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())
p = [[[] for _ in range(n)] for _ in range(4)]

for i in range(4):
    for j in range(n):
        r = list(map(int, list(input())))
        p[i][j] = r
    if i < 3: 
        input()

dif = [0] * 4

for k in range(4):
    o = 0
    for i in range(n):
        for j in range(n):
            if p[k][i][j] == (n * i + j) % 2: 
                o += 1        

    dif[k] = (o, n*n - o)

res = 10 ** 19
z = sum(dif[_][1] for _ in range(4))
for k1 in range(4):
    for k2 in range(k1 + 1, 4):
        res = min(res, dif[k1][0]+dif[k2][0]+z-dif[k1][1]-dif[k2][1])

print(res)