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;
string part[4][1000];
string board[1000];
int perm[4];
void create_board() {
  for (int i = 0; i < n; i++) {
    board[i] = part[perm[0]][i];
    for (int j = 0; j < n; j++) {
      board[i] += part[perm[2]][i][j];
    }
  }
  for (int i = n; i < 2 * n; i++) {
    board[i] = part[perm[1]][i - n];
    for (int j = 0; j < n; j++) {
      board[i] += part[perm[3]][i - n][j];
    }
  }
}
int solve(char st) {
  int ret = 0;
  for (int i = 0; i < 2 * n; i++) {
    for (int j = 0; j < 2 * n; j++) {
      if ((i + j) % 2 == 0) {
        if (board[i][j] != st) ret++;
      } else {
        if (board[i][j] == st) ret++;
      }
    }
  }
  return ret;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      cin >> part[i][j];
    }
  }
  for (int i = 0; i < 4; i++) perm[i] = i;
  int ret = 1e9;
  do {
    create_board();
    ret = min(ret, min(solve('1'), solve('0')));
  } while (next_permutation(perm, perm + 4));
  cout << ret << endl;
  return 0;
}
