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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys,bisect,string,math,time,functools,random,fractions
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
rep=range;R=range
def Golf():n,*t=map(int,open(0).read().split())
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def MI():return map(int,input().split())
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def RA():return map(int,open(0).read().split())
def RLI(n=8,a=1,b=10):return [random.randint(a,b)for i in range(n)]
def RI(a=1,b=10):return random.randint(a,b)
def Rtest(T):
    case,err=0,0
    for i in range(T):
        inp=INP()
        a1,ls=naive(*inp)
        a2=solve(*inp)
        if a1!=a2:
            print((a1,a2),inp)
            err+=1
        case+=1
    print('Tested',case,'case with',err,'errors')
def GI(V,E,ls=None,Directed=False,index=1):
    org_inp=[];g=[[] for i in range(V)]
    FromStdin=True if ls==None else False
    for i in range(E):
        if FromStdin:
            inp=LI()
            org_inp.append(inp)
        else:
            inp=ls[i]
        if len(inp)==2:
            a,b=inp;c=1
        else:
            a,b,c=inp
        if index==1:a-=1;b-=1
        aa=(a,c);bb=(b,c);g[a].append(bb)
        if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1):
    #h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage
    mp=[boundary]*(w+2);found={}
    for i in R(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
    mp+=[boundary]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def accum(ls):
    rt=[0]
    for i in ls:rt+=[rt[-1]+i]
    return rt
def bit_combination(n,base=2):
    rt=[]
    for tb in R(base**n):s=[tb//(base**bt)%base for bt in R(n)];rt+=[s]
    return rt
def gcd(x,y):
    if y==0:return x
    if x%y==0:return y
    while x%y!=0:x,y=y,x%y
    return y
def YN(x):print(['NO','YES'][x])
def Yn(x):print(['No','Yes'][x])
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)

mo=10**9+7
inf=float('inf')
FourNb=[(-1,0),(1,0),(0,1),(0,-1)];EightNb=[(-1,0),(1,0),(0,1),(0,-1),(1,1),(-1,-1),(1,-1),(-1,1)];compas=dict(zip('WENS',FourNb));cursol=dict(zip('LRUD',FourNb))
l_alp=string.ascii_lowercase
#sys.setrecursionlimit(10**9)
read=sys.stdin.buffer.read;readline=sys.stdin.buffer.readline;input=lambda:sys.stdin.readline().rstrip()

inf=1<<20
def dijkstra(edge,st):
    n=len(edge)
    d=[(0 if st==i else inf) for i in range(n)]
    q=[(0,st)]
    heapify(q)
    v=[False]*n
    while q:
        dist,cur=heappop(q)
        if v[cur]:
            continue
        v[cur]=True
        for dst,dist in edge[cur]:
            alt=d[cur]+dist
            if alt<d[dst]:
                d[dst]=alt
                heappush(q,(alt,dst))
    return d

# Under construction
# To be verified by https://atcoder.jp/contests/abc176/tasks/abc176_d

class GridGraph:
    def __init__(self,h,w,search=None,replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1):
        self.h=h+2
        self.w=w+2
        self.n=self.h*self.w
        self.edge=[[]for i in range(self.n)]
        self.nb=[-1,1,-self.w,self.w]
        #h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage
        self.mp=[boundary]*self.w
        self.found={}
        for i in range(self.h-2):
            s=input()
            self.mp+=[boundary]
            for i in range(self.w-2):
                char=s[i]
                if search and char in search:
                    self.found[char]=((i+1)*self.w+i+1)
                    mp_def[char]=mp_def[replacement_of_found]
                self.mp+=[mp_def[char]]
            self.mp+=[boundary]
        self.mp+=[boundary]*self.w
        self.h,self.w,self.mp,self.found
        return

    def create_edge(self,cost_func=lambda x,y:1):
        w=self.w
        nbw=[2,2*w+1,2*w+2,w+1,w+2,+2*w,2*w-1,2*w-2,w-1,w-2]
        for i in range(self.n):
            if self.mp[i]==1:
                continue
            for di in self.nb:
                nx=i+di
                if self.mp[nx]!=1:
                    #self.edge[i].append((nx,cost_func(self.mp[i],self.mp[nx])))
                    self.edge[i].append((nx,0))
            
            for di in nbw:
                nx=i+di
                if 0<=nx<self.n and self.mp[nx]!=1:
                    self.edge[i].append((nx,1))
                    self.edge[nx].append((i,1))
            
        return self.edge


    def dfs(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0):
        q=deque([x])
        v=[None]*self.node_size
        v[x]=root_v
        while q:
            c=q.pop()
            for nb,d in self.edges[c]:
                if v[nb]==None:
                    q.append(nb)
                    v[nb]=func(c,v[c],nb,d)
        return v
 
    def bfs(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0):
        q=deque([x])
        v=[None]*self.node_size
        v[x]=root_v
        while q:
            c=q.popleft()
            for nb,d in self.edges[c]:
                if v[nb]==None:
                    q.append(nb)
                    v[nb]=func(c,v[c],nb,d)
        return v

    def __str__(self):
        for i in range(self.h):
            print(self.mp[i*self.w:(i+1)*self.w])
        return ''
 
    def show_map(self,length=2):
        for i in range(self.h):
            print(*[' '*(length-(len(str(j))))+str(j) for j in self.mp[i*self.w:(i+1)*self.w]])

    def show_node_num(self,length=2):
        for i in range(self.h):
            print(*[' '*(length-(len(str(j))))+str(j) for j in range(i*self.w,(i+1)*self.w)])

    def show_map_w_node_num(self,length=2):
        for i in range(self.h):
            print(*[[' '*(length-(len(str(j))))+str(j),self.mp[j]] for j in range(i*self.w,(i+1)*self.w)])
    
    def show_edge(self,length=2):
        for i in range(self.h):
            print(*[[' '*(length-(len(str(j))))+str(j),self.edge[j]] for j in range(i*self.w,(i+1)*self.w)])


    def dfs2(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0):
        q=deque([x])
        v=[None]*self.node_size
        v[x]=root_v
        dfs_tr=[x]
        while q:
            c=q.pop()
            for nb,d in self.edges[c]:
                if v[nb]==None:
                    q.append(nb)
                    v[nb]=func(c,v[c],nb,d)
                    dfs_tr+=nb,
        return v,dfs_tr

show_flg=False
show_flg=True

ans=0

h,w=LI()
sh,sw=LI()
gh,gw=LI()

gg=GridGraph(h,w)
gg.create_edge()
d=dijkstra(gg.edge,sh*gg.w+sw)
ans=d[gh*gg.w+gw]
if ans==inf:
    ans=-1
print(ans)