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 num[4][99][99];
int nsize = 0;
int cnt[4][2];
int min(int a, int b) {
  if (a < b) return a;
  return b;
}
int main() {
  scanf("%d", &nsize);
  int i = 0;
  while (i < 4) {
    int j = 0;
    while (j < nsize) {
      int k = 0;
      while (k < nsize) {
        scanf("%1d", &num[i][j][k]);
        k++;
      }
      j++;
    }
    i++;
  }
  i = 0;
  while (i < 4) {
    int temp = 0;
    while (temp < 2) {
      int start = temp;
      int j = 0;
      while (j < nsize) {
        int k = 0;
        while (k < nsize) {
          if (num[i][j][k] != start) cnt[i][temp]++;
          start = !start;
          k++;
        }
        j++;
      }
      temp++;
    }
    i++;
  }
  int ans = cnt[0][0] + cnt[1][0] + cnt[2][1] + cnt[3][1];
  ans = min(ans, cnt[0][0] + cnt[1][1] + cnt[2][0] + cnt[3][1]);
  ans = min(ans, cnt[0][0] + cnt[1][1] + cnt[2][1] + cnt[3][0]);
  ans = min(ans, cnt[0][1] + cnt[1][0] + cnt[2][0] + cnt[3][1]);
  ans = min(ans, cnt[0][1] + cnt[1][0] + cnt[2][1] + cnt[3][0]);
  ans = min(ans, cnt[0][1] + cnt[1][1] + cnt[2][0] + cnt[3][0]);
  printf("%d\n", ans);
  return 0;
}
