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 main() {
  int n, q[4][2];
  char c[100][100];
  for (int i = 0; i < 100; i++)
    for (int j = 0; j < 100; j++)
      if (i % 2 && j % 2 || i % 2 == 0 && j % 2 == 0)
        c[i][j] = '1';
      else
        c[i][j] = '0';
  for (int i = 0; i < 4; i++) {
    q[i][0] = 0;
    q[i][1] = 0;
  }
  cin >> n;
  for (int i = 0; i < 4; i++)
    for (int j = 0; j < n; j++)
      for (int k = 0; k < n; k++) {
        char a;
        cin >> a;
        if (a != c[j][k])
          q[i][0]++;
        else
          q[i][1]++;
      }
  int ans1 = 1000 * 1000 * 1000;
  for (int i = 0; i < 4; i++) ans1 = min(ans1, q[i][0]);
  for (int i = 0; i < 4; i++)
    if (q[i][0] == ans1) {
      q[i][0] = 1000 * 1000 * 1000;
      break;
    }
  int ans2 = 1000 * 1000 * 1000;
  for (int i = 0; i < 4; i++) ans2 = min(ans2, q[i][0]);
  int ans = ans1 + ans2;
  ans1 = 1000 * 1000 * 1000;
  for (int i = 0; i < 4; i++) ans1 = min(ans1, q[i][1]);
  for (int i = 0; i < 4; i++)
    if (q[i][1] == ans1) {
      q[i][1] = 1000 * 1000 * 1000;
      break;
    }
  ans2 = 1000 * 1000 * 1000;
  for (int i = 0; i < 4; i++) ans2 = min(ans2, q[i][1]);
  ans += ans2 + ans1;
  cout << ans;
  return 0;
}
