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 board[207][207];
int piece[4][107][107];
char st[107];
int main() {
  int n;
  scanf("%d", &n);
  for (int k = 0; k < 4; ++k)
    for (int i = 0; i < n; ++i) {
      scanf("%s", st);
      for (int j = 0; j < n; ++j) piece[k][i][j] = st[j] - '0';
    }
  int ans = 4 * n * n;
  for (int p0 = 0; p0 < 4; ++p0)
    for (int p1 = 0; p1 < 4; ++p1)
      for (int p2 = 0; p2 < 4; ++p2)
        for (int p3 = 0; p3 < 4; ++p3) {
          if (p0 == p1 || p0 == p2 || p0 == p3) continue;
          if (p1 == p2 || p1 == p3) continue;
          if (p2 == p3) continue;
          for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j) {
              board[i][j] = piece[p0][i][j];
              board[i][j + n] = piece[p1][i][j];
              board[i + n][j] = piece[p2][i][j];
              board[i + n][j + n] = piece[p3][i][j];
            }
          int cnt0 = 0, cnt1 = 0;
          for (int i = 0; i < 2 * n; ++i)
            for (int j = 0; j < 2 * n; ++j) {
              if ((i + j) % 2 == 0) {
                cnt0 += board[i][j];
                cnt1 += 1 - board[i][j];
              }
              if ((i + j) % 2 == 1) {
                cnt0 += 1 - board[i][j];
                cnt1 += board[i][j];
              }
            }
          ans = min(ans, cnt0);
          ans = min(ans, cnt1);
        }
  printf("%d\n", ans);
  return 0;
}
