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 n, ans, chess[5][100][100], sumZero[5], sumOne[5];
vector<int> zero, one;
string s;
int main() {
  cin >> n;
  for (int k = 1; k < 5; k++) {
    for (int i = 1; i <= n; i++) {
      cin >> s;
      for (int j = 1; j <= n; j++) {
        chess[k][i][j] = (int)s[j - 1] - '0';
      }
    }
  }
  for (int k = 1; k < 5; k++) {
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        if ((i + j) & 1) {
          if (chess[k][i][j])
            sumOne[k]++;
          else
            sumZero[k]++;
        } else {
          if (chess[k][i][j] == 0)
            sumOne[k]++;
          else
            sumZero[k]++;
        }
      }
    }
    one.push_back(sumOne[k]);
    zero.push_back(sumZero[k]);
  }
  sort(one.begin(), one.end());
  sort(zero.begin(), zero.end());
  for (int i = 0; i < 2; i++) {
    ans += zero[i];
    ans += one[i];
  }
  cout << ans;
}
