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
#!/usr/bin/env python3

import sys

n = int(sys.stdin.readline().strip())
blks = []
for i in range(4):
	blks.append([])
	for j in range(n):
		blks[-1].append(sys.stdin.readline().strip())
	if i != 3:
		sys.stdin.readline()

# start from B
def to_BW(blk):
	n = len(blk)
	BW = [0, 0]
	for i in range(n):
		for j in range(n):
			BW[(i + j + int(blk[i][j])) % 2] += 1
	return BW

BWs = [to_BW(blk) for blk in blks]

res = 4 * n**2

for i in range(4):
	for j in range(i):
		kl = list(set(range(4)) - {i, j})
		res = min(res, BWs[i][0] + BWs[j][0] + BWs[kl[0]][1] + BWs[kl[1]][1])

print (res)
