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
from itertools import permutations

def solve(TL, TR, BL, BR, s, n):
	A = []

	for i in range(n):
		X = TL[i].copy()
		X.extend(TR[i])
		A.append(X)

	for i in range(n):
		X = BL[i].copy()
		X.extend(BR[i])
		A.append(X)

	c = 0
	ans = 0

	for i in range(2 * n):
		if i % 2 == 1:
			c = s ^ 1
		else:
			c = s

		for j in range(2 * n):
			if A[i][j] != c:
				ans += 1
				A[i][j] = c

			c ^= 1

	return ans


n = int(input())

P = []

for _ in range(4):
	A = []

	for i in range(n):
		A.append(list(map(int, list(input()))))

	if _ != 3:
		input()

	P.append(A)

ans = (4 * n * n) + 1

for S in permutations(range(4)):

	for s in range(2):

		cur = solve(P[S[0]],P[S[1]],P[S[2]],P[S[3]], s, n)

		ans = min(ans, cur)

print(ans)