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())

parts = []
for i in range(4):
    part = []
    for _i in range(n):
        part.append([int(x) for x in input()])
    parts.append(part)

    if i < 3:input()

processed_parts = []
for part in parts:
    dt1 = 0
    exp = 1

    for h in range(n):
        for w in range(n):
            if part[h][w] != exp:
                dt1 += 1
            exp = (exp+1) % 2

    dt2 = 0
    for h in range(n):
        for w in range(n):
            if part[h][w] != exp:
                dt2 += 1
            exp = (exp+1) % 2

    processed_parts.append([dt1, dt2])

ans = n*n*4

for i in range(3):
    for j in range(i+1, 4):
        a = 0
        for k, part in enumerate(processed_parts):
            if k == i or k == j:
                a += part[0]
            else:
                a += part[1]
        ans = min(ans, a)

print(ans)