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 n;
string b[4][110];
string board[210];
vector<int> perm;
void clean_board() {
  for (int i = 0; i < 2 * n; ++i) board[i] = "";
}
void form_board() {
  for (int i = 0; i < 4; ++i) {
    for (int j = 0; j < n; ++j) {
      board[(i > 1 ? n : 0) + j] += b[perm[i]][j];
    }
  }
}
int calc_change(int flag) {
  string mask1 = "";
  string mask2 = "";
  for (int i = 0; i < n; ++i) {
    mask1 += "10";
    mask2 += "01";
  }
  if (flag) swap(mask1, mask2);
  int change = 0;
  for (int i = 0; i < 2 * n; ++i) {
    for (int j = 0; j < 2 * n; ++j) {
      if (i % 2) {
        if (board[i][j] != mask1[j]) change++;
      } else {
        if (board[i][j] != mask2[j]) change++;
      }
    }
  }
  return change;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (int a = 0; a < 4; ++a) {
    for (int i = 0; i < n; ++i) {
      cin >> b[a][i];
    }
  }
  int mini = 1e5;
  perm = {0, 1, 2, 3};
  do {
    clean_board();
    form_board();
    mini = min(mini, min(calc_change(1), calc_change(0)));
  } while (next_permutation(perm.begin(), perm.end()));
  cout << mini << endl;
}
