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: Accepted)

 #include <bits/stdc++.h>
 

//tabaicho  see https://boostjp.github.io/tips/multiprec-int.html   
// #include <boost/multiprecision/cpp_int.hpp>
// using namespace boost::multiprecision;

// cpp_int
// int128_t
// int256_t
// int512_t
// int1024_t

// uint128_t
// uint256_t
// uint512_t
// uint1024_t



 #define int long long
 #define inf  1000000007
// #define inf  998244353

 #define pa pair<int,int>
 #define ll long long
 #define PI 3.14159265358979323846
 #define  mp make_pair
 #define  pb push_back
 #define EPS (1e-8)
 
      using namespace std;
                                          
 int dx[8]={0,1,0,-1,1,1,-1,-1};
 int dy[8]={1,0,-1,0,-1,1,1,-1};
                                            
class pa3{
	public:
	int x;
	int y,z;
	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
	bool operator < (const pa3 &p) const{
		if(x!=p.x) return x<p.x;
		if(y!=p.y) return y<p.y;
		 return z<p.z;
		//return x != p.x ? x<p.x: y<p.y;
	}
	bool operator > (const pa3 &p) const{
		if(x!=p.x) return x>p.x;
		if(y!=p.y) return y>p.y;
		 return z>p.z;
		//return x != p.x ? x<p.x: y<p.y;
	}
	bool operator == (const pa3 &p) const{
		return x==p.x && y==p.y && z==p.z;
	}
		bool operator != (const pa3 &p) const{
			return !( x==p.x && y==p.y && z==p.z);
	}

};

class pa4{
	public:
	int x;
	int y,z,w;
	pa4(int x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
	bool operator < (const pa4 &p) const{
		if(x!=p.x) return x<p.x;
		if(y!=p.y) return y<p.y;
		if(z!=p.z)return z<p.z;
		return w<p.w;
		//return x != p.x ? x<p.x: y<p.y;
	}
	bool operator > (const pa4 &p) const{
		if(x!=p.x) return x>p.x;
		if(y!=p.y) return y>p.y;
		if(z!=p.z)return z>p.z;
		return w>p.w;
		//return x != p.x ? x<p.x: y<p.y;
	}
	bool operator == (const pa4 &p) const{
		return x==p.x && y==p.y && z==p.z &&w==p.w;
	}
		

};
class pa2{
	public:
	int x,y;
	pa2(int x=0,int y=0):x(x),y(y) {}
	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
	bool operator < (const pa2 &p) const{
		return y != p.y ? y<p.y: x<p.x;
	}
	bool operator > (const pa2 &p) const{
		return x != p.x ? x<p.x: y<p.y;
	}
	bool operator == (const pa2 &p) const{
		return abs(x-p.x)==0 && abs(y-p.y)==0;
	}
	bool operator != (const pa2 &p) const{
		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
	}
		

};



string itos( int i ) {
	ostringstream s ;
	s << i ;
	return s.str() ;
}
 
int Gcd(int v,int b){
	if(v==0) return b;
	if(b==0) return v;
	if(v>b) return Gcd(b,v);
	if(v==b) return b;
	if(b%v==0) return v;
	return Gcd(v,b%v);
}


 int mod;
int extgcd(int a, int b, int &x, int &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    int d = extgcd(b, a%b, y, x);
    y -= a/b * x;
    return d;
}
pa operator+(const pa & l,const pa & r) {   
    return {l.first+r.first,l.second+r.second};                                    
}    
pa operator-(const pa & l,const pa & r) {   
    return {l.first-r.first,l.second-r.second};                                    
}  

ostream& operator<<(ostream& os, const vector<int>& VEC){
	for(auto v:VEC)os<<v<<" ";
    return os;
}

ostream& operator<<(ostream& os, const pa& PAI){
	os<<PAI.first<<" : "<<PAI.second;
    return os;
}

ostream& operator<<(ostream& os, const pa3& PAI){
	os<<PAI.x<<" : "<<PAI.y<<" : "<<PAI.z;
    return os;
}

ostream& operator<<(ostream& os, const pa4& PAI){
	os<<PAI.x<<" : "<<PAI.y<<" : "<<PAI.z<<" : "<<PAI.y;
    return os;
}




int beki(int wa,int rr,int warukazu){
	if(rr==0) return 1%warukazu;
	if(rr==1) return wa%warukazu;
	wa%=warukazu;
	if(rr%2==1) return ((ll)beki(wa,rr-1,warukazu)*(ll)wa)%warukazu;
	ll zx=beki(wa,rr/2,warukazu);
	return (zx*zx)%warukazu;
}

              
int pr[100000];
int inv[100000];



int comb(int nn,int rr){
	if(rr<0 || rr>nn || nn<0) return 0;
	int r=pr[nn]*inv[rr];
	r%=mod;
	r*=inv[nn-rr];
	r%=mod;
	return r;
}

void gya(int ert){
	pr[0]=1;
	for(int i=1;i<=ert;i++){
		pr[i]=((ll)pr[i-1]*i)%mod;
	}
		inv[ert]=beki(pr[ert],mod-2,mod);
	for(int i=ert-1;i>=0;i--){
		inv[i]=(ll)inv[i+1]*(i+1)%mod;
	}
}


                


                
              //   cin.tie(0);
    		//	ios::sync_with_stdio(false);
    			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
                 //sort(ve.begin(),ve.end(),greater<int>());
 //   mt19937(clock_per_sec);
  //  mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()) ;
  

struct hoge{
	int a;
	int b;
	bool operator<(const hoge &x)const{return a<x.a;}
	bool operator==(const hoge &x)const{return a==x.a && b==x.b;}
	
	
};
bool operator!=(const hoge &x,const hoge &y){return !(x==y) ;}

struct radix_heap32{

	private:
	public:
	using T=pa;
	
	struct kv{
		int key;
		T val;
	};
	
	
	int sz=0;
	int mn=0;
	
	vector<kv> VEC[33];
	
	
	int msb(int r){
		if(r==0)return 0;
		return 32-__builtin_clz(r);
	}
	
	int size(){
		return sz;
	}
	
	void push(int key,T val){
		assert(mn<=key);
		VEC[msb(mn^key)].pb((kv){key,val});
		sz++;
	}

	kv pop(){
		assert(sz>0);
		if(!VEC[0].size()){
			int it=-1;
			for(int i=1;i<=32;i++)if(VEC[i].size()){
				it=i;
				break;
			}
			assert(it>0);
			int mi=2147483647;
			for(auto v:VEC[it])mi=min(mi,v.key);
			while(VEC[it].size()){
				VEC[msb(mi^VEC[it].back().key)].pb(VEC[it].back());
				VEC[it].pop_back();
			}
		}
		
		
		kv ans=VEC[0].back();
		mn=ans.key;
		sz--;
		VEC[0].pop_back();
		return ans;

	}
	
};

struct radix_heap64{

	private:
	public:
	using T=pa;
	
	struct kv{
		ll key;
		T val;
	};
	
	
	int sz=0;
	ll  mn=0ll;
	
	vector<kv> VEC[65];
	
	
	int msb(ll r){
		if(r==0)return 0;
		return 64-__builtin_clzll((ll)r);
	}
	
	int size(){
		return sz;
	}
	
	
	
	void push(ll key,T val){
		VEC[msb(mn^key)].pb((kv){key,val});
		sz++;
	}
	

	
	kv pop(){
		assert(sz>0);
		if(!VEC[0].size()){
			int it=-1;
			for(int i=1;i<=32;i++)if(VEC[i].size()){
				it=i;
				break;
			}
			ll mi=9223372036854775807ll;
			for(auto v:VEC[it])mi=min(mi,v.key);
			while(VEC[it].size()){
				VEC[msb(mi^VEC[it].back().key)].pb(VEC[it].back());
				VEC[it].pop_back();
			}
		}
		
		
		kv ans=VEC[0].back();
		mn=ans.key;
		sz--;
		VEC[0].pop_back();
		return ans;

	}
	
};



string s[1020];
bool vis[1020][1020]={};
void solve(){
	
	int h,w;
	cin>>h>>w;
	
	int sx,sy;
	cin>>sx>>sy;
	int gx,gy;
	cin>>gx>>gy;
	gx--,gy--;
	sx--,sy--;
	for(int i=0;i<h;i++)cin>>s[i];
 radix_heap64 qu;
//	priority_queue<pa3,vector<pa3>,greater<pa3>> qu;  
			qu.push(0,{sx,sy});
	
	while(qu.size()){
		auto  z=qu.pop();
		if(vis[z.val.first][z.val.second])continue;
		vis[z.val.first][z.val.second]=1;
		if(z.val.first==gx&& z.val.second==gy){
			cout<<z.key<<endl;
			return;
		}
		for(int r=0;r<4;r++){
			int x=z.val.first+dx[r];
			int y=z.val.second+dy[r];
			if(0>x || 0>y || x>=h || y>=w)continue;
			if(vis[x][y])continue;
			if(s[x][y]=='#')continue;
				qu.push(z.key,{x,y});
		}	
		
		for(int i=-2;i<=2;i++)for(int j=-2;j<=2;j++){
			int x=z.val.first+i;
			int y=z.val.second+j;
			if(0>x || 0>y || x>=h || y>=w)continue;
			if(vis[x][y])continue;
			if(s[x][y]=='#')continue;
				qu.push(z.key+1,{x,y});
		}
	}
	
	cout<<-1<<endl;
}
 
signed main(){
	
	cin.tie(0);
	ios::sync_with_stdio(false);
int n=1;
	//cin>>n;
 
	
	for(int i=0;i<n;i++)solve();
	
	return 0;
 }