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() {
  int n;
  cin >> n;
  string s;
  int m;
  vector<int> w_b(4);
  vector<int> w_w(4);
  for (int i = 0; i < 4; ++i) {
    w_b[i] = 0;
    w_w[i] = 0;
  }
  for (int i = 0; i < 4; ++i) {
    for (int j = 1; j <= n; j++) {
      cin >> s;
      m = s.size();
      if (j % 2 == 0) {
        for (int u = 1; u <= m; ++u) {
          if (s[u - 1] == '0' && u % 2 == 0) {
            w_b[i]++;
          }
          if (s[u - 1] == '1' && u % 2 == 0) {
            w_w[i]++;
          }
          if (s[u - 1] == '0' && u % 2 == 1) {
            w_w[i]++;
          }
          if (s[u - 1] == '1' && u % 2 == 1) {
            w_b[i]++;
          }
        }
      } else {
        for (int u = 1; u <= m; ++u) {
          if (s[u - 1] == '0' && u % 2 == 0) {
            w_w[i]++;
          }
          if (s[u - 1] == '1' && u % 2 == 0) {
            w_b[i]++;
          }
          if (s[u - 1] == '0' && u % 2 == 1) {
            w_b[i]++;
          }
          if (s[u - 1] == '1' && u % 2 == 1) {
            w_w[i]++;
          }
        }
      }
    }
  }
  int res = 0;
  res =
      min(w_w[0] + w_w[1] + w_b[2] + w_b[3], w_w[0] + w_w[2] + w_b[1] + w_b[3]);
  res = min(res, w_w[0] + w_w[3] + w_b[2] + w_b[1]);
  res = min(res, w_w[2] + w_w[3] + w_b[0] + w_b[1]);
  res = min(res, w_w[1] + w_w[3] + w_b[0] + w_b[2]);
  res = min(res, w_w[2] + w_w[1] + w_b[0] + w_b[3]);
  cout << res;
  return 0;
}
