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>
std::vector<char> one_way, two_way;
static long long goint(std::vector<std::vector<char>>& board,
                       std::vector<std::vector<char>>& layout) {
  long long ret = 0;
  for (long long i = 0; i < board.size(); ++i) {
    for (long long j = 0; j < board[i].size(); ++j) {
      ret += board[i][j] != layout[i % 2][j];
    }
  }
  return ret;
}
static long long go(std::vector<std::vector<char>>& board) {
  std::vector<std::vector<char>> option = {one_way, two_way};
  long long a = goint(board, option);
  std::reverse(option.begin(), option.end());
  long long b = goint(board, option);
  return std::min(a, b);
}
int main(void) {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  long long n;
  std::cin >> n;
  std::vector<std::vector<std::string>> boards(4, std::vector<std::string>(n));
  for (auto& board : boards) {
    for (auto& row : board) std::cin >> row;
  }
  one_way.resize(2 * n);
  two_way.resize(2 * n);
  char start = '1';
  for (long long i = 0; i < one_way.size(); ++i) {
    one_way[i] = start;
    start = start == '1' ? '0' : '1';
    two_way[i] = start;
  }
  std::vector<long long> perm = {0, 1, 2, 3};
  long long ret = 4 * n * n;
  do {
    std::vector<std::vector<char>> one_board(2 * n, std::vector<char>(2 * n));
    for (long long i = 0; i < n; ++i)
      for (long long j = 0; j < n; ++j) one_board[i][j] = boards[perm[0]][i][j];
    for (long long i = 0; i < n; ++i)
      for (long long j = 0; j < n; ++j)
        one_board[i][j + n] = boards[perm[1]][i][j];
    for (long long i = 0; i < n; ++i)
      for (long long j = 0; j < n; ++j)
        one_board[i + n][j] = boards[perm[2]][i][j];
    for (long long i = 0; i < n; ++i)
      for (long long j = 0; j < n; ++j)
        one_board[i + n][j + n] = boards[perm[3]][i][j];
    long long va = go(one_board);
    ret = std::min(ret, va);
  } while (std::next_permutation(perm.begin(), perm.end()));
  std::cout << ret << "\n";
  return 0;
}
