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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define fix(f,n) std::fixed<<std::setprecision(n)<<f
#define fast ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
typedef long long int ll;
typedef unsigned long long int ull;
#define vi vector<int>
#define pii pair<int,int>
#define vii vector<pii>
#define max(a,b) ((a>b)?a:b)
#define min(a,b) ((a>b)?b:a)
#define max3(a,b,c) ((a>b)?(a>c)?a:c:(b>c)?b:c)
#define min3(a,b,c) ((a<b)?(a<c)?a:c:(b<c)?b:c)
#define REP(i,a,n) for(ll i=a;i<n;i++)
#define pb push_back
#define mp make_pair
#define mod 998244353
#define MAX 1000000001

int X[4]={1,-1,0,0};
int Y[4]={0,0,1,-1};
bool vis[1001][1001]={};
char arr[1001][1001];
int h,w;
int cal[1001][1001]={};

bool valid(int x,int y){
    if(x<0 || y<0 || x>=h || y>=w || arr[x][y]=='#' || vis[x][y]){
        return 0;
    }
    return 1;
}

int main(){
	fast;
	int test=1;
	//cin >> test;
	while(test--){
	    cin >> h >> w;
	    queue<pair<int,int>>q;
	    int cx,cy,ex,ey;
	    cin >> cx >> cy >> ex >> ey;
	    cx--;cy--;ex--;ey--;
	    q.push({cx,cy});
	    vis[cx][cy]=1;
	    cal[cx][cy]=0;
	    for(int i=0 ; i<h ; i++){
	        for(int j=0 ; j<w ; j++){
	            cin >> arr[i][j];
	            cal[i][j]=0;
	        }
	    }
	    int arr[h][w];
	    memset(arr,-1,sizeof arr);
	    while(!q.empty()){
	        int x=q.front().first;
	        int y=q.front().second;
	        q.pop();
	        bool b=0;
	        for(int i=0 ; i<4 ; i++){
	            int dx=x+X[i];
	            int dy=y+Y[i];
	            if(valid(dx,dy)){
	                b=1;
	                cal[dx][dy]=cal[x][y];
	                vis[dx][dy]=1;
	                q.push({dx,dy});
	            }
	        }
	        if(!b){
	            for(int i=(x-2) ; i<=(x+2) ; i++){
	                for(int j=(y-2) ; j<=(y+2) ; j++){
	                    if(valid(i,j)){
	                        cal[i][j]=cal[x][y]+1;
	                        vis[i][j]=1;
	                        q.push({i,j});
	                    }
	                }
	            }
	        }
	    }
	    if(vis[ex][ey]){
	        cout << cal[ex][ey] << endl;
	    }else{
	        cout << -1 << endl;
	    }
	}
	return 0;
}