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;
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  while (TESTS--) {
    long long n;
    cin >> n;
    string s[2 * n];
    for (long long i = 0; i < 2 * n; i++) {
      for (long long j = 0; j < 2 * n; j++) {
        s[i].push_back((i + j) % 2 + '0');
      }
    }
    vector<vector<string>> str(4, vector<string>(n));
    for (long long i = 0; i < 4; i++)
      for (long long j = 0; j < n; j++) cin >> str[i][j];
    long long ans = 1000000007;
    sort((str).begin(), (str).end());
    do {
      string tmp[2 * n];
      for (long long i = 0; i < n; i++) {
        for (auto j : str[0][i]) tmp[i].push_back(j);
        for (auto j : str[1][i]) tmp[i].push_back(j);
      }
      for (long long i = 0; i < n; i++) {
        for (auto j : str[2][i]) tmp[i + n].push_back(j);
        for (auto j : str[3][i]) tmp[i + n].push_back(j);
      }
      long long cnt = 0;
      for (long long i = 0; i < 2 * n; i++)
        for (long long j = 0; j < 2 * n; j++)
          if (tmp[i][j] != s[i][j]) cnt++;
      ans = min(ans, min(cnt, 2 * n * 2 * n - cnt));
    } while (next_permutation((str).begin(), (str).end()));
    cout << ans;
  }
  return 0;
}
