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 n;
const int MAXN = 105;
int p[4][MAXN][MAXN];
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      string s;
      getline(cin, s);
      if (s.empty()) getline(cin, s);
      for (int k = 0; k < n; k++) p[i][j][k] = (s[k] - '0');
    }
  }
  int ans = 400005;
  for (int a = 0; a < 4; a++)
    for (int b = 0; b < 4; b++) {
      if (b == a) continue;
      for (int c = 0; c < 4; c++) {
        if (c == a || c == b) continue;
        for (int d = 0; d < 4; d++) {
          int sum = 0;
          if (d == a || d == b || d == c) continue;
          for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++) {
              if ((j % 2 == 0 && i % 2 == 0) || (j % 2 == 1 && i % 2 == 1)) {
                sum += abs(p[a][i][j] - 1);
                sum += abs(p[b][i][j] - 1);
              } else {
                sum += abs(p[a][i][j]);
                sum += abs(p[b][i][j]);
              }
            }
          for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++) {
              if ((j % 2 == 0 && i % 2 == 1) || (j % 2 == 1 && i % 2 == 0)) {
                sum += abs(p[c][i][j] - 1);
                sum += abs(p[d][i][j] - 1);
              } else {
                sum += abs(p[c][i][j]);
                sum += abs(p[d][i][j]);
              }
            }
          ans = min(ans, sum);
        }
      }
    }
  cout << ans << "\n";
  return 0;
}
