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 calc(vector<vector<char>> a, vector<vector<char>> b, vector<vector<char>> c,
         vector<vector<char>> d) {
  int ans = 0;
  int n = a.size() - 1;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if ((i + j) % 2 == 0 && a[i][j] == '0') {
        ans++;
      } else if ((i + j) % 2 == 1 && a[i][j] == '1')
        ans++;
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if ((i + j) % 2 == 0 && b[i][j] == '1') {
        ans++;
      } else if ((i + j) % 2 == 1 && b[i][j] == '0')
        ans++;
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if ((i + j) % 2 == 0 && c[i][j] == '1') {
        ans++;
      } else if ((i + j) % 2 == 1 && c[i][j] == '0')
        ans++;
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if ((i + j) % 2 == 0 && d[i][j] == '0') {
        ans++;
      } else if ((i + j) % 2 == 1 && d[i][j] == '1')
        ans++;
    }
  }
  return ans;
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  vector<vector<vector<char>>> a;
  a.resize(4, vector<vector<char>>(n + 1, vector<char>(n + 1)));
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) cin >> a[0][i][j];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) cin >> a[1][i][j];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) cin >> a[2][i][j];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) cin >> a[3][i][j];
  }
  int ans = 1e8;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      if (i == j) continue;
      for (int k = 0; k < 4; k++) {
        if (i == k || j == k) continue;
        for (int l = 0; l < 4; l++) {
          if (i == l || j == l || k == l) continue;
          ans = min(ans, calc(a[i], a[j], a[k], a[l]));
        }
      }
    }
  }
  cout << ans;
  return 0;
}
