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: Time Limit Exceeded)

#include "bits/stdc++.h"
using namespace std;
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx,avx2,fma")

//wierd debugging stuff
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
  enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << "\n" ; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (auto it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
//end of weird debugging stuff
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int,int> ii;
typedef vector<ll> vll;
typedef vector<vector<int>> vvi;
#define all(c) (c).begin(), (c).end()
#define sz(x) (int)(x).size()
 
#define F_OR(i, a, b, s) for (int i = (a); ((s) > 0 ? i < (b) : i > (b)); i += (s))
#define F_OR1(e) F_OR(i, 0, e, 1)
#define F_OR2(i, e) F_OR(i, 0, e, 1)
#define F_OR3(i, b, e) F_OR(i, b, e, 1)
#define F_OR4(i, b, e, s) F_OR(i, b, e, s)
#define GET5(a, b, c, d, e, ...) e
#define F_ORC(...) GET5(__VA_ARGS__, F_OR4, F_OR3, F_OR2, F_OR1)
#define fo(...) F_ORC(__VA_ARGS__)(__VA_ARGS__)
#define foe(i,x) for(auto& i: x)
#define ar array
#define pb push_back
#define vt vector
#define F first
#define S second

template<class T> bool umin(T& a,const T& b){return b<a?a=b,1:0;}
template<class T> bool umax(T& a,const T& b){return b>a?a=b,1:0;}

template<class A> void read(vt<A>& v);
template<class A, size_t S> void read(ar<A, S>& a);
template<class T> void read(T& x) {cin>>x;}
void read(double& d) {string t;read(t);	d=stod(t);}
void read(long double& d) {	string t;read(t);d=stold(t);}
template<class H, class... T> void read(H& h, T&... t) {read(h);read(t...);}
template<class A> void read(vt<A>& x) {	foe(a, x)read(a);}
int nxt(){int a;cin>>a;return a;}

// no change 
const ll MOD = 1e9+7;  
void Titan(){
	int h,w;
	read(h,w);
	ii st,ed;
	read(st.F,st.S,ed.F,ed.S);
	st.F--,st.S--,ed.F--,ed.S--;

	vt<string> G(h);
	fo(h)cin >> G[i];
	vvi dis(h,vi(w,MOD));
	dis[st.F][st.S] = 0;
	deque<ii> q;
	q.pb(st);
	vi dir= {1,0,-1,0,1};
	while(!q.empty()){
		int a,b;
		tie(a,b) = q.front();
		q.pop_front();
		fo(4){
			int ny = a + dir[i];
			int nc = b + dir[i+1];

			if(ny<0||ny>=h||nc<0||nc>=w)continue;
			if(G[ny][nc] == '#') continue;
			if(dis[ny][nc] > dis[a][b]){
				dis[ny][nc] = dis[a][b];
				q.pb({ny,nc});
			}
		}
		for(int i = -2;i<=2;i++){
			for(int j = -2;j<=2;j++){
				int ny = a +i;
				int nc = b + j;

				if(ny<0||ny>=h||nc<0||nc>=w)continue;
				if(G[ny][nc] == '#') continue;
				if(dis[ny][nc] > dis[a][b]+1){
					dis[ny][nc] = dis[a][b]+1;
					q.pb({ny,nc});
				}
			}
		}

	}

	if(dis[ed.F][ed.S] == MOD) dis[ed.F][ed.S] = -1;
	cout << dis[ed.F][ed.S] <<endl;
	


	
}

int main() {
	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	int T = 1;
	//cin >> T;		//cmt if one test case
    fo(T){
		//cout << "Case #" << i+1 << ": " ;
		Titan();
	}
}
/*///////////////////////////////////////////////////////////
Important Notes : 
* check long long 
* check base cases
* do not loose Hope
* if case fails on 2nd test case maybe some cases are missing check them
* do not sit idle
* try to do it using pen/paper.
*/