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;
  bool b[4][n][n];
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      char c[n + 1];
      scanf("%s", &c);
      for (int k = 0; k < n; k++) b[i][j][k] = c[k] == '1' ? 1 : 0;
    }
  }
  int s[] = {0, 1, 2, 3}, mi = 1e9, co = 0;
  bool o = 0;
  do {
    for (int k = 0; k < 4; k += 2) {
      for (int j = 0; j < n; j++) {
        for (int i = 0; i < n; i++) {
          if (b[s[k]][j][i] != o) co++;
          o ^= 1;
        }
        for (int i = 0; i < n; i++) {
          if (b[s[k + 1]][j][i] != o) co++;
          o ^= 1;
        }
        o ^= 1;
      }
    }
    mi = min(mi, co);
    co = 0;
  } while (next_permutation(s, s + 4));
  cout << mi << "\n";
  return 0;
}
