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 one(string s) {
  long long k = 0, c = 1;
  for (long long p = 0; p < s.size(); p++) {
    k += ((c + '0') != s[p]);
    c = 1 - c;
  }
  return k;
}
long long ze(string s) {
  long long k = 0, c = 0;
  for (long long p = 0; p < s.size(); p++) {
    k += ((c + '0') != s[p]);
    c = 1 - c;
  }
  return k;
}
int main() {
  long long t, i, j, k, ans, m, n, x, y;
  t = 1;
  while (t--) {
    cin >> n;
    string s, a = "", b = "", c = "", d = "";
    for (long long p = 0; p < n; p++) {
      cin >> s;
      a += s;
    }
    for (long long p = 0; p < n; p++) {
      cin >> s;
      b += s;
    }
    for (long long p = 0; p < n; p++) {
      cin >> s;
      c += s;
    }
    for (long long p = 0; p < n; p++) {
      cin >> s;
      d += s;
    }
    vector<long long> o, z;
    o.push_back(one(a));
    o.push_back(one(b));
    o.push_back(one(c));
    o.push_back(one(d));
    z.push_back(ze(a));
    z.push_back(ze(b));
    z.push_back(ze(c));
    z.push_back(ze(d));
    sort(o.begin(), o.end());
    sort(z.begin(), z.end());
    cout << o[0] + o[1] + z[0] + z[1];
  }
  return 0;
}
