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 a[5][105][105], n;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= 4; i++)
    for (int j = 1; j <= n; j++)
      for (int k = 1; k <= n; k++) scanf("%01d", &a[i][j][k]);
  int ans = 100000;
  int id[5] = {0, 1, 2, 3, 4};
  do {
    int tcnt1 = 0, tcnt2 = 0;
    for (int i = 1; i <= n; i++)
      for (int j = 1; j <= n; j++) {
        tcnt1 += a[id[1]][i][j] != ((i + j) & 1);
        tcnt2 += a[id[1]][i][j] == ((i + j) & 1);
        tcnt1 += a[id[2]][i][j] != ((i + n + j) & 1);
        tcnt2 += a[id[2]][i][j] == ((i + n + j) & 1);
        tcnt1 += a[id[3]][i][j] != ((i + n + j) & 1);
        tcnt2 += a[id[3]][i][j] == ((i + n + j) & 1);
        tcnt1 += a[id[4]][i][j] != ((i + 2 * n + j) & 1);
        tcnt2 += a[id[4]][i][j] == ((i + 2 * n + j) & 1);
      }
    ans = min(ans, min(tcnt1, tcnt2));
  } while (next_permutation(id + 1, id + 4 + 1));
  printf("%d\n", ans);
}
