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;
long long n;
char a[7][505][505];
long long ar[5];
long long arr[505][505];
long long getmin(long long f[]) {
  for (int i = 1; i <= 2 * n; i++)
    arr[i][2 * n + 1] = arr[i][0] = arr[0][i] = arr[2 * n + 1][i] = -1;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      arr[i][j] = a[f[1]][i][j] - '0';
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = n + 1; j <= 2 * n; j++) {
      arr[i][j] = a[f[2]][i][j - n] - '0';
    }
  }
  for (int i = n + 1; i <= 2 * n; i++) {
    for (int j = 1; j <= n; j++) {
      arr[i][j] = a[f[3]][i - n][j] - '0';
    }
  }
  for (int i = n + 1; i <= 2 * n; i++) {
    for (int j = n + 1; j <= 2 * n; j++) {
      arr[i][j] = a[f[4]][i - n][j - n] - '0';
    }
  }
  long long cnt = 0;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if (arr[i][j] == arr[i][j - 1] or arr[i][j] == arr[i - 1][j]) {
        cnt++;
        arr[i][j] = arr[i][j] + 1;
        arr[i][j] %= 2;
      }
    }
  }
  return min(cnt, 4 * n * n - cnt);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      for (int j1 = 1; j1 <= n; j1++) {
        cin >> a[i][j][j1];
      }
    }
  }
  for (int i = 1; i <= 4; i++) ar[i] = i;
  long long ans = 1e18;
  ans = min(ans, getmin(ar));
  while (next_permutation(ar + 1, ar + 5)) {
    ans = min(ans, getmin(ar));
  }
  cout << ans;
}
