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;
string s[4][105];
string t[205];
int per[4];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) cin >> s[i][j];
  }
  per[0] = 0, per[1] = 1, per[2] = 2, per[3] = 3;
  int ans = 1e9;
  do {
    for (int i = 0; i < n; i++) t[i] = s[per[0]][i] + s[per[1]][i];
    for (int i = 0; i < n; i++) t[i + n] = s[per[2]][i] + s[per[3]][i];
    int res1 = 0, res2 = 0;
    for (int i = 0; i < 2 * n; i++) {
      for (int j = 0; j < 2 * n; j++) {
        res1 += (t[i][j] - '0' != (i + j) % 2);
        res2 += (t[i][j] - '0' != (i + j + 1) % 2);
      }
    }
    ans = min(ans, res1);
    ans = min(ans, res2);
  } while (next_permutation(per, per + 4));
  printf("%d\n", ans);
}
