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 c[2][4], n;
string grid[111];
int count(int st) {
  char cur;
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    if (!st) {
      if (i % 2)
        cur = '1';
      else
        cur = '0';
    } else {
      if (i % 2)
        cur = '0';
      else
        cur = '1';
    }
    for (int j = 0; j < n; j++) {
      if (cur != grid[i][j]) cnt++;
      if (cur == '1')
        cur = '0';
      else
        cur = '1';
    }
  }
  return cnt;
}
int go(int ind, int zs, int os) {
  if (ind == 4) {
    if (zs == os)
      return 0;
    else
      return 1e9;
  }
  return min(go(ind + 1, zs + 1, os) + c[0][ind],
             go(ind + 1, zs, os + 1) + c[1][ind]);
}
int main() {
  cin >> n;
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < n; i++) cin >> grid[i];
    c[0][k] = count(0);
    c[1][k] = count(1);
  }
  cout << go(0, 0, 0) << endl;
}
