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
#include <bits/stdc++.h>
using namespace std;
int n, f[2][4], map[110][110];
char buf[110];
int main() {
  scanf("%d", &n);
  for (int i = 0; i < 4; ++i) {
    for (int j = 1; j <= n; ++j) {
      scanf("%s", buf);
      for (int k = 1; k <= n; ++k)
        f[0][i] += ((j & 1) ^ (k & 1)) ^ (buf[k - 1] == '0'),
            f[1][i] += ((j & 1) ^ (k & 1)) ^ (buf[k - 1] == '1');
    }
  }
  printf("%d\n", min(f[0][0] + f[0][1] + f[1][2] + f[1][3],
                     min(f[0][0] + f[1][1] + f[0][2] + f[1][3],
                         min(f[1][0] + f[0][1] + f[0][2] + f[1][3],
                             min(f[0][0] + f[1][1] + f[1][2] + f[0][3],
                                 min(f[1][0] + f[0][1] + f[1][2] + f[0][3],
                                     min(f[1][0] + f[1][1] + f[0][2] + f[0][3],
                                         0x7fffffff)))))));
  return 0;
}
