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())
a = [0,1] * N
a2 = [1,0] * N
pt1 = []
pt2 = []

cnt = 0
for j in range(N):
	arr = input()	
	for k in range(N):
		if j % 2 == 1 and int(arr[k]) == a2[k]:
			cnt += 1

		elif j % 2 == 0 and int(arr[k]) == a[k]:
			cnt += 1

	
pt1.append(cnt)
pt2.append(N*N-cnt)
	



cnt = 0
s = input()
for j in range(N):
	arr = input()
	for k in range(N):
		if j % 2 == 1 and int(arr[k]) == a2[k]:
			cnt += 1
			
		elif j % 2 == 0 and int(arr[k]) == a[k]:
			cnt += 1

pt1.append(cnt)
pt2.append(N*N-cnt)
s = input()
cnt = 0
for j in range(N):
	arr = input()
	for k in range(N):
		if j % 2 == 1 and int(arr[k]) == a2[k]:
			cnt += 1
			
		elif j % 2 == 0 and int(arr[k]) == a[k]:
			cnt += 1

pt1.append(cnt)
pt2.append(N*N-cnt)

s = input()

cnt = 0
for j in range(N):
	arr = input()
	for k in range(N):
		if j % 2 == 1 and int(arr[k]) == a2[k]:
			cnt += 1
			
		elif j % 2 == 0 and int(arr[k]) == a[k]:
			cnt += 1

pt1.append(cnt)
pt2.append(N*N-cnt)

pt1.sort()
pt2.sort()
print(pt1[0]+pt1[1]+pt2[0]+pt2[1])

