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;
char pat1[101][101];
char pat2[101][101];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i + j) % 2 == 0)
        pat1[i][j] = '1';
      else
        pat1[i][j] = '0';
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i + j) % 2 == 0)
        pat2[i][j] = '0';
      else
        pat2[i][j] = '1';
    }
  }
  long long pt1[4];
  long long pt2[4];
  for (int t = 0; t < 4; t++) {
    long long c1 = 0, c2 = 0;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        char x;
        cin >> x;
        if (x != pat1[i][j]) c1++;
        if (x != pat2[i][j]) c2++;
      }
    }
    pt1[t] = c1;
    pt2[t] = c2;
  }
  long long ans = 1000000000;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      for (int k = 0; k < 4; k++) {
        for (int l = 0; l < 4; l++) {
          if (i == j || i == k || i == l) continue;
          if (j == k || j == l) continue;
          if (k == l) continue;
          long long sum = pt1[i] + pt1[j] + pt2[k] + pt2[l];
          ans = min(ans, sum);
        }
      }
    }
  }
  cout << ans << "\n";
}
