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;
string ar[] = {"1234", "1243", "1342", "1324", "1423", "1432", "2341", "2314",
               "2413", "2431", "2134", "2143", "3412", "3421", "3124", "3142",
               "3241", "3214", "4123", "4132", "4231", "4213", "4312", "4321"};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int n;
  cin >> n;
  long long int mt[205][205];
  for (long long int i = 1; i <= 2 * n; i++) {
    for (long long int j = 1; j <= 2 * n; j++) {
      if ((i + j) % 2 == 0)
        mt[i][j] = 0;
      else
        mt[i][j] = 1;
    }
  }
  vector<string> v[5];
  string s;
  for (long long int i = 1; i <= 4; i++) {
    for (long long int j = 1; j <= n; j++) {
      cin >> s;
      v[i].push_back(s);
    }
  }
  long long int ans = 1000000007;
  for (long long int i = 0; i < 24; i++) {
    vector<string> a, b, c, d, vv;
    long long int cn = 0;
    a = v[ar[i][0] - '0'];
    b = v[ar[i][1] - '0'];
    c = v[ar[i][2] - '0'];
    d = v[ar[i][3] - '0'];
    for (long long int j = 0; j < n; j++) {
      s = a[j] + b[j];
      vv.push_back(s);
    }
    for (long long int j = 0; j < n; j++) {
      s = c[j] + d[j];
      vv.push_back(s);
    }
    for (long long int j = 0; j < vv.size(); j++) {
      for (long long int k = 0; k < vv[j].size(); k++) {
        if (vv[j][k] - '0' != mt[j + 1][k + 1]) cn += 1;
      }
    }
    ans = min(ans, cn);
  }
  cout << ans << '\n';
}
