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())


def to_change_white_corners(b):
    n = len(b)

    return sum([1 for i, x in enumerate(b) if int(x) == i%2])


def to_change_black_corners(b):
    n = len(b)

    return sum([1 for i, x in enumerate(b) if int(x) == (i + 1)%2])


to_change = []

for i in range(4):
    b = ""

    for _ in range(n):
        b += input()
    
    to_change.append((to_change_white_corners(b), to_change_black_corners(b)))

    if (i != 3):
        input()

min_ = 40000

for a, b, c, d in [(2, 3, 0, 1), (1, 3, 0, 2), (1, 2, 0, 3), (0, 3, 1, 2), (0, 2, 1, 3), (0, 1, 2, 3)]:
    min_ = min(min_, to_change[a][0] + to_change[b][0] + to_change[c][1] + to_change[d][1])

print(min_)