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;
string str[5];
int n;
int func(int idx, int val) {
  val += 48;
  bool ok = 1;
  int len = n * n;
  int i, cnt = 0;
  for (i = 0; i < len; i++) {
    if (ok) {
      if (str[idx][i] != val) cnt++;
      ok = 0;
    } else {
      if (str[idx][i] == val) cnt++;
      ok = 1;
    }
  }
  return cnt;
}
int main() {
  scanf("%d", &n);
  char st[105];
  string s;
  int i, j, k, p, q, ans = INT_MAX;
  for (i = 0; i < 4; i++) {
    str[i] = "";
    for (j = 0; j < n; j++) {
      scanf("%s", st);
      s = string(st);
      str[i] = str[i] + s;
    }
  }
  vector<int> vec = {0, 1, 2, 3};
  do {
    p = func(vec[0], 0) + func(vec[1], 0) + func(vec[2], 1) + func(vec[3], 1);
    ans = min(ans, p);
  } while (next_permutation(vec.begin(), vec.end()));
  return !printf("%d\n", ans);
}
