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;
long long one[5] = {0}, zero[5] = {0};
int main() {
  long long n, i, j, k, on, ze, a, s, ans = 0;
  cin >> n;
  char line[200];
  getchar();
  for (i = 0; i < 4; i++) {
    on = ze = s = 0;
    for (j = 0; j < n; j++) {
      scanf("%s", line);
      for (k = 0; k < n; k++) {
        if (j == 0 && k == 0 && line[k] == '1') {
          on++;
          a = 1;
        } else if (j == 0 && k == 0 && line[k] == '0') {
          ze++;
          a = 0;
        }
        if (on != 0) {
          if (line[k] - '0' != a) {
            s++;
          }
          a = 1 - a;
        } else if (ze != 0) {
          if (line[k] - '0' != a) {
            s++;
          }
          a = 1 - a;
        }
      }
      if (i != 3) getchar();
    }
    if (on == 1) {
      one[i] = s;
      zero[i] = n * n - s;
    } else {
      zero[i] = s;
      one[i] = n * n - s;
    }
  }
  long long node1 = 0, node2 = 0;
  sort(one, one + 4);
  for (i = 0; i < 2; i++) {
    ans += one[i];
  }
  for (i = 0; i < 4; i++) {
    if (n * n - zero[i] == one[1] && node1 == 0) {
      node1 = 1;
      continue;
    }
    if (n * n - zero[i] == one[0] && node2 == 0) {
      node2 = 1;
      continue;
    }
    ans += zero[i];
  }
  cout << ans << endl;
  return 0;
}
