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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  vector<pair<long long, long long> > v;
  for (long long i = 1; i <= 4; i++) {
    string s[n];
    for (long long j = 0; j < n; j++) cin >> s[j];
    long long zero, one;
    long long temp = 0;
    char c = '1';
    for (long long j = 0; j < n; j++) {
      if (c == '1')
        c = '0';
      else
        c = '1';
      for (long long k = 0; k < n; k += 2) {
        if (k == 0 && s[j][k] != c) temp++;
        if ((k + 1) < n && s[j][k + 1] == c) temp++;
        if ((k + 2) < n && s[j][k + 2] != c) temp++;
      }
    }
    zero = temp;
    temp = 0;
    c = '0';
    for (long long j = 0; j < n; j++) {
      if (c == '1')
        c = '0';
      else
        c = '1';
      for (long long k = 0; k < n; k += 2) {
        if (k == 0 && s[j][k] != c) temp++;
        if ((k + 1) < n && s[j][k + 1] == c) temp++;
        if ((k + 2) < n && s[j][k + 2] != c) temp++;
      }
    }
    one = temp;
    v.push_back(make_pair(zero, one));
  }
  long long mini = 1e18;
  long long temp = v[0].first + v[1].first + v[2].second + v[3].second;
  mini = min(mini, temp);
  temp = v[0].first + v[2].first + v[1].second + v[3].second;
  mini = min(mini, temp);
  temp = v[0].first + v[3].first + v[1].second + v[2].second;
  mini = min(mini, temp);
  temp = v[0].second + v[1].second + v[2].first + v[3].first;
  mini = min(mini, temp);
  temp = v[0].second + v[2].second + v[1].first + v[3].first;
  mini = min(mini, temp);
  temp = v[0].second + v[3].second + v[1].first + v[2].first;
  mini = min(mini, temp);
  cout << mini << '\n';
  return 0;
}
