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;
const int N = 100009;
string s[4][109];
int a[4], b[4];
int main() {
  int n;
  cin >> n;
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < n; i++) {
      cin >> s[k][i];
    }
  }
  for (int k = 0; k < 4; k++) {
    int x = n * n;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (x % 2 == 1) {
          if (s[k][i][j] == '0')
            a[k]++;
          else
            b[k]++;
        } else {
          if (s[k][i][j] == '1')
            a[k]++;
          else
            b[k]++;
        }
        x--;
      }
    }
  }
  int ans = INT_MAX;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      if (j != i) {
        for (int k = 0; k < 4; k++) {
          if (k != i && k != j) {
            for (int l = 0; l < 4; l++) {
              if (l != i && l != j && l != k) {
                ans = min(ans, a[i] + a[j] + b[k] + b[l]);
              }
            }
          }
        }
      }
    }
  }
  cout << ans << "\n";
  return 0;
}
