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())
l = list()
for i in range(4):
    l.append([list(input()) for x in range(n)])
    if i < 3:
        input()
lt = [0, 0, 0, 0]
min_f = (n * 2) ** 2
for i in range(1, 4):
    ll = [1, 2, 3]
    lt[1] = ll.pop(i - 1)
    for x in range(2):
        lb = list()
        lt[2] = ll[x]
        lt[3] = ll[x - 1]
        for y in range(n * 2):
            if y < n:
                lb.append(list(map(int, l[lt[0]][y % n] + l[lt[1]][y % n])))
            else:
                lb.append(list(map(int, l[lt[2]][y % n] + l[lt[3]][y % n])))
        for y in range(2):
            f = 0
            for y1 in range(n * 2):
                for x1 in range(n * 2):
                    if (x1 + y1) % 2:
                        if lb[y1][x1] != y:
                            f += 1
                    else:
                        if lb[y1][x1] == y:
                            f += 1
            if f < min_f:
                min_f = f
print(min_f)