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 changeZero[4];
int main() {
  ios::sync_with_stdio(false);
  memset(changeZero, 0, sizeof(changeZero));
  int n;
  cin >> n;
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        char ch;
        cin >> ch;
        if ((((i + j) & 1) && ch == '0') || (!((i + j) & 1) && ch == '1'))
          changeZero[k]++;
      }
    }
  }
  sort(changeZero + 0, changeZero + 4);
  int ans = changeZero[0] + changeZero[1] + ((n * n) << 1) - changeZero[2] -
            changeZero[3];
  cout << ans << endl;
  return 0;
}
