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:

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Main {

   private static final String INPUT_FILE_PATH = "";

   void solve() {
      int h = in.nextInt(), w = in.nextInt();
      int ch = in.nextInt(), cw = in.nextInt();
      ch--; cw--;
      int dh = in.nextInt(), dw = in.nextInt();
      dh--; dw--;
      char[][] s = new char[h][w];
      for (int i = 0; i < h; i++) {
         s[i] = in.nextToken().toCharArray();
      }

      int[][] dist = new int[h][w];
      for (int i = 0; i < h; i++) Arrays.fill(dist[i], -1);
      dist[ch][cw] = 0;

      PriorityQueue<State> pq = new PriorityQueue<>();
      pq.add(new State(0, ch, cw));
      while (!pq.isEmpty()) {
         State top = pq.poll();
         if (top.h == dh && top.w == dw) {
            out.println(top.d);
            return;
         }

         for (int i = Math.max(0, top.h - 1); i <= Math.min(h - 1, top.h + 1); i++) {
            for (int j = Math.max(0, top.w - 1); j <= Math.min(w - 1, top.w + 1); j++) {
               if (i == top.h && j == top.w) continue;
               if (i != top.h && j != top.w) continue;
               if (s[i][j] == '#') continue;
               if (dist[i][j] != -1 && top.d >= dist[i][j]) continue;
               dist[i][j] = top.d;
               pq.add(new State(top.d, i, j));
            }
         }

         for (int i = Math.max(0, top.h - 2); i <= Math.min(h - 1, top.h + 2); i++) {
            for (int j = Math.max(0, top.w - 2); j <= Math.min(w - 1, top.w + 2); j++) {
               if (i == top.h && j == top.w) continue;
               if (s[i][j] == '#') continue;
               if (dist[i][j] != -1 && top.d + 1 >= dist[i][j]) continue;
               dist[i][j] = top.d + 1;
               pq.add(new State(top.d + 1, i, j));
            }
         }

      }

      out.println(-1);
   }

   static class State implements Comparable<State> {
      int d;
      int h;
      int w;

      public State(int d, int h, int w) {
         this.d = d;
         this.h = h;
         this.w = w;
      }

      public int compareTo(State other) {
         return Integer.compare(this.d, other.d);
      }
   }

   private final InputReader in;
   private final PrintWriter out;

   private Main(InputReader in, PrintWriter out) {
      this.in = in;
      this.out = out;
   }

   private static class InputReader {
      private BufferedReader br;
      private StringTokenizer st;

      public InputReader(InputStream inputStream) {
         this.br = new BufferedReader(new InputStreamReader(inputStream), 32768);
         this.st = null;
      }

      public String nextToken() {
         while (st == null || !st.hasMoreTokens()) {
            try {
               st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
               throw new RuntimeException(e);
            }
         }
         return st.nextToken();
      }

      public int nextInt() {
         return Integer.parseInt(nextToken());
      }

      public long nextLong() {
         return Long.parseLong(nextToken());
      }

      public double nextDouble() {
         return Double.parseDouble(nextToken());
      }
   }

   public static void main(String[] args) throws Exception {
      InputStream inputStream = INPUT_FILE_PATH.isEmpty()
         ? System.in
         : new FileInputStream(new File(INPUT_FILE_PATH));
      OutputStream outputStream = System.out;

      InputReader inputReader = new InputReader(inputStream);
      PrintWriter printWriter = new PrintWriter(outputStream);

      new Main(inputReader, printWriter).solve();

      printWriter.close();
   }

}