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, i, j, n, k, x, c1 = 0, c2 = 0, mn = 10000000;
  cin >> n;
  vector<long long> v1, v2;
  char ch[n + 1][n + 1];
  for (k = 0; k < 4; k++) {
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        cin >> ch[i][j];
        if ((i + j) % 2 == 0) {
          if (ch[i][j] == '1')
            c1++;
          else
            c2++;
        } else {
          if (ch[i][j] == '0')
            c1++;
          else
            c2++;
        }
      }
    }
    v1.push_back(c1);
    v2.push_back(c2);
    c1 = 0;
    c2 = 0;
  }
  mn = min(v1[0] + v1[1] + v2[2] + v2[3], mn);
  mn = min(v1[0] + v1[2] + v2[1] + v2[3], mn);
  mn = min(v1[0] + v1[3] + v2[1] + v2[2], mn);
  mn = min(v1[1] + v1[2] + v2[0] + v2[3], mn);
  mn = min(v1[1] + v1[3] + v2[0] + v2[2], mn);
  mn = min(v1[2] + v1[3] + v2[1] + v2[0], mn);
  cout << mn;
}
