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;
template <typename Tp>
inline void outarr(Tp _array, const std::size_t _N, const char* _delim = " ") {
  Tp end = _array + _N;
  for (Tp current = _array; current != end; ++current) {
    std::cout << *current << _delim;
  }
  std::cout << '\n';
}
using ll = int64_t;
using pii = std::pair<int, int>;
constexpr int INF = INT_MAX;
constexpr int MOD = static_cast<const int>(1e9 + 7);
string arr[4][100];
int perm[4] = {0, 1, 2, 3};
inline int check(int y, int c, int n) {
  int cnt = 0;
  int cur = c;
  for (int i = 0; i < n; ++i) {
    if (i & 1) {
      cur = c ^ 1;
    } else {
      cur = c;
    }
    for (int j = 0; j < n; ++j) {
      if (arr[y][i][j] - '0' != cur) {
        ++cnt;
      }
      cur ^= 1;
    }
  }
  return cnt;
}
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);
  int n;
  cin >> n;
  for (int i = 0; i < (4); ++i) {
    for (int j = 0; j < n; ++j) {
      cin >> arr[i][j];
    }
  }
  int ans = INF;
  do {
    int res = 0;
    for (int i = 0; i < (4); ++i) {
      int col = 0;
      if (i == 1 || i == 2) {
        col = n & 1;
      } else if (i == 3) {
        col = ((n & 1) + (n & 1)) & 1;
      }
      res += check(perm[i], col, n);
    }
    res = min(res, (n + n) * (n + n) - res);
    ans = min(res, ans);
  } while (next_permutation(perm, perm + 4));
  cout << ans << "\n";
  return 0;
}
