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 main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  char c;
  string s;
  int z[2] = {0};
  int r[4];
  int w[4];
  int p;
  int ans = 0;
  for (int j = 0; j < 4; j++) {
    int flag = 0;
    ans = 0;
    for (int k = 0; k < n; k++) {
      for (int i = 0; i < n; i++) {
        cin >> c;
        if (flag == 0) {
          flag = 1;
          p = c - '0';
          if (z[p] == 2) {
            if (p == 0) {
              p = 1;
            } else {
              p = 0;
            }
            ans++;
            z[p]++;
          } else
            z[p]++;
        } else {
          if (p == c - '0') {
            ans++;
            if (p)
              p = 0;
            else
              p = 1;
          } else
            p = c - '0';
        }
      }
    }
    if (p) {
      w[j] = ans;
      r[j] = n * n - ans;
    } else {
      r[j] = ans;
      w[j] = n * n - ans;
    }
    getline(cin, s);
  }
  sort(w, w + 4);
  sort(r, r + 4);
  cout << w[0] + w[1] + r[0] + r[1] << endl;
  return 0;
}
