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;
const int N = 1e2 + 10;
int a[4][N][N];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      string s;
      cin >> s;
      for (int k = 0; k < n; k++) {
        a[i][j][k] = s[k] - '0';
      }
    }
  }
  vector<int> order = {0, 1, 2, 3};
  int ans = 1e9;
  do {
    int cnt = 0;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 == a[order[0]][i][j]) {
          cnt++;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 == a[order[1]][i][j]) {
          cnt++;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 != a[order[2]][i][j]) {
          cnt++;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 != a[order[3]][i][j]) {
          cnt++;
        }
      }
    }
    ans = min(ans, cnt);
    cnt = 0;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 != a[order[0]][i][j]) {
          cnt++;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 != a[order[1]][i][j]) {
          cnt++;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 == a[order[2]][i][j]) {
          cnt++;
        }
      }
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 == a[order[3]][i][j]) {
          cnt++;
        }
      }
    }
    ans = min(ans, cnt);
  } while (next_permutation(order.begin(), order.end()));
  cout << ans << "\n";
}
