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.*;
import java.util.*;
import java.math.*;
import java.lang.*;
 
import static java.lang.Math.*;

public class Main implements Runnable 
{
    static class InputReader 
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        
        public int read()
        {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars) 
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() 
        {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
        
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do
            {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
        
            return res * sgn;
        }
		
        public long nextLong() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
		
        public double nextDouble() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') 
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
    
        public String readString() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next()
        {
            return readString();
        }
        
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
		
    }
	
	static int dirx[]={1,-1,0,0};
	static int diry[]={0,0,1,-1};
	
	
    public static void main(String args[]) throws Exception 
    {
        new Thread(null, new Main(),"Main",1<<27).start();
    }
	// **just change the name of class from Main to reuquired**
    public void run()
    {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
		
		int n=sc.nextInt(),m=sc.nextInt();
		int sx=sc.nextInt()-1,sy=sc.nextInt()-1;
		int dx=sc.nextInt()-1,dy=sc.nextInt()-1;
		
		char grid[][]=new char[n][m];
		for(int i=0;i<n;++i)
		{
			grid[i]=sc.next().toCharArray();
		}
		
		//System.out.println("c1");
		
		Pair pair[][]=new Pair[n][m];
		for(int i=0;i<n;++i)
		{
			for(int j=0;j<m;++j)
			{
				pair[i][j]=new Pair(i,j,0,false);
			}
		}
		
		//System.out.println("c2");
		
		PriorityQueue<Pair> pq = new PriorityQueue<>();
		pq.add(new Pair(sx,sy,0,true));
		pair[sx][sy].magic=0;
		pair[sx][sy].visited=true;
		
		//System.out.println("c3");
		
		while(!pq.isEmpty())
		{
			Pair p=pq.poll();
			//System.out.println(p);
			int x=p.x;
			int y=p.y;
			if(x==dx && y==dy) break;
			
		
			for(int i=0;i<4;++i)
			{
				int xx=x+dirx[i];
				int yy=y+diry[i];
				
				if(xx>=0 && xx<n && yy>=0 && yy<m && grid[xx][yy]=='.')
				{
					if(pair[xx][yy].visited)
					{
						if(pair[xx][yy].magic>pair[x][y].magic)
						{
							pq.add(new Pair(xx,yy,pair[x][y].magic,true));
							pair[xx][yy].magic=pair[x][y].magic;
							pair[xx][yy].visited=true;
						}
					}
					else 
					{
						pq.add(new Pair(xx,yy,pair[x][y].magic,true));
						pair[xx][yy].visited=true;
						pair[xx][yy].magic=pair[x][y].magic;
					}
				}
			}
			
			for(int i=x-2;i<=x+2;++i)
			{
				for(int j=y-2;j<=y+2;++j)
				{
					int xx=i,yy=j;
					if(xx>=0 && xx<n && yy>=0 && yy<m && grid[xx][yy]=='.')
					{
						if(pair[xx][yy].visited)
						{
							if(pair[xx][yy].magic>pair[x][y].magic+1)
							{
								pair[xx][yy].visited=true;
								pair[xx][yy].magic=pair[x][y].magic+1;
								pq.add(new Pair(xx,yy,pair[x][y].magic+1,true));
							}
						}
						else
						{
							pair[xx][yy].magic=pair[x][y].magic+1;
							pair[xx][yy].visited=true;
							pq.add(new Pair(xx,yy,pair[x][y].magic+1,true));
						}
					}
				}
			}
			
			//System.out.println(pq);
		}
		
		
		if(!pair[dx][dy].visited) w.println("-1");
		else w.println(pair[dx][dy].magic);
		
        System.out.flush();
        w.close();
    }
}

class Pair implements Comparable<Pair>
{
	int x,y,magic;
	boolean visited;
	Pair(int x,int y)
	{
		this.x=x;
		this.y=y;
	}
	Pair(int x,int y,int magic,boolean visited)
	{
		this.x=x;
		this.y=y;
		this.magic=magic;
		this.visited=visited;
	}
	
	public String toString()
	{
		String s="("+x+","+y+","+magic+")";
		return s;
	}
	
	public int compareTo(Pair p)
	{
		return this.magic-p.magic;
	}
}