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 score(grid, tl):
    n = len(grid)
    ans = 0
    for i in range(n):
        for j in range(n):
            ans += int(grid[i][j]) ^ (i & 1) ^ (j & 1) ^ tl

    return ans

def main():
    n = int(input())
    first = True
    grids = []
    for _ in range(4):
        if not first:
            input()
        first = False
        grids.append([input() for _ in range(n)])

    a = [score(grid, 0) for grid in grids]
    b = [score(grid, 1) for grid in grids]

    ans = float('inf')
    for i in range(4):
        for j in range(i + 1, 4):
            ans = min(ans, sum(a) - a[i] - a[j] + b[i] + b[j])

    print(ans)

main()
