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;
char s[5][105][105];
char m[3][105][105];
int ans[3][5];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  for (int i = 1; i <= 2; i++) {
    for (int j = 1; j <= 100; j++) {
      for (int k = 1; k <= 100; k++) {
        if ((i + j + k) % 2 == 1) {
          m[i][j][k] = '1';
        } else
          m[i][j][k] = '0';
      }
    }
  }
  memset(ans, 0, sizeof(ans));
  cin >> n;
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      for (int k = 1; k <= n; k++) {
        cin >> s[i][j][k];
      }
    }
  }
  for (int i = 1; i <= 2; i++) {
    for (int j = 1; j <= 4; j++) {
      for (int k = 1; k <= n; k++) {
        for (int r = 1; r <= n; r++) {
          if (s[j][k][r] != m[i][k][r]) {
            ans[i][j]++;
          }
        }
      }
    }
  }
  int result = 1e6;
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= 4; j++) {
      if (i == j) continue;
      for (int k = 1; k <= 4; k++) {
        if (i == k || j == k) continue;
        result = min(
            result, ans[1][i] + ans[1][j] + ans[2][k] + ans[2][10 - i - j - k]);
      }
    }
  }
  cout << result << endl;
  return 0;
}
