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 Julia (1.4.0) (judge verdict: Wrong Answer)

function main()
    H,W = reads(Int,Int)
    c = reads(Int,Int)
    d = reads(Int,Int)
    kabe = zeros(Bool, H,W)
    for i in 1:H
        s = pread(String)
        for j in 1:W
            kabe[i,j] = s[j] == '.'
        end
    end
    reachable = false
    checked = zeros(Bool, H,W)
    checked[c...] = true
    wcs = zeros(Int, H, W)
    wcs[c...] = 1
    st = Set([c])
    ss = Set(Tuple{Int,Int}[])
    while !isempty(st)
        while !isempty(st)
            p = pop!(st)
            if p == d
                reachable = true
                st = []
                ss = []
                break
            end
            for sa in [(-1,0),(1,0),(0,-1),(0,1)]
                sp = p.+sa
                if 0 < sp[1] <= H && 0 < sp[2] <= W
                    if !checked[sp...] && kabe[p...] == kabe[sp...]
                        checked[sp...] = true
                        wcs[sp...] = wcs[p...]
                        push!(st, sp)
                    end
                end
            end
            push!(ss, p)
        end
        while !isempty(ss)
            p = pop!(ss)
            for i in -2:2, j in -2:2
                rp = p[1]+i,p[2]+j
                if 0 < rp[1] <= H && 0 < rp[2] <= W  && !checked[rp...] && kabe[rp...] && (wcs[rp...] == 0 || wcs[rp...] > wcs[p...]+1)
                    checked[rp...] = true
                    wcs[rp...] = wcs[p...]+1
                    push!(st, rp)
                    break
                end
            end
        end
    end
    println(reachable ? wcs[d...]-1 : -1)
end

import Base.parse
import Base.StringVector

parse(::Type{String},  str::AbstractString) = str
isdelim(x::UInt8, xs::Set{UInt8}) = x in xs
const delimset = Set([0x0a, 0x20])

function myreaduntil(s::IO, delims::Set{UInt8})::Vector{UInt8}
    out = StringVector(0)
    c::UInt8 = 0x00
    while !eof(s)
        c = read(s, UInt8)
        !isdelim(c, delims) && break
    end
    push!(out, c)
    eof(s) && return out
    while !eof(s)
        c = read(s, UInt8)
        isdelim(c, delims) && break
        push!(out, c)
    end
    return out
end

function readword(io::IO = stdin, delims = delimset)::String
    word = myreaduntil(io, delims)
    i = length(word)
    if i == 0 || word[i] != 0x0a
        return String(word)
    elseif i < 2 || word[i-1] != 0x0d
        return String(resize!(word,i-1))
    else
        return String(resize!(word,i-2))
    end
end

pread(ty) = parse(ty, readword())

reads(tys...)::Tuple{tys...} = Tuple{tys...}(pread(ty) for ty in tys)

function readvec(tys::Tuple , len::Signed)::Tuple{map(x -> Vector{x},tys)...}
    rv = Tuple{map(x -> Vector{x},tys)...}(Vector{ty}(undef,len) for ty in tys)
    for i in 1:len
        for j in 1:length(tys)
            @inbounds rv[j][i] = pread(tys[j])
        end
    end
    rv
end

readvec(ty::Type, len::Signed)::Vector{ty} = @inbounds ty[pread(ty) for i in 1:len]

function readmat(ty::Type, s...)::Matrix{ty}
    v = Matrix{ty}(undef, s...)
    @inbounds for i in 1:s[1]
        v[i,:] = readvec(ty, s[2])
    end
    v
end

main()