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;
const int MAXN = 1e2 + 3;
char a[4][MAXN][MAXN];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) scanf("%s", a[i][j]);
  }
  int dif[4];
  for (int k = 0; k < 4; k++) {
    dif[k] = 0;
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++) dif[k] += (i + j) % 2 == a[k][i][j] - '0';
  }
  int minn = 4 * n * n;
  int ans = 3000000;
  int xx[6][4] = {{1, 0, 1, 0}, {1, 1, 0, 0}, {1, 0, 0, 1},
                  {0, 0, 1, 1}, {0, 1, 0, 1}, {0, 1, 1, 0}};
  for (int i = 0; i < 6; i++) {
    int sum = 0;
    for (int j = 0; j < 4; j++) {
      if (xx[i][j]) {
        sum += dif[j];
      } else
        sum += n * n - dif[j];
    }
    ans = min(ans, sum);
  }
  cout << ans << endl;
  return 0;
}
