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
from itertools import permutations

n = int(input())
a = []
for i in range(4):
    a.append([list(map(int, list(input()))) for j in range(n)])
    if i < 3:
        input()

ans = 10 ** 10
for i in permutations(a, 4):
    cnt = 0
    total = 0
    for j in i:
        if cnt < 2:
            cnt2 = 0
            for p in j:
                for q in p:
                    if q != cnt2 % 2:
                        total += 1
                    cnt2 += 1
        else:
            cnt2 = 1
            for p in j:
                for q in p:
                    if q != cnt2 % 2:
                        total += 1
                    cnt2 += 1
        cnt += 1

    ans = min(ans, total)

print(ans)