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.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.net.ConnectException;
import java.rmi.dgc.Lease;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;

import static java.util.Comparator.*;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
		main.out.close();
	}
	// ======================================================================
	int H, W, SH, SW, GH, GW;
	char[][] C;
	boolean[][] F;
	Deque<PPKEY> DQ = new ArrayDeque();
	int[][] d = { {-1, 0}, {0, -1}, {0, 1}, {1, 0} };
	boolean check(int sh, int sw) {
//		out.println("check : sh = " + sh + "  sw = " + sw);
		if(sh == GH && sw == GW)	return true;
		DQ.clear();
		DQ.addLast(new PPKEY(sh, sw));
		PPKEY pp;
		int h, w;
		while(!DQ.isEmpty()) {
			pp = DQ.pollFirst();
			for (int i = 0; i < 4; i++) {
				h = pp.key + d[i][0];
				w = pp.val + d[i][1];
				if(h < 0 || h >= H || w < 0 || w >= W)	continue;
				if(h == GH && w == GW)					return true;
				if(C[h][w] == '#' || F[h][w])			continue;
				F[h][w] = true;
				setUsed.add(new PPKEY(h, w));
				DQ.addLast(new PPKEY(h, w));
			}
		}
		return false;
	}
	Set<PPKEY> setUsed = new HashSet();
	Set<PPKEY> set = new HashSet();
	public void solve() {
		H = ni();		W = ni();
		SH = ni()-1;	SW = ni()-1;
		GH = ni()-1;	GW = ni()-1;
		C = new char[H][];
		for (int i = 0; i < H; i++)		C[i] = ns().toCharArray();
		F = new boolean[H][W];
		set.add(new PPKEY(SH, SW));
		int h, w;
		for (int i = 0; ; i++) {
			setUsed.clear();
			for(PPKEY pp : set) {
				h = pp.key;		w = pp.val;
				F[h][w] = true;
				setUsed.add(new PPKEY(h, w));
				if(check(h, w)) {
					out.println(i);
					return;
				}
			}
			set.clear();
			for(PPKEY pp : setUsed) {
				h = pp.key;		w = pp.val;
				for (int j = -2; j <= 2; j++) {
					for (int j2 = -2; j2 <= 2; j2++) {
						if(h+j < 0 || h+j >= H 
							|| w+j2 < 0 || w+j2 >= W)			continue;
						if(C[h+j][w+j2] == '#' || F[h+j][w+j2])	continue;
						set.add(new PPKEY(h+j, w+j2));
					}
				}
			}
			if(set.isEmpty())	break;
			setUsed.clear();
		}
		out.println("-1");
	}
	// HashMap のキーに使う　→　Set に入れるのもこれ（PPでは値での比較が行われない）
	public class PPKEY{
		private final int key, val;
		public PPKEY(int key, int val) {
			this.key = key;
			this.val = val;
		}
		public int getKey() {
			return key;
		}
		public int getVal() {
			return val;
		}
		@Override
		public boolean equals(Object obj) {
			if (obj instanceof PPKEY) {
				PPKEY dest = (PPKEY) obj;
				return this.key == dest.key && this.val == dest.val;
			} else {
				return false;
			}
		}
		@Override
		public int hashCode() {
			return Objects.hash(key, val);
		}
	}


	// ------------------------------------------
	// ライブラリ
	// ------------------------------------------
	// Print
	private PrintWriter out = new PrintWriter(System.out);
	
	// Scanner
	private FastScanner scan = new FastScanner();
	int ni(){ return scan.nextInt();}
	int[] ni(int n){int[] a = new int[n]; for(int i = 0; i < n; i++){a[i] = ni();} return a;}
	int[][] ni(int y, int x){int[][] a = new int[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ni();}} return a;}
	long nl(){return scan.nextLong();}
	long[] nl(int n){long[] a = new long[n]; for(int i = 0; i < n; i++){a[i] = nl();} return a;}
	long[][] nl(int y, int x){long[][] a = new long[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = nl();}} return a;}
	String ns(){return scan.next();}
	String[] ns(int n){String[] a = new String[n]; for(int i = 0; i < n; i++){a[i] = ns();} return a;}
	String[][] ns(int y, int x){String[][] a = new String[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ns();}} return a;}
}
class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() { return Double.parseDouble(next());}
}