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>
#define ll long long int
#define ld long double
#define f first
#define s second
#define pb push_back
#define eb emplace_back
#define mk make_pair
#define mt make_tuple
#define MOD 1000000007
#define fo(i,a,b) for(i=a;i<b;i++)
#define foe(i,a,b) for(i=a;i<=b;i++)
#define all(x) x.begin(), x.end()
#define vi vector<int>
#define vl vector <long long int>
#define pii pair <int,int>
#define pll pair <long long int, long long int>
#define vpii vector< pair<int,int> >
#define vpll vector < pair <long long int,long long int> > 
#define boost ios::sync_with_stdio(false); cin.tie(0)
using namespace std;
const int inf = 1e9 + 5;
const ll inf64 = 1e18 + 5;

const int MAX = 1e3 + 5;
int id[MAX][MAX];
char arr[MAX][MAX];
bool vis[MAX][MAX];
vector <int> adj[MAX];

int dx[] = {1, -1, 0, 0};
int dy[] = {0, 0, 1, -1};
void flood(int x, int y, int n, int m, int cnt)
{
    if(x <= 0 || y <= 0 || x > n || y > m || arr[x][y] == '#' || vis[x][y]) return;
    vis[x][y] = 1;
    id[x][y] = cnt;
    
    for(int i = 0; i < 4; i++)
    flood(x + dx[i], y + dy[i], n, m, cnt);
}
int main()
{
	boost;
	int n, m, i, j, i1, j1;
	cin >> n >> m;
	
	int ch, cw;
	cin >> ch >> cw;
	
	int dh, dw;
	cin >> dh >> dw;
	
	foe(i, 1, n) {
	    foe(j, 1, m)
	    cin >> arr[i][j];
	}
	
	int cnt = 0;
	foe(i, 1, n) {
	    foe(j, 1, m) {
	        if(arr[i][j] == '#' || vis[i][j]) continue;
	        ++cnt;
	        flood(i, j, n, m, cnt);
	    }
	}
	foe(i, 1, n) {
	    foe(j, 1, m) {
	        if(arr[i][j] == '#') continue;
	        
	        foe(i1, max(1, i - 2), min(n, i + 2)) {
	            foe(j1, max(1, j - 2), min(m, j + 2)) {
	                if(arr[i1][j1] == '#' || id[i1][j1] == id[i][j]) continue;
	                int x = id[i][j], y = id[i1][j1];
	                adj[x].pb(y);
	                adj[y].pb(x);
	            }
	        }
	    }
	}
	
	int st = id[ch][cw], en = id[dh][dw];
	bool vs[cnt + 1];
	int dist[cnt + 1];
	fill(dist, dist + cnt + 1, inf);
	memset(vs, 0, sizeof vs);
	
	queue <int> q;
	dist[st] = 0;
	q.push(st);
	vs[st] = 1;
	
	while(!q.empty()) {
	    int p = q.front();
	    q.pop();
	    
	    for(int v : adj[p]) {
	        if(!vs[v]) {
	            vs[v] = 1;
	            dist[v] = dist[p] + 1;
	            q.push(v);
	        }
	    }
	}
	cout << (dist[en] == inf ? -1 : dist[en]);
}