961_C. Chessboard
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
```python
import itertools

n = int(input())
a = []
for i in range(4):
    a.append([input() for _ in range(n)])
    if i < 3:
        assert input() == ''

best = 4*n*n
for p in itertools.permutations(a):
    for s in range(2):
        count = 0
        for i in range(4):
            for r in range(n):
                for c in range(n):
                    if p[i][r][c] != str((s + (i//2 + r) + (i % 2 + c)) % 2):
                        count += 1
        best = min(best, count)
print(best)

```