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())
a1 = [[(i + n * j) % 2 for i in range(n)] for j in range(n)]
b1 = [[abs((i + n * j) % 2 - 1) for i in range(n)] for j in range(n)]
cell1 = [list(map(int, list(input()))) for i in range(n)]
l = input()
cell2 = [list(map(int, list(input()))) for i in range(n)]
l = input()
cell3 = [list(map(int, list(input()))) for i in range(n)]
l = input()
cell4 = [list(map(int, list(input()))) for i in range(n)]
count = [[0 , 0] for i in range(4)]
for i in range(n):
    for j in range(n):
        if cell1[i][j] != a1[i][j]:
            count[0][0] += 1
        if cell1[i][j] != b1[i][j]:
            count[0][1] += 1
        if cell2[i][j] != a1[i][j]:
            count[1][0] += 1
        if cell2[i][j] != b1[i][j]:
            count[1][1] += 1
        if cell3[i][j] != a1[i][j]:
            count[2][0] += 1
        if cell3[i][j] != b1[i][j]:
            count[2][1] += 1
        if cell4[i][j] != a1[i][j]:
            count[3][0] += 1
        if cell4[i][j] != b1[i][j]:
            count[3][1] += 1
min_1 = min(count[0][0] + count[1][0] + count[2][1] + count[3][1], count[0][0] + count[1][1] + count[2][0] + count[3][1], count[0][1] + count[1][0] + count[2][0] + count[3][1], count[0][0] + count[1][1] + count[2][1] + count[3][0], count[0][1] + count[1][0] + count[2][1] + count[3][0], count[0][1] + count[1][1] + count[2][0] + count[3][0])
print(min_1)