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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using static System.Math;
using static Program.IO.Scanner;
using Number = System.Int64;
using System.Numerics;
#region IO
namespace Program.IO {
	using System.IO;
	using System.Text;
	using System.Globalization;

	public class Printer : StreamWriter {
		public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
		public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	}
	static public class Scanner {
		public static StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
		public static int ri => sc.Integer();
		public static long rl => sc.Long();
		public static string rs => sc.Scan();
		public static double rd => sc.Double();
	}
	public class StreamScanner {
		public StreamScanner(Stream stream) { str = stream; }

		public readonly Stream str;
		private readonly byte[] buf = new byte[1024];
		private int len, ptr;
		public bool isEof = false;
		public bool IsEndOfStream { get { return isEof; } }

		private byte read() {
			if (isEof) return 0;
			if (ptr >= len) {
				ptr = 0;
				if ((len = str.Read(buf, 0, 1024)) <= 0) {
					isEof = true;
					return 0;
				}
			}
			return buf[ptr++];
		}

		public char Char() {
			byte b = 0;
			do b = read(); while ((b < 33 || 126 < b) && !isEof);
			return (char)b;
		}
		public string Scan() {
			var sb = new StringBuilder();
			for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
			return sb.ToString();
		}
		public string ScanLine() {
			var sb = new StringBuilder();
			for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
			return sb.ToString();
		}
		public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
		public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
		public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
	}

}

#endregion

#region main
static class Ex {
	static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
	static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
		return string.Join(st, ie);
	}

	static public void Main() {
		Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
		var solver = new Program.Solver();
		var t = new System.Threading.Thread(solver.Solve, 50000000);
		t.Start();
		t.Join();
		//*/
		//solver.Solve();
		Console.Out.Flush();
	}
}
#endregion

namespace Program {
	public class Solver {
		Random rnd = new Random(0);
		public void Solve() {
			var n=ri;
			var m=ri;
			var s=new  int[]{ri-1,ri-1};
			var t=new int[]{ri-1,ri-1};
			var mat=Enumerate(n, x => rs);
			var dist=Enumerate(n, x => new int[m]);
			for (int i = 0; i < n; i++)
			for (int j = 0; j < m; j++)dist[i][j]=1000050;
			
			dist[s[0]][s[1]]=0;
			var q=new Deque<(int,int)>();
			q.PushBack((s[0],s[1]));
			while (q.Count>0)
			{
				var (x,y)=q.PopFront();
				for (int dx = -2; dx <= 2; dx++)
				for (int dy = -2; dy <= 2; dy++){
					var (nx,ny)=(x+dx,y+dy);
					if(nx<0||nx>=n||ny<0||ny>=m)continue;
					if(mat[nx][ny]=='#')continue;
					var d= Abs(dx)+Abs(dy)==1?0:1;
					if(dist[nx][ny]>dist[x][y]+d){
						dist[nx][ny]=dist[x][y]+d;
						if(d==0)q.PushFront((nx,ny));
						else q.PushBack((nx,ny));
					}
				}
			}
			if(dist[t[0]][t[1]]>=100000){
				Console.WriteLine(-1);
			}else Console.WriteLine(dist[t[0]][t[1]]);
			
		}
		const long INF = 1L << 60;
		static int[] dx = { -1, 0, 1, 0 };
		static int[] dy = { 0, 1, 0, -1 };
		static T[] Enumerate<T>(int n, Func<int, T> f) {
			var a = new T[n]; for (int i = 0; i < a.Length; ++i) a[i] = f(i); return a;
		}
		static T[][] Enumerate<T>(int n, int m, Func<int, int, T> f) {
			return Enumerate(n, x => Enumerate(m, y => f(x, y)));
		}
		static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
	}
}


class X : IComparable<X> {
	public long l, r, h;
	public X(long L, long R, long H) {
		l = L; r = R; h = H;
	}
	public int CompareTo(X r) => this.l.CompareTo(r.l);
}

#region ModInt
/// <summary>
/// [0,<see cref="Mod"/>) までの値を取るような数
/// </summary>
public struct ModInt {
	public const long Mod = (int)1e9 + 7;
	public long num;
	public ModInt(long n) { num = n; }
	public override string ToString() { return num.ToString(); }
	public static ModInt operator +(ModInt l, ModInt r) { return new ModInt(l.num + r.num < Mod ? l.num + r.num : l.num + r.num - Mod); }
	public static ModInt operator -(ModInt l, ModInt r) { return new ModInt(l.num + Mod - r.num < Mod ? l.num + Mod - r.num : l.num - r.num); }
	public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
	public static ModInt operator /(ModInt l, ModInt r) { return l * Inverse(r); }
	public static implicit operator ModInt(long n) { return n.mod(); }
	public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }
	public static ModInt Pow(long v, long k) {
		long ret = 1;
		for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
			if ((k & 1) == 1) ret = ret * v % Mod;
		return new ModInt(ret);
	}
	public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
}
public static partial class ModIntEx {
	public static ModInt mod(this long v) {
		v %= ModInt.Mod;
		if (v < 0) v += ModInt.Mod;
		return new ModInt(v);
	}
	public static ModInt mod(this int v) {
		var u = v % ModInt.Mod;
		if (u < 0) u += ModInt.Mod;
		return new ModInt(u);
	}
	public static ModInt m(this long v) { return new ModInt(v); }
	public static ModInt m(this int v) { return new ModInt(v); }
}
#endregion
class Deque<T> {
    T[] buf;
    int offset, count, capacity;
    public int Count { get { return count; } }
    public Deque(int cap) { buf = new T[capacity = cap]; }
    public Deque() { buf = new T[capacity = 16]; }
    public T this[int index] {
        get { return buf[getIndex(index)]; }
        set { buf[getIndex(index)] = value; }
    }
    private int getIndex(int index) {
        if (index >= capacity)
            throw new IndexOutOfRangeException("out of range");
        var ret = index + offset;
        if (ret >= capacity)
            ret -= capacity;
        return ret;
    }
    public void PushFront(T item) {
        if (count == capacity) Extend();
        if (--offset < 0) offset += buf.Length;
        buf[offset] = item;
        ++count;
    }
    public T PopFront() {
        if (count == 0)
            throw new InvalidOperationException("collection is empty");
        --count;
        var ret = buf[offset++];
        if (offset >= capacity) offset -= capacity;
        return ret;
    }
    public void PushBack(T item) {
        if (count == capacity) Extend();
        var id = count++ + offset;
        if (id >= capacity) id -= capacity;
        buf[id] = item;
    }
    public T PopBack() {
        if (count == 0)
            throw new InvalidOperationException("collection is empty");
        return buf[getIndex(--count)];
    }
    public void Insert(int index, T item) {
        if (index > count) throw new IndexOutOfRangeException();
        this.PushFront(item);
        for (int i = 0; i < index; i++)
            this[i] = this[i + 1];
        this[index] = item;
    }
    public T RemoveAt(int index) {
        if (index < 0 || index >= count) throw new IndexOutOfRangeException();
        var ret = this[index];
        for (int i = index; i > 0; i--)
            this[i] = this[i - 1];
        this.PopFront();
        return ret;
    }
    private void Extend() {
        T[] newBuffer = new T[capacity << 1];
        if (offset > capacity - count) {
            var len = buf.Length - offset;
            Array.Copy(buf, offset, newBuffer, 0, len);
            Array.Copy(buf, 0, newBuffer, len, count - len);
        }
        else Array.Copy(buf, offset, newBuffer, 0, count);
        buf = newBuffer;
        offset = 0;
        capacity <<= 1;
    }
    public T[] Items//デバッグ時に中身を調べるためのプロパティ
    {
        get {
            var a = new T[count];
            for (int i = 0; i < count; i++)
                a[i] = this[i];
            return a;
        }
    }
}