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;
bool delimiter, unof = 1;
inline namespace IO {
template <class t>
using con = vector<t>;
template <class t, class u>
using pi = pair<t, u>;
template <class t, class u>
istream& operator>>(istream& is, pi<t, u>& pr) {
  is >> pr.first >> pr.second;
  return is;
}
template <class t, class u>
ostream& operator<<(ostream& os, const pi<t, u>& pr) {
  delimiter = 0;
  os << (unof ? "\t{" : "") << pr.first << (unof ? " , " : " ") << pr.second
     << (unof ? "}" : "");
  return os;
}
template <class t>
istream& operator>>(istream& is, con<t>& v) {
  for (auto& i : v) is >> i;
  return is;
}
template <class t>
ostream& operator<<(ostream& os, const con<t>& v) {
  delimiter = 1;
  os << (unof ? "[" : "");
  bool fst = 0;
  for (auto e : v)
    os << (unof and fst ? ", " : "") << e << (delimiter ? ' ' : '\n'), fst = 1;
  os << (unof ? "]" : "");
  return os;
}
}  // namespace IO
const int N = 2e5 + 9, mod = 1e9 + 7;
int n;
int solve(char top_lf, con<string> grid) {
  int ret = 0;
  for (int i = 0; i < n << 1; ++i)
    for (int j = 0; j < n << 1; ++j) {
      if (grid[i][j] == top_lf and ((i + j) & 1)) ++ret;
      if (grid[i][j] != top_lf and !((i + j) & 1)) ++ret;
    }
  return ret;
}
int go(con<int> seq, con<con<string>> vec) {
  for (int i = 0; i < n; ++i) {
    vec[seq[0]][i] += vec[seq[1]][i];
    vec[seq[2]][i] += vec[seq[3]][i];
  }
  for (int i = 0; i < n; ++i) {
    vec[seq[0]].push_back(vec[seq[2]][i]);
  }
  return min(solve('0', vec[seq[0]]), solve('1', vec[seq[0]]));
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  con<con<string>> vec(4);
  for (auto& i : vec) {
    i.resize(n);
    cin >> i;
  }
  int ans = 4 * n * n;
  con<int> _ = {0, 1, 2, 3};
  do {
    ans = min(ans, go(_, vec));
  } while (next_permutation(_.begin(), _.end()));
  cout << ans;
  return 0;
}
