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::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  cin >> n;
  vector<vector<string>> c(4);
  vector<pair<int, int>> p(4);
  vector<string> a(2);
  for (int i = 0; i < 2; ++i) a[i].resize(n);
  for (int i = 0; i < n; ++i) {
    a[0][i] = (i % 2) ? '0' : '1';
    a[1][i] = (i % 2) ? '1' : '0';
  }
  for (int i = 0; i < 4; ++i) {
    c[i].resize(n);
    for (int j = 0; j < n; ++j) {
      cin >> c[i][j];
    }
  }
  for (int i = 0; i < 4; ++i) {
    for (int j = 0; j < n; ++j) {
      for (int k = 0; k < n; ++k) {
        for (int l = 0; l < 2; ++l) {
          if (l == 0 && c[i][j][k] != a[0][k])
            (j % 2) ? p[i].first++ : p[i].second++;
          else if (l == 1 && c[i][j][k] != a[1][k])
            (j % 2) ? p[i].second++ : p[i].first++;
        }
      }
    }
  }
  int ans = INT_MAX;
  vector<int> pm(4);
  for (int i = 0; i < 4; ++i) pm[i] = i;
  do {
    ans = min(ans, p[pm[0]].first + p[pm[1]].second + p[pm[2]].second +
                       p[pm[3]].first);
    ans = min(ans, p[pm[0]].second + p[pm[1]].first + p[pm[2]].first +
                       p[pm[3]].second);
  } while (next_permutation(pm.begin(), pm.end()));
  cout << ans << "\n";
}
