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 check_white(vector<vector<int> > &p1, int n) {
  int ans = 0;
  int k = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (p1[i][j] != k) ans++;
      k = (k + 1) % 2;
    }
  }
  return ans;
}
int check_black(vector<vector<int> > &p1, int n) {
  int ans = 0;
  int k = 1;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (p1[i][j] != k) ans++;
      k = (k + 1) % 2;
    }
  }
  return ans;
}
void scan(vector<vector<int> > &p1, int n) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      char c;
      string s;
      cin >> c;
      s += c;
      p1[i][j] = stoi(s);
    }
  }
}
int main() {
  int n;
  cin >> n;
  vector<vector<int> > p1(n, vector<int>(n));
  vector<vector<int> > p2(n, vector<int>(n));
  vector<vector<int> > p3(n, vector<int>(n));
  vector<vector<int> > p4(n, vector<int>(n));
  scan(p1, n);
  scan(p2, n);
  scan(p3, n);
  scan(p4, n);
  vector<pair<int, int> > dos(5);
  dos[1].first = check_white(p1, n);
  dos[1].second = check_black(p1, n);
  dos[2].first = check_white(p2, n);
  dos[2].second = check_black(p2, n);
  dos[3].first = check_white(p3, n);
  dos[3].second = check_black(p3, n);
  dos[4].first = check_white(p4, n);
  dos[4].second = check_black(p4, n);
  int b2 = min(dos[3].first + dos[4].second, dos[4].first + dos[3].second);
  int b1 = dos[3].first + dos[4].first;
  int b3 = dos[3].second + dos[4].second;
  int b4 = dos[1].second + min(b1 + dos[2].second, b2 + dos[2].first);
  int b5 = dos[1].first + min(b3 + dos[2].first, b2 + dos[2].second);
  cout << min(b4, b5);
}
