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 cal(arr,flag):
    ans = 0
    for i in range(n):
            for j in range(n):
                ans += (arr[i][j]+i+j+flag)%2
    return ans



n = input()
costs = []
ret = n*n*4
for i in range(4):
    mat = []
    for j in range(n):
        arr = map(int,raw_input())
        mat.append(arr)
    costs.append([cal(mat,0),cal(mat,1)])
    if i!=3:
        tmp = raw_input()

for i in range(16):
    tmp = []
    for j in range(4):
        if i&(1<<j):
            tmp.append(j)
    ans = 0
    if len(tmp) == 2:
        for j in range(4):
            if j in tmp:
                ans += costs[j][1]
            else:
                ans += costs[j][0]
        ret = min(ret,ans)
print ret

	 					 	 			      							 	 		