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;
  int map[n][n][4];
  string str;
  for (int i0 = 0; i0 < 4; i0++) {
    for (int i = 0; i < n; i++) {
      cin >> str;
      for (int j = 0; j < n; j++) {
        map[i][j][i0] = 0;
        map[i][j][i0] = (str[j] - '0');
      }
    }
  }
  int sums[4];
  int sum;
  for (int i0 = 0; i0 < 4; i0++) {
    sum = 0;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 == 0 and map[i][j][i0] == 1) sum++;
        if ((i + j) % 2 == 1 and map[i][j][i0] == 0) sum++;
      }
    }
    sums[i0] = sum;
  }
  int min = 1000000;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      if (i != j) {
        int i1, j1;
        if (i != 0 and j != 0)
          i1 = 0;
        else {
          if (i != 1 and j != 1)
            i1 = 1;
          else
            i1 = 2;
        }
        j1 = 6 - (i + j + i1);
        sum = sums[i1] + sums[j1] + 2 * n * n - sums[i] - sums[j];
        if (sum < min) min = sum;
      }
    }
  }
  cout << min << endl;
  return 0;
}
