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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedHashSet;

public class Main {

	static BufferedReader reader;
	final static boolean MODE_DEBUG = false;
	static int[] read_line_int;
	static int read_line_int_ptr;
	static long[] read_line_long;
	static int read_line_long_ptr;
	static String[] read_line;
	static int read_line_ptr;
	//static field here
	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		reader = new BufferedReader(new InputStreamReader(System.in));
		//code here
		int H = readInt();
		int W = readInt();
		int Ch = readInt()-1;
		int Cw = readInt()-1;
		int Dh = readInt()-1;
		int Dw = readInt()-1;
		int[][] map = new int[H][];
		for(int h=0;h<H;h++) {
			map[h] = new int[W];
			char[] cs = readLine()[0].toCharArray();
			for(int w=0;w<W;w++) {
				map[h][w] = cs[w]=='#'?-2:Integer.MAX_VALUE;
			}
		}
		Integer[][] poses = new Integer[W][H];
		for(int h=0;h<H;h++) {
			for(int w=0;w<W;w++) {
				poses[w][h] = w*H+h;
			}
		}
		int ptr = 0;
		int seccnt = 0;
		int maxsize = 1;
		int nowsize = 1;
		ArrayList<LinkedHashSet<Integer>> frs = new ArrayList<>();
		LinkedHashSet<Integer> frt = new LinkedHashSet<>();
		frs.add(frt);
		frt.add(poses[Cw][Ch]);
		map[Ch][Cw]=0;
		for(int num=0;num<frs.size();num++) {
			LinkedHashSet<Integer> fr = frs.get(num);
			while(!fr.isEmpty()) {
				int p = fr.iterator().next();
				int X = p/H;
				int Y = p%H;
				fr.remove(p);
				nowsize--;
				int nowscore = map[Y][X];
				boolean xp = false;
				boolean xm = false;
				boolean yp = false;
				boolean ym = false;
				if(X>0) {
					if(map[Y][X-1]!=-2&&map[Y][X-1]>nowscore) {
						map[Y][X-1] = nowscore;
						fr.add(poses[X-1][Y]);
						nowsize++;
						xm=true;
					}
				}
				if(Y>0) {
					if(map[Y-1][X]!=-2&&map[Y-1][X]>nowscore) {
						map[Y-1][X] = nowscore;
						fr.add(poses[X][Y-1]);
						nowsize++;
						ym=true;
					}
				}
				if(X<W-1) {
					if(map[Y][X+1]!=-2&&map[Y][X+1]>nowscore) {
						map[Y][X+1] = nowscore;
						fr.add(poses[X+1][Y]);
						nowsize++;
						xp=true;
					}
				}
				if(Y<H-1) {
					if(map[Y+1][X]!=-2&&map[Y+1][X]>nowscore) {
						map[Y+1][X] = nowscore;
						fr.add(poses[X][Y+1]);
						nowsize++;
						yp=true;
					}
				}
				for(int x=xm?X:Math.max(0,X-2);x<=(xp?X:Math.min(W-1,X+2));x++) {
					for(int y=ym?Y:Math.max(0,Y-2);y<=(yp?Y:Math.min(H-1,Y+2));y++) {
						if(map[y][x]!=-2&&map[y][x]>nowscore+1) {
							map[y][x] = nowscore+1;
							if(frs.size()<=nowscore+1) {
								frs.add(new LinkedHashSet<>());
							}
							frs.get(nowscore+1).add(poses[x][y]);
							nowsize++;
						}
					}
				}
				
				maxsize = Math.max(maxsize,nowsize);
				//print(fr.size());
				/*for(int y=0;y<H;y++) {
					StringBuilder sb = new StringBuilder();
					for(int x=0;x<W;x++) {
						if(map[y][x]==Integer.MAX_VALUE) {
							sb.append("?? ");
						}else if(map[y][x]==-2) {
							sb.append("xx ");
						}else {
							sb.append(map[y][x]+" ");
						}
					}
					for(int x=0;x<W;x++) {
						if(fr.contains(x*H+y)) {
							sb.append("o ");
						}else{
							sb.append("x ");
						}
					}
					print(sb.toString());
				}
				print("");*/
			}
		}
		if(map[Dh][Dw]>=0&&map[Dh][Dw]!=Integer.MAX_VALUE) {
			print(map[Dh][Dw]);
		}else {
			print("-1");
		}
		//print(maxsize);
	}
	
	//functions here
	//note that all methods should be STATIC


	private static <T> int arraySearch(T needle, T[] heystack) {
		for(int i=0;i<heystack.length;i++) {
			if(needle.equals(heystack[i])) {
				return i;
			}
		}
		return -1;
	}
	private static int[] sort(int[] base) {
		int[] copy = array_copy(base);
		Arrays.sort(copy);
		return copy;
	}
	private static int[] array_copy(int[] base) {
		int[] copy = new int[base.length];
		for(int i=0;i<base.length;i++) {
			copy[i] = base[i];
		}
		return copy;
	}
	private static int[] asArray(ArrayList<Integer> ints) {
		int[] intlist = new int[ints.size()];
		for(int i=0;i<intlist.length;i++) {
			intlist[i] = ints.get(i);
		}
		return intlist;
	}
	private static int readInt() {
		if(read_line_int==null||read_line_int_ptr==read_line_int.length) {
			read_line_int = readLineInt();
			read_line_int_ptr=0;
		}
		return read_line_int[read_line_int_ptr++];
	}
	private static long readLong() {
		if(read_line_long==null||read_line_long_ptr==read_line_long.length) {
			read_line_long = readLineLong();
			read_line_long_ptr=0;
		}
		return read_line_long[read_line_long_ptr++];
	}
	private static String readString() {
		if(read_line==null||read_line_int_ptr==read_line.length) {
			read_line = readLine();
			read_line_ptr=0;
		}
		return read_line[read_line_ptr++];
	}
	private static String[] readLine(){
		try{
			return reader.readLine().split(" ");
		}catch(Exception e){
			e.printStackTrace();
			return new String[]{e.getMessage()};
		}
	}
	private static int[] readLineInt(){
		try{
			String[] s = readLine();
			int[] ints = new int[s.length];
			for(int i=0;i<ints.length;i++) {
				ints[i] = Integer.parseInt(s[i]);
			}
			return ints;
		}catch(Exception e){
			e.printStackTrace();
			return null;
		}
	}
	private static long[] readLineLong(){
		try{
			String[] s = readLine();
			long[] ints = new long[s.length];
			for(int i=0;i<ints.length;i++) {
				ints[i] = Long.parseLong(s[i]);
			}
			return ints;
		}catch(Exception e){
			e.printStackTrace();
			return null;
		}
	}
	private static byte[] readLineByte(){
		try{
			String[] s = readLine();
			byte[] bytes = new byte[s.length];
			for(int i=0;i<bytes.length;i++) {
				bytes[i] = Byte.parseByte(s[i]);
			}
			return bytes;
		}catch(Exception e){
			e.printStackTrace();
			return null;
		}
	}
	private static char[] readLineChar(){
		try{
			String[] s = readLine();
			char[] chars = new char[s.length];
			for(int i=0;i<chars.length;i++) {
				chars[i] = (char)Integer.parseInt(s[i]);
			}
			return chars;
		}catch(Exception e){
			e.printStackTrace();
			return null;
		}
	}
	private static void print(Object o){
		System.out.println(o);
	}
	private static void print(){
		System.out.println();
	}
	private static void printd(Object o){
		if(MODE_DEBUG)System.err.println(o);
	}
	private static void printd(){
		if(MODE_DEBUG)System.err.println();
	}
}