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.util.logging.Logger;

import static java.lang.System.*;

public class Main{
    static BufferedReader br;
    static  long mod  = 998244353;
    static HashSet<Integer> p  = new HashSet<>();
  static   protected int a = 9;
 static    protected int b =10;

    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));

        int testcCase = 1;

           int[] nm =readArray(2,0,0);
           int[] ss= readArray(2,0,0);
           int[] dd = readArray(2,0,0);
                a=nm[0];b= nm[1];
           int[][] grid  =new int[nm[0]][nm[1]];


           for(int i=0;i<nm[0];i++){
               char[] ar =cin().toCharArray();
               for(int j=0;j<nm[1];j++){
                   if(ar[j]=='.'){
                       grid[i][j]=1;
                   }
                   else{
                       grid[i][j]=0;
                   }
               }
           }
           ArrayDeque<Integer> sx = new ArrayDeque<>();

           ArrayDeque<Integer> sy  =new ArrayDeque<>();
           int ix = ss[0]-1;
           int iy = ss[1]-1;

           sx.addFirst(ix);sy.addFirst(iy);

           int[] dx = {-1,1,0,0};
           int[] dy = {0,0,1,-1};
            int[][] dist = new int[nm[0]][nm[1]];
           for(int i=0;i<nm[0];i++){

               Arrays.fill(dist[i],Integer.MAX_VALUE);
           }
            dist[ix][iy]=0;
           while (sx.isEmpty()==false){

               int i =sx.removeFirst();int j=sy.removeFirst();

               for(int k=0;k<4;k++){
                   int newx = i+dx[k];int newy =j+dy[k];
                   if(legal(newx,newy,grid)==true){
                       if(dist[newx][newy]>dist[i][j]) {
                           dist[newx][newy] = dist[i][j];
                               sx.addFirst(newx);sy.addFirst(newy);
                       }
                   }
               }

               for(int k =i-2;k<=i+2;k++){


                   for(int l = j-2;l<=j+2;l++){
                    //   System.out.println(k+" "+l+" "+i+" "+j);

                       if(legal(k,l,grid)==true){
                           if(dist[k][l]>dist[i][j]+1){
                               dist[k][l]=dist[i][j]+1;
                               sx.addLast(k);sy.addLast(l);
                           }
                       }
                   }
               }
           }
        System.out.println(dist[dd[0]-1][dd[1]-1]==Integer.MAX_VALUE?-1:dist[dd[0]-1][dd[1]-1]);











    }

    public static boolean legal(int x,int y,int[][] grid){

        if(x<0 || x>=a || y<0 || y>=b){

         return false;

        }
        if(grid[x][y]==1){
            return true;
        }
        else{
            return false;
        }

    }












    public static long min(long a,long b) {
        return Math.min(a,b);
    }
    public static int min(int a,int b) {
        return Math.min(a,b);
    }
    public  static  int[] readArray(int n,int x ,int z)throws Exception{
        int[] arr= new int[n];
        //   System.out.println(arr.length);
        String[] ar= cinA();
        for(int i =x ;i<n;i++){
            //   System.out.println(i-x);
            //  int  y  =getI(ar[i-x]);
            arr[i]=getI(ar[i-x]);
        }
        return arr;
    }
    public  static  long[] readArray(int n,int x )throws Exception{
        long[] arr= new long[n];
        String[] ar= cinA();
        for(int i =x ;i<n+x;i++){
            arr[i]=getL(ar[i-x]);
        }
        return arr;
    }

    public static void arrinit(String[] a,long[] b)throws Exception{
        for(int i=0;i<a.length;i++){
            b[i]=Long.parseLong(a[i]);
        }
    }
    public  static HashSet<Integer>[]  Graph(int n,int edge,int directed)throws Exception{
        HashSet<Integer>[] tree=  new HashSet[n];

        for(int j=0;j<edge;j++){

            String[] uv = cinA();
            int u = getI(uv[0]);
            int v = getI(uv[1]);
            if(directed==0){

                tree[v].add(u);
            }
            tree[u].add(v);
        }
        return tree;
    }
    public static void arrinit(String[] a,int[] b)throws Exception{
        for(int i=0;i<a.length;i++){
            b[i]=Integer.parseInt(a[i]);
        }
    }
    static double findRoots(int a, int b, int c) {
        // If a is 0, then equation is not
        //quadratic, but linear


        int d = b * b - 4 * a * c;
        double sqrt_val = Math.sqrt(Math.abs(d));


        // System.out.println("Roots are real and different \n");

        return Math.max((double) (-b + sqrt_val) / (2 * a),
                (double) (-b - sqrt_val) / (2 * a));


    }

    public static String cin() throws Exception {
        return br.readLine();
    }

    public static String[] cinA() throws Exception {
        return br.readLine().split(" ");
    }
    public static String[] cinA(int x) throws Exception{
        return br.readLine().split("");
    }

    public static String ToString(Long x) {
        return Long.toBinaryString(x);
    }

    public static void cout(String s) {
        System.out.println(s);
    }

    public static Integer cinI() throws Exception {
        return Integer.parseInt(br.readLine());
    }

    public static int getI(String s) throws Exception {
        return Integer.parseInt(s);
    }

    public static long getL(String s) throws Exception {
        return Long.parseLong(s);
    }

    public static long max(long a, long b) {
        return Math.max(a, b);
    }
    public static int max(int a, int b) {
        return Math.max(a, b);
    }

    public static void coutI(int x) {
        System.out.println(String.valueOf(x));
    }

    public static void coutI(long x) {
        System.out.println(String.valueOf(x));
    }

    public static Long cinL() throws Exception {
        return Long.parseLong(br.readLine());
    }

    public static void arrInit(String[] arr, int[] arr1) throws Exception {
        for (int i = 0; i < arr.length; i++) {
            arr1[i] = getI(arr[i]);
        }

    }
}