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;
const int MAXN = 1e2 + 7;
long long int n, jad[4][MAXN][MAXN];
long long int check(long long int ul[MAXN][MAXN], long long int ur[MAXN][MAXN],
                    long long int dl[MAXN][MAXN], long long int dr[MAXN][MAXN],
                    long long int st) {
  long long int ans = 0;
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < n; j++) {
      if (st != ul[i][j]) ans++;
      st = 1 - st;
    }
    for (long long int j = 0; j < n; j++) {
      if (st != ur[i][j]) ans++;
      st = 1 - st;
    }
    st = 1 - st;
  }
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < n; j++) {
      if (st != dl[i][j]) ans++;
      st = 1 - st;
    }
    for (long long int j = 0; j < n; j++) {
      if (st != dr[i][j]) ans++;
      st = 1 - st;
    }
    st = 1 - st;
  }
  return ans;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  long long int per[] = {0, 1, 2, 3};
  long long int ans = 1e9;
  for (long long int ii = 0; ii < 4; ii++) {
    for (long long int i = 0; i < n; i++) {
      for (long long int j = 0; j < n; j++) {
        char c;
        cin >> c;
        jad[ii][i][j] = c - '0';
      }
    }
  }
  do {
    ans =
        min(ans, check(jad[per[0]], jad[per[1]], jad[per[2]], jad[per[3]], 0));
    ans =
        min(ans, check(jad[per[0]], jad[per[1]], jad[per[2]], jad[per[3]], 1));
  } while (next_permutation(per, per + 4));
  cout << ans;
}
