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;
int marks[5][3];
int main() {
  cin >> n;
  for (int k = 0; k < 4; ++k) {
    marks[k][0] = marks[k][1] = 0;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j < n; ++j) {
        char b;
        cin >> b;
        int a = b - 48;
        if (a != 1 && a != 0) assert(false);
        if ((i + j) % 2)
          marks[k][a]++;
        else
          marks[k][1 - a]++;
      }
    }
  }
  int minrecolor = 100000;
  for (int i = 0; i < 4; ++i) {
    for (int j = i + 1; j < 4; ++j) {
      int cnt = 0;
      for (int k = 0; k < 4; ++k) {
        if (k == i || k == j)
          cnt += marks[k][1];
        else
          cnt += marks[k][0];
      }
      minrecolor = min(minrecolor, cnt);
    }
  }
  cout << minrecolor << "\n";
  return 0;
}
