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 answer(vector<vector<char> > b1, vector<vector<char> > b2,
                 vector<vector<char> > b3, vector<vector<char> > b4,
                 vector<vector<char> > config1, vector<vector<char> > config2,
                 long long N) {
  long long ans = 0;
  for (long long i = 0; i < N; i++) {
    for (long long j = 0; j < N; j++) {
      if (b1[i][j] != config1[i][j]) ans = ans + 1;
      if (b2[i][j] != config1[i][j]) ans = ans + 1;
      if (b3[i][j] != config2[i][j]) ans = ans + 1;
      if (b4[i][j] != config2[i][j]) ans = ans + 1;
    }
  }
  return ans;
}
int main() {
  long long N;
  cin >> N;
  vector<vector<char> > b1;
  char color;
  for (long long i = 0; i < N; i++) {
    vector<char> temp;
    for (long long j = 0; j < N; j++) {
      cin >> color;
      temp.push_back(color);
    }
    b1.push_back(temp);
  }
  vector<vector<char> > b2;
  for (long long i = 0; i < N; i++) {
    vector<char> temp;
    for (long long j = 0; j < N; j++) {
      cin >> color;
      temp.push_back(color);
    }
    b2.push_back(temp);
  }
  vector<vector<char> > b3;
  for (long long i = 0; i < N; i++) {
    vector<char> temp;
    for (long long j = 0; j < N; j++) {
      cin >> color;
      temp.push_back(color);
    }
    b3.push_back(temp);
  }
  vector<vector<char> > b4;
  for (long long i = 0; i < N; i++) {
    vector<char> temp;
    for (long long j = 0; j < N; j++) {
      cin >> color;
      temp.push_back(color);
    }
    b4.push_back(temp);
  }
  vector<vector<char> > config1, config2;
  for (long long i = 0; i < N; i++) {
    vector<char> temp1, temp2;
    for (long long j = 0; j < N; j++) {
      if ((i + j) % 2 == 0) {
        temp1.push_back('1');
        temp2.push_back('0');
      } else {
        temp1.push_back('0');
        temp2.push_back('1');
      }
    }
    config1.push_back(temp1);
    config2.push_back(temp2);
  }
  long long finalans = INT_MAX;
  finalans = min(finalans, answer(b1, b2, b3, b4, config1, config2, N));
  finalans = min(finalans, answer(b1, b3, b2, b4, config1, config2, N));
  finalans = min(finalans, answer(b1, b4, b2, b3, config1, config2, N));
  finalans = min(finalans, answer(b1, b2, b3, b4, config2, config1, N));
  finalans = min(finalans, answer(b1, b3, b2, b4, config2, config1, N));
  finalans = min(finalans, answer(b1, b4, b2, b3, config2, config1, N));
  cout << finalans << endl;
}
