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

n = int(input())
boards = []
for i in range(4):
    boards.append([])
    for j in range(n):
        boards[-1].append(list(map(int, list(input()))))
    if i < 3: input()

ans = n * n * 4


def check_board(corner, board):
    ans = 0
    for i in range(n):
        for j in range(n):
            if board[i][j] != corner:
                ans += 1
            corner = 1 - corner
    return ans


def solve(corner, p):
    ans = check_board(corner, boards[p[0]])
    ans += check_board(1- corner, boards[p[1]])
    ans += check_board(1 - corner, boards[p[2]])
    ans += check_board(corner, boards[p[3]])

    return ans


for p in itertools.permutations(range(4), 4):
    ans = min(ans, solve(1, p))
    ans = min(ans, solve(0, p))

print(ans)