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 11.0.6) (judge verdict: Accepted)

import java.util.*; import java.io.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		solve();flush();
	}
	//Don't have to see. end------------------------------------------
	static void solve(){//Here is the main function
		int[] dy = {-1, 0, 1, 0};
		int[] dx = {0, -1, 0, 1};
		ArrayList<Integer> one = nextIntArray();
		int H = one.get(0);
		int W = one.get(1);
		one = nextIntArray();
		int sy = one.get(0) - 1;
		int sx = one.get(1) - 1;
		one = nextIntArray();
		int ey = one.get(0) - 1;
		int ex = one.get(1) - 1;
		Node[][] list = new Node[H][W];
		for(int i = 0; i < H; i++){
			ArrayList<String> tmp = nextCharArray();
			for(int j = 0; j < W; j++){
				list[i][j] = new Node(tmp.get(j));
			}
		}
		int group = 0;
		for(int i = 0; i < H; i++){
			for(int j = 0; j < W; j++){
				if(list[i][j].s.equals(".")){
					if(!list[i][j].access){
						list[i][j].group = group;
			        	group++;
			        	ArrayDeque<Integer[]> queue = new ArrayDeque<Integer[]>();
						list[i][j].access = true;
						Integer[] first = new Integer[]{i, j};
						queue.add(first);
						while(queue.size() > 0){
							Integer[] now = queue.pollFirst();
							int nowY = now[0];
							int nowX = now[1];
							for(int k = 0; k < dy.length; k++){
								int nextY = nowY + dy[k];
						        int nextX = nowX + dx[k];
						        if(nextY >= 0 && nextY < H && nextX >= 0 && nextX < W){
						          if(!list[nextY][nextX].access && list[nextY][nextX].s.equals(".")){
						          	Integer[] ne = new Integer[]{nextY, nextX};
						            queue.addLast(ne);
						            list[nextY][nextX].group = list[nowY][nowX].group;
						            list[nextY][nextX].access = true;
						          }
						        }
							}
						}
					}
			    }
			}
		}

		GroupNode[] groupList = new GroupNode[group];
		for(int i = 0; i < group; i++){
			groupList[i] = new GroupNode(i);
		}
		for(int i = 0; i < H; i++){
			for(int j = 0; j < W; j++){
				if(list[i][j].s.equals(".")){
					for(int k = i - 2; k <= i + 2; k++){
						for(int l = j - 2; l <= j + 2; l++){
							if(k >= 0 && k < H && l >= 0 && l < W){
								if(list[k][l].s.equals(".") && list[k][l].group != list[i][j].group){
									groupList[list[k][l].group].child.add(list[i][j].group);
                					groupList[list[i][j].group].child.add(list[k][l].group);
								}
							}
						}
					}
				}
			}
		}
		ArrayDeque<GroupNode> groupQueue = new ArrayDeque<GroupNode>();
		groupQueue.add(groupList[list[sy][sx].group]);
		groupList[list[sy][sx].group].access = true;
		while(groupQueue.size() > 0){
			GroupNode nowGroup = groupQueue.pollFirst();
			if(nowGroup.no == list[ey][ex].group){
				myout(nowGroup.count);
				return;
			}
			Iterator child = nowGroup.child.iterator();
			while(child.hasNext()){
				int ne = (int)child.next();
				if(!groupList[ne].access){
					groupList[ne].access = true;
					groupList[ne].count = nowGroup.count + 1;
					groupQueue.addLast(groupList[ne]);
				}
			}
		}
		
		myout(-1);

	}
	//Method addition frame start

static class Node{
	String s;
	boolean access = false;
	int group = -1;
	Node(String s){
		this.s = s;
	}
}

static class GroupNode{
	int no;
	HashSet<Integer> child = new HashSet<Integer>();
	boolean access = false;
	int count = 0;
	GroupNode(int i){
		no = i;
	}
	public String toString(){
		return "{ child : " + child + ", count : " + count + ", no : " + no + "}";
	}
}

static void bfs(int y, int x){
	
}

	//Method addition frame end
}