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 main() {
  int n, i, j, b, cnt = 0;
  long long tot;
  char a[5][105][105];
  int arr[5];
  cin >> n;
  for (int k = 0; k < 4; k++) {
    for (i = 0; i < n; i++)
      for (j = 0; j < n; j++) {
        cin >> a[k][i][j];
      }
  }
  char h = '1';
  for (int k = 0; k < 4; k++) {
    h = '1';
    for (i = 0; i < n; i++)
      for (j = 0; j < n; j++) {
        if (a[k][i][j] != h) cnt++;
        if (h == '1')
          h = '0';
        else
          h = '1';
      }
    arr[k] = cnt;
    cnt = 0;
  }
  sort(arr, arr + 4);
  tot = arr[0] + arr[1] + n * n * 2 - arr[2] - arr[3];
  cout << tot;
}
