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())
row1 = [0, 1] * (n // 2) + [0]
row2 = [1, 0] * (n // 2) + [1]

d = []
for i in range(4):
    d.append([0, 0])
    for j in range(n):
        row = [int(x) for x in input()]
        for k in range(n):
            # print(i, j, k)
            if j % 2 == 0:
                d[i][0] += abs(row1[k] - row[k])
                d[i][1] += abs(row2[k] - row[k])
            else:
                d[i][1] += abs(row1[k] - row[k])
                d[i][0] += abs(row2[k] - row[k])
    if i < 3:
        input()

# min_ = min([(d[0][0] + d[1][0] + d[2])])
m = [0] * 6
m[0] = d[0][0] + d[1][0] + d[2][1] + d[3][1]
m[1] = d[0][0] + d[1][1] + d[2][0] + d[3][1]
m[2] = d[0][0] + d[1][1] + d[2][1] + d[3][0]
m[3] = d[0][1] + d[1][0] + d[2][0] + d[3][1]
m[4] = d[0][1] + d[1][0] + d[2][1] + d[3][0]
m[5] = d[0][1] + d[1][1] + d[2][0] + d[3][0]


print(min(m))
