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;
 
#define int long long
 
#define PB	push_back
#define ALL(x)	(x).begin(), (x).end()
#define ALLR(x)	(x).rbegin(), (x).rend()
#define MP	make_pair
 
template <typename A, typename B>
string to_string(pair<A, B> p);
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
 
string to_string(const string& s) {
  return '"' + s + '"';
}
 
string to_string(const char* s) {
  return to_string((string) s);
}
 
string to_string(bool b) {
  return (b ? "true" : "false");
}
 
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
 
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
 
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}
 
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
 
void debug_out() { cerr << endl; }
 
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
//~ #define LOCAL
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
 
#define FAST_IO ios::sync_with_stdio(false); cin.tie(0)
 
typedef pair<int, int> ii;
typedef pair<pair<int, int>, int> iii;
typedef vector<int> vi;
typedef vector<iii> viii;
typedef vector<vi> vvi;
typedef vector<ii> vii;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef unsigned long long ull;
 
const int INF = LONG_LONG_MAX;
const int NINF = LONG_LONG_MIN/2;
const double PI = 3.141592653589793238;

//MODULAR ARITHMATIC
const int mmod = 1000000000+7 ;

int add(int a, int b, int m=mmod) {
	return (a%m + b%m)%m;
}

int sub(int a, int b, int m=mmod) {
    return (a%m - b%m + m)%m;
}

int mul(int a, int b, int m=mmod) {
	return ((a%m) * (b%m) % m);
}

int pwr(int a, int b, int m=mmod) {
    a %= m;
    int r = 1;
    while (b) {
		if (b&1) r = r*a%m;
		b >>= 1;
		a = a*a%m;
    }
    return r;
}

int inv(int a, int m=mmod) {
	return pwr(a, m-2, m);
}

bool multi = false;
struct Solve {
	string endl = "\n";
	
	Solve() {
		int h, w;
		cin >> h >> w;
		int ch, cw;
		cin >> ch >> cw;
		int dh, dw;
		cin >> dh >> dw;
		
		string s[h];
		for (int i = 0; i < h; i++) {
			cin >> s[i];
		}
		
		vvi vis(h+1, vi(w+1));
		
		
		queue<ii> q;
		int cnt = 0;
		q.push({ch, cw});
		
		bool ok = true;
		vector<ii> list;
		set<ii> list2;
		while (true) {	
			for (int i = 0; i < (int)list.size(); i++) {
				for (int j = -2; j <= 2; j++) {
					for (int k = -2; k <= 2; k++) {
						if (list[i].first + j >= 1 && list[i].second + k >= 1 &&
						    list[i].first + j <= h && list[i].second + k <= w) {
							if (s[list[i].first+j-1][list[i].second+k-1] == '.' && !vis[list[i].first+j][list[i].second+k]) {
								if (vis[list[i].first+j][list[i].second+k] == false) {
									list2.insert({list[i].first+j, list[i].second+k});
								}
						//		vis[list[i].first+j][list[i].second+k] = true;
							}
						}
					}
				}
			}
			for (ii x: list2) q.push(x);
			
			debug(list);
			debug(vis);
			if (q.size() == 0) {
				ok = false;
				break;
			}

			list.clear();
			list2.clear();
			while (!q.empty()) {
				ii cur = q.front();
				q.pop();
				debug(cur);
				list.PB(cur);
				vis[cur.first][cur.second] = 1;
				if (cur.first + 1 <= h && s[cur.first][cur.second-1] == '.' && !vis[cur.first+1][cur.second]) {
					q.push({cur.first+1, cur.second});
				}
				if (cur.first - 1 >= 1 && s[cur.first-2][cur.second-1] == '.' && !vis[cur.first-1][cur.second]) {
					q.push({cur.first-1, cur.second});			
				}
				if (cur.second + 1 <= w && s[cur.first-1][cur.second] == '.' && !vis[cur.first][cur.second+1]) {
					q.push({cur.first, cur.second+1});
				}
				if (cur.second - 1 >= 1 && s[cur.first-1][cur.second-2] == '.' && !vis[cur.first][cur.second-1]) {
					q.push({cur.first, cur.second-1});
				}
			}
			if (vis[dh][dw]) {
				break;
			}
			cnt++;
		}
		
		if (ok) {
			cout << cnt << endl;
		} else {
			cout << -1 << endl;
		}
		
	}
};

int32_t main() {
	FAST_IO;
	
	int T=1;
	if (multi)
		cin >> T;
	for (int i = 1; i <= T; i++) {
		Solve me;
	}
}
// g++ -Wall -Wextra -pedantic -std=c++17 -O2 -Wshadow -Wformat=2 -Wfloat-equal -Wconversion -Wlogical-op -Wshift-overflow=2 -Wduplicated-cond -Wcast-qual -Wcast-align -D_GLIBCXX_DEBUG -D_GLIBCXX_DEBUG_PEDANTIC -D_FORTIFY_SOURCE=2 -fsanitize=address -fsanitize=undefined -fno-sanitize-recover -fstack-protector