as it


def board_to_color_costs(board):
    "(white_top_left_cost, black_top_left_cost)"
    a, b = 0, 0
    n = len(board)
    for i in range(n):
        for j in range(n):
            if (i + j) % 2 == 0:
                if board[i][j] == '1':
                    a += 1
            else:
                if board[i][j] == '0':
                    a += 1
    for i in range(n):
        for j in range(n):
            if (i + j) % 2 == 0:
                if board[i][j] == '0':
                    b += 1
            else:
                if board[i][j] == '1':
                    b += 1
    return (a, b)


n = int(input())

board_costs = []

for board_index in range(4):
    board = []
    for _ in range(n):
        board += [input()]
    if board_index != 3:
        input()
    board_costs += [board_to_color_costs(board)]


best = (2 * n) ** 2

for perm in it.permutations(board_costs):
    best = min([best, perm[0][0] + perm[1][1] + perm[2][1] + perm[3][0]])

# Probably the below is not needed due to symetries
#for perm in it.permutations(board_costs):
#    best = min([best, perm[0][1] + perm[1][0] + perm[2][0] + perm[3][1]])


print(best)
