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)


/**
 *    Coded by : lucky_21
 *               --------Lokesh Singh
**/

#include<bits/stdc++.h>
using namespace std;

#include<ext/pb_ds/tree_policy.hpp>
#include<ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T> using oset=tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;

#define     F           first
#define     S           second
#define     pb          push_back
#define     lb          lower_bound
#define     ub          upper_bound
#define     pii         pair<int,int>
#define     all(x)      x.begin(),x.end()
#define     fix         fixed<<setprecision(10)
#define     rep(i,a,b)  for(int i=int(a);i<=int(b);i++)
#define     repb(i,b,a) for(int i=int(b);i>=int(a);i--)
#define     FastIO      ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0)

typedef double db;
typedef long long ll;

const int N=1005;
const int mod=1e9+7;

int R,C,a,b,c,d,dp[N][N];
char g[N][N];
int rec(int i,int j){
    if(i<=0 or j<=0 or i>R or j>C) return 1e9;
    if(g[i][j]=='#') return 1e9;
    if(i==c and j==d) return 0;
    int &cache=dp[i][j];
    if(cache!=-1) return cache;
    cache=1e9;
    rep(u,-2,2) rep(v,-2,2){
        if(u==0 and v==0) continue;
        int t=1;
        if(abs(u)+abs(v)==1) t=0;
        cache=min(cache,t+rec(i+u,j+v));
    }
    return cache==1e9?-1:cache;
}
signed main(){
    FastIO;
    cin>>R>>C>>a>>b>>c>>d;
    memset(dp,-1,sizeof dp);
    rep(i,1,R) rep(j,1,C) cin>>g[i][j];
    cout<<rec(a,b);
    return 0;
}