Problem: A maze is composed of a grid of H \times W squares - H vertical, W horizontal.

The square at the i-th row from the top and the j-th column from the left - (i,j) - is a wall if S_{ij} is `#` and a road if S_{ij} is `.`.

There is a magician in (C_h,C_w). He can do the following two kinds of moves:

* Move A: Walk to a road square that is vertically or horizontally adjacent to the square he is currently in.
* Move B: Use magic to warp himself to a road square in the 5\times 5 area centered at the square he is currently in.



In either case, he cannot go out of the maze.

At least how many times does he need to use the magic to reach (D_h, D_w)?

Constraints

* 1 \leq H,W \leq 10^3
* 1 \leq C_h,D_h \leq H
* 1 \leq C_w,D_w \leq W
* S_{ij} is `#` or `.`.
* S_{C_h C_w} and S_{D_h D_w} are `.`.
* (C_h,C_w) \neq (D_h,D_w)

Input

Input is given from Standard Input in the following format:


H W
C_h C_w
D_h D_w
S_{11}\ldots S_{1W}
\vdots
S_{H1}\ldots S_{HW}


Output

Print the minimum number of times the magician needs to use the magic. If he cannot reach (D_h,D_w), print `-1` instead.

Examples

Input

4 4
1 1
4 4
..#.
..#.
.#..
.#..


Output

1


Input

4 4
1 4
4 1
.##.


.##.


Output

-1


Input

4 4
2 2
3 3
....
....
....
....


Output

0


Input

4 5
1 2
2 5
.###
.
..##
..##


Output

2

Solution (in JAVA):

Solution:
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
What do you think? What do you think?
1st on Billboard, what do you think of it
Next is a Grammy, what do you think of it
However you think, I’m sorry, but shit, I have no fcking interest
*******************************
I'm standing on top of my Monopoly board
That means I'm on top of my game and it don't stop
til my hip don't hop anymore
https://www.a2oj.com/Ladder16.html
*******************************
300iq as writer = Sad!
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class Main
   {
      public static void main(String hi[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         int M = Integer.parseInt(st.nextToken());
         st = new StringTokenizer(infile.readLine());
         int sx = Integer.parseInt(st.nextToken())-1;
         int sy = Integer.parseInt(st.nextToken())-1;
         st = new StringTokenizer(infile.readLine());
         int ex = Integer.parseInt(st.nextToken())-1;
         int ey = Integer.parseInt(st.nextToken())-1;
         char[][] label = new char[N][M];
         for(int i=0; i < N; i++)
            label[i] = infile.readLine().toCharArray();
         int[][] grid = new int[N][M];
         for(int i=0; i < N; i++)
            Arrays.fill(grid[i], Integer.MAX_VALUE);
         ArrayDeque<Integer> q = new ArrayDeque<Integer>();
         q.add(sx);  q.add(sy);
         grid[sx][sy] = 0;
         while(q.size() > 0)
         {
            int R = q.poll();
            int C = q.poll();
            //normal moves
            if(R > 0 && grid[R-1][C] > grid[R][C] && label[R-1][C] == '.')
            {
               grid[R-1][C] = grid[R][C];
               q.addFirst(C); q.addFirst(R-1);
            }
            if(C > 0 && grid[R][C-1] > grid[R][C] && label[R][C-1] == '.')
            {
               grid[R][C-1] = grid[R][C];
               q.addFirst(C-1);  q.addFirst(R);
            }
            if(R+1 < N && grid[R+1][C] > grid[R][C] && label[R+1][C] == '.')
            {
               grid[R+1][C] = grid[R][C];
               q.addFirst(C); q.addFirst(R+1);
            }
            if(C+1 < M && grid[R][C+1] > grid[R][C] && label[R][C+1] == '.')
            {
               grid[R][C+1] = grid[R][C];
               q.addFirst(C+1);  q.addFirst(R);
            }
            //magic
            for(int dx=-2; dx <= 2; dx++)
               for(int dy=-2; dy <= 2; dy++)
               {
                  int newx = R+dx;
                  int newy = C+dy;
                  if(Math.min(newx,newy) < 0 || newx >= N || newy >= M || label[newx][newy] == '#')
                     continue;
                  if(grid[newx][newy] > grid[R][C]+1)
                  {
                     grid[newx][newy] = grid[R][C]+1;
                     q.add(newx);   q.add(newy);
                  }
               }
         }
         int res = grid[ex][ey];
         if(res == Integer.MAX_VALUE)
            res = -1;
         System.out.println(res);
      }
   }