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 read_data():
    n = int(input().strip())
    pieces = []
    for j in range(4):
        a = []
        for i in range(n):
            a.append(input().strip())
        if j<3:
            input().strip()
        pieces.append(a)
    return n, pieces

def solve():
    counts = []
    for piece in pieces:
        cur = 0
        sum = 0
        for i in range(n):
            for j in range(n):
                if ord(piece[i][j])-48 == cur:
                    sum += 1
                cur += 1
                cur %= 2
        counts.append(sum)
    max= n*n
    counts.sort()
    sum = 0
    for i in range(4):
        if i < 2:
            sum += counts[i]
        else:
            sum += max - counts[i]
    return sum

n, pieces = read_data()
print(solve())