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 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;
import java.math.*;
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //class  Declaration
 
static class pair implements Comparable < pair > {
long x;
long y;
pair(long i, long j) {
    x = i;
    y = j;
}
public int compareTo(pair p) {
    if (this.x != p.x) {
        return Long.compare(this.x,p.x);
    } else {
        return Long.compare(this.y,p.y);
    }
}
public int hashCode() {
    return (x + " " + y).hashCode();
}
public String toString() {
    return x + " " + y;
}
public boolean equals(Object o) {
    pair x = (pair) o;
    return (x.x == this.x && x.y == this.y);
}
}

 
final int[] dx = {0,0,1,-1};
final  int[] dy = {1,-1,0,0};
// int[] ddx = {0,0,1,-1,1,-1,1,-1}; 
// int[] ddy = {1,-1,0,0,1,-1,-1,1};

 
final int inf = (int) 1e9 + 9;
final long biginf  = (long)1e18 + 7 ;
final long mod =  (long)1e9+7;  
int n,m;
int[][] g ;
int[] val,to,from ;
boolean[] vis ;
HashSet<Integer> got,have ;
void solve() throws Exception {
    int h=ni(),w=ni();
    int ch=ni()-1,cw=ni()-1;
    int dh=ni()-1,dw=ni()-1;
    char[][] mat= nm(h,w);
    int[][] cost = new int[h][w];
    for(int i=0;i<h;++i) Arrays.fill(cost[i],-1);

    boolean[][] vis = new boolean[h][w];
    LinkedList<pair> endpoints= new LinkedList<>();
    endpoints.add(new pair(ch,cw));
    int magic = 0;
    while(!endpoints.isEmpty()){
        LinkedList<pair> q= new LinkedList<>();
        while(!endpoints.isEmpty()) q.add(endpoints.pollFirst());
        LinkedList<pair> exploreThis = new LinkedList<>();
        while(!q.isEmpty()){
            pair p = q.pollFirst();
            int xc = (int)p.x, yc= (int)p.y;
            if(vis[xc][yc]) continue;
            vis[xc][yc]=true;
            cost[xc][yc] =magic ;
            int newAdded = 0;

            for(int i=0;i<4;++i){
                int newi = xc + dx[i];
                int newj = yc + dy[i];
                if(newi>=0 && newi < h && newj>=0 && newj < w && mat[newi][newj]=='.' && (!vis[newi][newj])){
                    q.add(new pair(newi,newj));
                    newAdded++;
                }

            }
            
                exploreThis.add(new pair(xc,yc));
            

        }

        magic++;
        for(pair p : exploreThis){
            int xc = (int)p.x, yc= (int)p.y;
            for(int mdx= -2;mdx<=2;mdx++){
                for(int mdy = -2; mdy<=2;mdy++){
                    if(mdx==0 && mdy ==0) continue ;
                    int newi = xc + mdx;
                    int newj = yc + mdy;
                    if(newi>=0 && newi < h && newj>=0 && newj < w && mat[newi][newj]=='.' && (!vis[newi][newj])){
                        endpoints.add(new pair(newi,newj));
                    }
                }
            }
        }


    }
    pn(cost[dh][dw]);

}

long pow(long a, long b) {
    long result = 1;
    while (b > 0) {
        if (b % 2 == 1) result = (result * a) % mod;
        b /= 2;
        a = (a * a) % mod;
    }
    return result;
}
long gcd(long a, long b) {
    if (b == 0)
        return a;
    return gcd(b, a % b);
}
void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
 
        long s = System.currentTimeMillis();
        solve();
        out.flush();
       // System.err.println(System.currentTimeMillis() - s + "ms");
}
public static void main(String[] args) throws Exception {
    new Main().run();
}
 
//output methods
private void dbg(Object... o){ System.err.println(Arrays.deepToString(o));}
void p(Object... o){for(Object oo:o)out.print(oo+" ");}
void pn(Object... o){for(int i = 0; i< o.length; i++)out.print(o[i]+(i+1 < o.length?" ":"\n"));}
void pni(Object... o){for(Object oo:o)out.print(oo+" ");out.println();out.flush();}
 
//input methods

private int[][] ng(int n, int e, int[] from, int[] to, boolean f){
    int[][] g = new int[n+1][];int[]cnt = new int[n+1];
    for(int i = 0; i< e; i++){
        cnt[from[i]]++;
        if(f)cnt[to[i]]++;
    }
    for(int i = 0; i<= n; i++)g[i] = new int[cnt[i]];
    for(int i = 0; i< e; i++){
        g[from[i]][--cnt[from[i]]] = to[i];
        if(f)g[to[i]][--cnt[to[i]]] = from[i];
    }
    return g;
}
private int[][][] nwg(int n, int e, int[] from, int[] to, boolean f){
    int[][][] g = new int[n+1][][];int[]cnt = new int[n+1];
    for(int i = 0; i< e; i++){
        cnt[from[i]]++;
        if(f)cnt[to[i]]++;
    }
    for(int i = 0; i<= n; i++)g[i] = new int[cnt[i]][];
    for(int i = 0; i< e; i++){
        g[from[i]][--cnt[from[i]]] = new int[]{to[i], i, 0};
        if(f) g[to[i]][--cnt[to[i]]] = new int[]{from[i], i, 1};
    }
    return g;
}


private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
 
 
private int readByte() {
    if (lenbuf == -1) throw new InputMismatchException();
    if (ptrbuf >= lenbuf) {
        ptrbuf = 0;
        try {
            lenbuf = is.read(inbuf);
        } catch (IOException e) {
            throw new InputMismatchException();
        }
        if (lenbuf <= 0) return -1;
    }
    return inbuf[ptrbuf++];
}
private boolean isSpaceChar(int c) {
    return !(c >= 33 && c <= 126);
}
private int skip() {
    int b;
    while ((b = readByte()) != -1 && isSpaceChar(b));
    return b;
}
 
private double nd() {
    return Double.parseDouble(ns());
}
private char nc() {
    return (char) skip();
}
 
private String ns() {
    int b = skip();
    StringBuilder sb = new StringBuilder();
    while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
        sb.appendCodePoint(b);
        b = readByte();
    }
    return sb.toString();
}
 
private char[] ns(int n) {
    char[] buf = new char[n];
    int b = skip(), p = 0;
    while (p < n && !(isSpaceChar(b))) {
        buf[p++] = (char) b;
        b = readByte();
    }
    return n == p ? buf : Arrays.copyOf(buf, p);
}
 
private char[][] nm(int n, int m) {
    char[][] map = new char[n][];
    for (int i = 0; i < n; i++) map[i] = ns(m);
    return map;
}
 
private int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++) a[i] = ni();
    return a;
}
 
private int ni() {
    int num = 0, b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}
 
private long nl() {
    long num = 0;
    int b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}

}