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 diff_start_zero(board):
	chars = ['0', '1']
	i = 0
	difference = 0
	for i in range(n*n):
		if board[i] != chars[i%2]:
			difference += 1
	return difference

n = int(input())

boards = []

for i in range(4):
	board = ""
	for j in range(n):
		board += input()
	boards.append(board)
	board = ""
	if i < 3:
		input()


zero_diffs = [diff_start_zero(i) for i in boards]
one_diffs = [n*n - i for i in zero_diffs]

pairs = [(a,b) for a, b in zip(zero_diffs, one_diffs)]

pairs.sort()

result = pairs[0][0] + pairs[1][0] + pairs[2][1] + pairs[3][1]

print(result)