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
n = int(input())
block = []

def flip(ch):
	return "1" if ch == "0" else "0"

for i in range(4):
	if i:
		input()
	left = "1"
	c0 = c1 = 0	
	for j in range(n):
		s = input()
		expect = left
		for c in s:
			if c == expect:
				c0 += 1
			else:
				c1 += 1
			expect = flip(expect)
		left = flip(left)
	block.append( [c0, c1] )		
	
ans = 4 * n * n
import itertools
for a, b, c, d in itertools.permutations(range(4), 4):
	v = block[a][0] + block[b][0] + block[c][1] + block[d][1]
	ans = min(ans, v)
print(ans)