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 n, a[5][110][110], x[5];
char s[110];
int ans = 0;
void dfs(int now, int rem) {
  if (now > 4 && rem == 0) {
    int c = 0;
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        for (int k = 1; k <= 4; k++) {
          c += (a[k][i][j] != (x[k] ^ ((i + j) & 1)));
        }
      }
    }
    ans = min(ans, c);
    return;
  } else if (now > 4) {
    return;
  }
  x[now] = 0;
  dfs(now + 1, rem);
  if (rem) {
    x[now] = 1;
    dfs(now + 1, rem - 1);
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      scanf("%s", s);
      for (int k = 1; k <= n; k++) {
        a[i][j][k] = s[k - 1] - '0';
      }
    }
  }
  ans = 110 * 110 * 110;
  dfs(1, 2);
  printf("%d\n", ans);
}
