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: Runtime Error)

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

template<typename T, typename U>
using pv=vector<pair<T,U>>;
template<typename T>
using matrix=vector<vector<T>>;
template<typename T>
using pque=priority_queue<T>;
template<typename T>
using lpque=priority_queue<T,vector<T>,greater<T>>;

using ll=long long;
using intpair=pair<int,int>;
using llpair=pair<ll,ll>;
using ilpair=pair<int,ll>;
using lipair=pair<ll,int>;
using intvec=vector<int>;
using llvec=vector<ll>;
using intq=queue<int>;
using llq=queue<ll>;
using intmat=vector<intvec>;
using llmat=vector<llvec>;

#define PI 3.141592653589793
#define INTINF ((1<<30)-1)
#define LLINF ((1LL<<62)-1)
#define MPRIME 1000000007
#define MPRIME9 998244353
#define MMPRIME ((1ll<<61)-1)

#define len length()
#define pushb push_back
#define fi first
#define se second

#define setpr fixed<<setprecision(15)
#define all(name) name.begin(),name.end()
#define rall(name) name.rbegin(),name.rend()
#define gsort(vbeg,vend) sort(vbeg,vend,greater<>())

template<class T>
inline bool chmin(T& a, T b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}

template<class T>
inline bool chmax(T& a, T b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}

template<class T>
inline void init(T& v) {
	for(auto &a: v) cin>>a;
}
template<class T, class U>
inline void init(vector<pair<T,U>>& v) {
	for(auto &a: v) cin>>a.first>>a.second;
}
template<class T, class N>
inline void init(T& v, N n) {
	v.resize(n);
	for(auto &a: v) cin>>a;
}
template<class T, class U, class N>
inline void init(vector<pair<T,U>>& v, N n) {
	v.resize(n);
	for(auto &a: v) cin>>a.first>>a.second;
}

inline void out() {
	cout<<endl;
}
template<class T, class... U>
inline void out(T a, U... alist) {
	cout<<a<<" ";
	out(forward<U>(alist)...);
}

template<class N>
void resiz(N n) {
	//empty
}
template<class N, class T, class... U>
void resiz(N n, T&& hd, U&&... tl) {
	hd.resize(n);
	resiz(n,forward<U>(tl)...);
}

bool isout(int h, int w, int H, int W) {
	return ( h<0 || h>=H || w<0 || w>=W );
}

ll binpow(ll a, ll ex, ll p) {
	ll result=1;
	while(ex>0) {
		if(ex&1) result=result*a%p;
		ex>>=1;
		a=a*a%p;
	}
	return result;
}

template<class T>
class Matrix{
	vector<vector<T>> mat;

public:

	Matrix() : Matrix(0,0) {}
	Matrix(int h, int w) { make(h,w); }
	Matrix(int h, int w, T init) { make(h,w,init); }

	void make(int h, int w) {
		mat=vector<vector<T>>(h,vector<T>(w));
	}
	void make(int h, int w, T init) {
		mat=vector<vector<T>>(h,vector<T>(w,init));
	};

	void in() {
		for(int i=0; i<mat.size(); i++) for(int j=0; j<mat[i].size(); j++) {
			cin>>mat[i][j];
		}
	}

	void out() {
		for(int i=0; i<mat.size(); i++) {
			int wm=mat[i].size();
			for(int j=0; j<wm; j++) {
				cout<<mat[i][j]<<(wm==j+1 ? '\n' : ' ');
			}
		}
		cout<<flush;
	}

	inline vector<T> &operator[](int idx) {
		assert(0<=idx && idx<mat.size());
		return mat[idx];
	}
};


int H,W,sh,sw,gh,gw;
Matrix<char> mp(1001,1001,'#');
Matrix<int> cost(1001,1001,INTINF);
int dy[]={0,1,0,-1}, dx[]={1,0,-1,0};
int ddy[]={-2,-2,-2,-2,-2,-1,-1,-1,-1,0,0,1,1,1,1,2,2,2,2,2}, ddx[]={-2,-1,0,1,2,-2,-1,1,2,-2,2,-2,-1,1,2,-2,-1,0,1,2};

void input() {
	cin>>H>>W>>sh>>sw>>gh>>gw;
	for(int i=1; i<=H; i++) for(int j=1; j<=W; j++) {
		cin>>mp[i][j];
	}
}

void solve() {
	intq qh,qw,qqh,qqw; qh.push(sh), qw.push(sw), qqh.push(sh), qqw.push(sw); cost[sh][sw]=0;
	while(!qh.empty()) {
		while(!qh.empty()) {
			int h=qh.front(), w=qw.front(); qh.pop(),qw.pop();
			for(int i=0; i<4; i++) {
				int nh=h+dy[i], nw=w+dx[i];
				qqh.push(nh), qqw.push(nw);
				if(nh<0 || nh>H || nw<0 || nw>W || mp[nh][nw]=='#' || cost[nh][nw]<=cost[h][w]) continue;
				cost[nh][nw]=cost[h][w];
				qh.push(nh), qw.push(nw);
			}
		}
		while(!qqh.empty()) {
			int h=qqh.front(), w=qqw.front(); qqh.pop(),qqw.pop();
			for(int i=0; i<20; i++) {
				int nh=h+ddy[i], nw=w+ddx[i];
				if(nh<0 || nh>H || nw<0 || nw>W || mp[nh][nw]=='#' || cost[nh][nw]<=cost[h][w]+1) continue;
				cost[nh][nw]=cost[h][w]+1;
				qh.push(nh), qw.push(nw);
			}
		}
	}
	cout<<(cost[gh][gw]==INTINF?-1:cost[gh][gw])<<endl;
}

int main() {
	cin.tie(nullptr);
	ios_base::sync_with_stdio(false);
	cout<<fixed<<setprecision(15);
	int t=1;
	while(t) {
		input();
		solve();
		t--;
	}
}