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() {
  long long t, m, n, i, j, k = 0, l = 0, p = 0, q, ct;
  cin >> n;
  char a[n][n];
  long long b[5], c[5];
  j = 4;
  for (k = 0; k < 4; k++) {
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) cin >> a[i][j];
    }
    l = 1;
    ct = 0;
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        if ((a[i][j] - '0') != l) ct++;
        l = abs(l - 1);
      }
    }
    b[k] = ct;
    l = 0;
    ct = 0;
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        if ((a[i][j] - '0') != l) ct++;
        l = abs(l - 1);
      }
    }
    c[k] = ct;
  }
  ct = 0;
  sort(b, b + 4);
  sort(c, c + 4);
  ct += b[0] + b[1] + c[0] + c[1];
  cout << ct << endl;
  return 0;
}
