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;
char b0[1100][1100];
long long typ1[4], typ2[4];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, i, j;
  cin >> n;
  for (long long k = 0; k < 4; k++) {
    long long t1 = 0, t2 = 0;
    for (i = 1; i <= n; i++) {
      for (j = 1; j <= n; j++) {
        cin >> b0[i][j];
        if (i % 2 != 0) {
          if ((j % 2 != 0 && b0[i][j] == '1') ||
              (j % 2 == 0 && b0[i][j] == '0'))
            t1++;
          else if ((j % 2 != 0 && b0[i][j] == '0') ||
                   (j % 2 == 0 && b0[i][j] == '1'))
            t2++;
        } else {
          if ((j % 2 != 0 && b0[i][j] == '0') ||
              (j % 2 == 0 && b0[i][j] == '1'))
            t1++;
          else if ((j % 2 != 0 && b0[i][j] == '1') ||
                   (j % 2 == 0 && b0[i][j] == '0'))
            t2++;
        }
      }
    }
    typ1[k] = t1;
    typ2[k] = t2;
  }
  long long ans = 9000000000000000000;
  ans = min(ans, typ1[0] + typ1[1] + typ2[2] + typ2[3]);
  ans = min(ans, typ1[0] + typ1[2] + typ2[1] + typ2[3]);
  ans = min(ans, typ1[0] + typ1[3] + typ2[2] + typ2[1]);
  ans = min(ans, typ2[0] + typ2[1] + typ1[2] + typ1[3]);
  ans = min(ans, typ2[0] + typ2[2] + typ1[1] + typ1[3]);
  ans = min(ans, typ2[0] + typ2[3] + typ1[2] + typ1[1]);
  cout << ans << "\n";
  return 0;
}
