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 em0[5], em1[5];
int main() {
  memset(em0, 0, sizeof em0);
  memset(em1, 0, sizeof em1);
  int n;
  cin >> n;
  string s;
  cin.ignore();
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < n; i++) {
      getline(cin, s);
      for (int j = 0; j < n; j++) {
        int val = s[j] - '0';
        int pos = (i + j) % 2;
        if (!pos) {
          if (val == 0) {
            em0[k]++;
          } else
            em1[k]++;
        } else {
          if (val == 0) {
            em1[k]++;
          } else
            em0[k]++;
        }
      }
    }
    if (k != 3) getline(cin, s);
  }
  int ans = 987654321;
  int aux1, aux2, aux3;
  aux1 =
      min(em0[0] + em0[1] + em1[2] + em1[3], em0[0] + em1[1] + em0[2] + em1[3]);
  aux2 =
      min(em0[0] + em1[1] + em1[2] + em0[3], em1[0] + em1[1] + em0[2] + em0[3]);
  aux3 =
      min(em1[0] + em0[1] + em1[2] + em0[3], em1[0] + em0[1] + em0[2] + em1[3]);
  aux1 = min(aux1, min(aux2, aux3));
  ans = min(ans, aux1);
  printf("%d\n", ans);
}
