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 INF = 1000 * 1000 * 1000 + 47;
const long long LINF = (long long)INF * INF;
const int MAX = 2e5;
const double EPS = 1e-9;
const double PI = acos(-1.);
int n;
int a[4][101][101];
int paint(int x, int col) {
  int cnt = 0;
  for (int i = (0); i < (n); ++i) {
    for (int j = (0); j < (n); ++j) {
      if (a[x][i][j] % 2 != (i + j + col) % 2) {
        cnt++;
      }
    }
  }
  return cnt;
}
int main() {
  ios_base::sync_with_stdio(0);
  int best = INF;
  cin >> n;
  for (int i = (0); i < (4); ++i) {
    for (int j = (0); j < (n); ++j) {
      string second;
      cin >> second;
      for (int k = (0); k < (n); ++k) {
        a[i][j][k] = second[k] - '0';
      }
    }
  }
  int p[4];
  for (int c = (0); c < (2); ++c) {
    for (int i = (0); i < (4); ++i) p[i] = i;
    do {
      int cur = 0;
      for (int i = (0); i < (4); ++i) {
        cur += paint(p[i], (i + c) % 2);
      }
      best = min(best, cur);
    } while (next_permutation(p, p + 4));
  }
  cout << best << endl;
}
