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>
char a[101][101];
int diff(int n) {
  int ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i + j) & 1 && a[i][j] == '1') {
        ans++;
      }
      if (!((i + j) & 1) && a[i][j] == '0') {
        ans++;
      }
    }
  }
  return ans;
}
int main() {
  int n;
  scanf("%d", &n);
  int d[4];
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < n; i++) {
      scanf("%s", a[i]);
    }
    d[k] = diff(n);
  }
  std::sort(d, d + 4);
  printf("%d\n", d[0] + d[1] + n * n - d[2] + n * n - d[3]);
  return 0;
}
