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 ans = 1e9;
string s[4][102];
int c1(int x, int n) {
  int cn = 0;
  string c, c1;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i + j) % 2 == 0)
        c = "1";
      else
        c = "0";
      c1 = s[x][i][j];
      if (c1 != c) cn++;
    }
  }
  return cn;
}
int c0(int x, int n) {
  int cn = 0;
  string c, c1;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i + j) % 2 == 0)
        c = "0";
      else
        c = "1";
      c1 = s[x][i][j];
      if (c1 != c) cn++;
    }
  }
  return cn;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int tt = 1;
  while (tt--) {
    int n;
    cin >> n;
    for (int i = 0; i < 4; i++) {
      for (int j = 0; j < n; j++) cin >> s[i][j];
    }
    for (int i = 0; i < 4; i++) {
      for (int j = i + 1; j < 4; j++) {
        int tmp = c1(i, n) + c1(j, n);
        for (int l = 0; l < 4; l++) {
          if (l != i && l != j) tmp += c0(l, n);
        }
        ans = min(ans, tmp);
      }
    }
    cout << ans;
  }
}
