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.*;

public class Main {
static class cell{
	int a, b;
	public cell(int a, int b) {
		this.a = a;
		this.b = b;
	}
}
public static void main(String[] args){

   new Thread(null, null, "Anshum Gupta", 99999999) {
        public void run() {
            try {
                solve();
            } catch(Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }.start();
}
static final long mxx = (long)(1e18+5);
static final int mxN = (int)(1e6);
static final int mxV = (int)(1e6), log = 18;
static long mod = (long)(1e9+7); //998244353;//̇
static final int INF = (int)1e9;
static boolean[][]vis;
static ArrayList<ArrayList<Integer>> adj;
static int n, m, k, q, p;
static char[]str;
static int[]a;
static char[][]arr;
static int[][]dist;
static int[]dx = {-1, 1, 0, 0}, dy = {0, 0, -1, 1}, wx = {-2, -1, 0, 1, 2}, wy = {-2, -1, 0, 1, 2};
public static void solve() throws Exception {
	   // solve the problem here
		s = new MyScanner();
   		out = new PrintWriter(new BufferedOutputStream(System.out), true);
//	   		out = new PrintWriter("output.txt");
        int tc = 1;//s.nextInt();
        while(tc-- > 0){
        	n = s.nextInt();
        	m = s.nextInt();
        	cell start = new cell(s.nextInt()-1, s.nextInt()-1);
        	cell dest = new cell(s.nextInt()-1, s.nextInt()-1);
        	dist = new int[n][m];
        	arr = new char[n][m];
        	for(int i=0; i<n; i++)Arrays.fill(dist[i], INF);
        	dist[start.a][start.b] = 0;
        	for(int i=0; i<n; i++) {
        		arr[i] = s.next().toCharArray();
        	}
        	ArrayDeque<Integer> xs = new ArrayDeque<Integer>(), ys = new ArrayDeque<Integer>();
        	xs.add(start.a);
        	ys.add(start.b);
        	while(!xs.isEmpty()) {
        		int a = xs.poll();
        		int b = ys.poll();
        		for(int k=0; k<4; k++) {
        			int x = a + dx[k];
        			int y = b + dy[k];
        			if(x < 0 || y < 0 || x >= n || y >= m || arr[x][y] == '#')continue;
        			if(dist[x][y] > dist[a][b]) {
        				xs.addFirst(x);
        				ys.addFirst(y);
        				dist[x][y] = dist[a][b];
        			}
        		}
        		for(int i=0; i<5; i++) {		
        			for(int j=0; j<5; j++) {
        				int x = a + wx[i];
        				int y = b + wy[j];
        				if(x < 0 || y < 0 || x >= n || y >= m || arr[x][y] == '#')continue;
        				if(dist[x][y] > dist[a][b] + 1) {
        					dist[x][y] = dist[a][b] + 1;
            				xs.addLast(x);
            				ys.addLast(y);
        				}
        			}
        		}
        	}
        	out.println(dist[dest.a][dest.b] == INF ? "-1" : dist[dest.a][dest.b]);
        } 
           
        out.flush();
        out.close();
}

public static PrintWriter out;
public static MyScanner s;
static class MyScanner {

    BufferedReader br;
    StringTokenizer st;

    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    public MyScanner(String fileName) {
    	try {
			br = new BufferedReader(new FileReader(fileName));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}
    }
    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()); }
    int[] nextIntArray(int n){
    	int[]a = new int[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    long[] nextlongArray(int n) {
    	long[]a = new long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    Integer[] nextIntegerArray(int n){
    	Integer[]a = new Integer[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    Long[] nextLongArray(int n) {
    	Long[]a = new Long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    char[][] next2DCharArray(int n, int m){
    	char[][]arr = new char[n][m];
    	for(int i=0; i<n; i++) {
    		arr[i] = this.next().toCharArray();
    	}
    	return arr;
    }
    ArrayList<ArrayList<Integer>> readUndirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i=0; i<=n; i++)adj.add(new ArrayList<Integer>());
    	for(int i=0; i<m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		adj.get(u).add(v);
    		adj.get(v).add(u);
    	}
    	return adj;
    }
    ArrayList<ArrayList<Integer>> readDirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i=0; i<=n; i++)adj.add(new ArrayList<Integer>());
    	for(int i=0; i<m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		adj.get(u).add(v);
    	}
    	return adj;
    }
    String nextLine(){
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}

 
}