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;
pair<int, int> oddeven(string arr[], int n) {
  int odd = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      int number = n * i + j;
      if ((number & 1) && (arr[i][j] == '1'))
        ++odd;
      else if ((number % 2 == 0) && (arr[i][j] == '0'))
        ++odd;
    }
  }
  int even = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      int number = n * i + j;
      if ((number & 1) && (arr[i][j] == '0'))
        ++even;
      else if ((number % 2 == 0) && (arr[i][j] == '1'))
        ++even;
    }
  }
  return {odd, even};
}
int main() {
  int n;
  cin >> n;
  vector<pair<int, int> > ans;
  for (int i = 0; i < 4; ++i) {
    string arr[n];
    for (int i = 0; i < n; ++i) cin >> arr[i];
    ans.push_back(oddeven(arr, n));
    string s;
    getline(cin, s);
    cin.clear();
  }
  long long anss = 2147483647;
  anss = min(anss,
             0ll + ans[0].first + ans[1].first + ans[2].second + ans[3].second);
  anss = min(anss,
             0ll + ans[0].first + ans[1].second + ans[2].first + ans[3].second);
  anss = min(anss,
             0ll + ans[0].first + ans[1].second + ans[2].second + ans[3].first);
  anss = min(anss,
             0ll + ans[0].second + ans[1].first + ans[2].first + ans[3].second);
  anss = min(anss,
             0ll + ans[0].second + ans[1].first + ans[2].second + ans[3].first);
  anss = min(anss,
             0ll + ans[0].second + ans[1].second + ans[2].first + ans[3].first);
  cout << anss;
}
