Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

1

For example, by walking to (2,2) and then using the magic to travel to (4,4), just one use of magic is enough.

Note that he cannot walk diagonally.

Sample Input 2

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

Sample Output 2

-1

He cannot move from there.

Sample Input 3

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

Sample Output 3

0

No use of magic is needed.

Sample Input 4

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

Sample Output 4

2

Solution in Java (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;
import java.lang.*;

public class Main {
    public static MyScanner scan;
    public static PrintWriter out;
    public static void main(String[] args) {
        scan=new MyScanner();
        out=new PrintWriter(new BufferedOutputStream(System.out));

        int t=1;
//        int t=scan.nextInt();
        while(t-->0) {

            h=scan.nextInt();
            w=scan.nextInt();
            int startX=scan.nextInt()-1,startY=scan.nextInt()-1,endX=scan.nextInt()-1,endY=scan.nextInt()-1,max=(int)1e7;
            char[][] maze=new char[h][w];
            int[][] cost=new int[h][w];
            int[] dirX={1,-1,0,0},dirY={0,0,1,-1};
            //djikstra init
            for(int i=0;i<h;i++) {
                String s=scan.nextLine();
                for(int j=0;j<w;j++) {
                    maze[i][j]=s.charAt(j);
                    cost[i][j]=max;
                }
            }

            //bfs
            ArrayDeque<Integer> queX=new ArrayDeque<>(),queY=new ArrayDeque<>();
            queX.add(startX);
            queY.add(startY);
            cost[startX][startY]=0;
            while(queX.size()>0) {
//                int size=queX.size();
//                while(size-->0) {
                    int curX=queX.poll(),curY=queY.poll();
                    //add adj
                    for(int c=0;c<4;c++) {
                        int nextX=curX+dirX[c],nextY=curY+dirY[c];
                        if(!legal(nextX,nextY,maze)) continue;
                        if(cost[nextX][nextY]>cost[curX][curY]) {
                            cost[nextX][nextY]=cost[curX][curY];
                            queX.add(nextX);
                            queY.add(nextY);
                        }
                    }
                    //teleport
                    for(int i=-2;i<=2;i++) {
                        for(int j=-2;j<=2;j++) {
                            int nextX=curX+i,nextY=curY+j;
                            if(!legal(nextX,nextY,maze)) continue;
                            if(cost[nextX][nextY]>cost[curX][curY]+1) {
                                cost[nextX][nextY]=cost[curX][curY]+1;
                                queX.add(nextX);
                                queY.add(nextY);
                            }
                        }
                    }
//                }
            } out.println((cost[endX][endY]==max)?-1:cost[endX][endY]);
        }
        out.close();
    }

    static int h,w;
    static boolean legal(int x,int y,char[][] maze) {
        if(x>=0&&y>=0&&x<h&&y<w&&maze[x][y]!='#') return true;
        return false;
    }

    //scanner
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static int[] nextIntArray(int n) {
        int[] a=new int[n];
        for(int c=0;c<n;c++) a[c]=scan.nextInt();
        return a;
    }

    public static Integer[] nextIntegerArray(int n) {
        Integer[] a=new Integer[n];
        for(int c=0;c<n;c++) a[c]=scan.nextInt();
        return a;
    }

    public static int[][] nextIntMatrix(int n,int m) {
        int[][] a=new int[n][m];
        for(int i=0;i<n;i++) for(int j=0;j<m;j++) a[i][j]=scan.nextInt();
        return a;
    }

    public static Integer[][] nextIntegerMatrix(int n,int m) {
        Integer[][] a=new Integer[n][m];
        for(int i=0;i<n;i++) for(int j=0;j<m;j++) a[i][j]=scan.nextInt();
        return a;
    }

    //print
    public static void printIntArray(int[] a) {
        for(int c:a) out.print(c+" ");
        out.println();
    }

    public static void printIntegerArray(Integer[] a) {
        for(int c:a) out.print(c+" ");
        out.println();
    }

    public static void printIntMatrix(int[][] a) {
        for(int[] i:a) {
            for(int j:i) out.print(j+" ");
            out.println();
        }
    }

    public static void printIntegerMatrix(Integer[][] a) {
        for(Integer[] i:a) {
            for(Integer j:i) out.print(j+" ");
            out.println();
        }
    }

    public static void help(int t,int n) { out.println("Test Case: "+(t+1)+" | Variable Output: "+n); }
    public static void help(int t,String n) { out.println("Test Case: "+(t+1)+" | Variable Output: "+n); }
    public static void help(int t,char[] n) { out.print("Test Case: "+(t+1)+" | Variable Output: "); for(char c:n) out.print(c+" "); out.println(); }
}