import itertools

alphabet = "01234567"

cet = "0246"

necet = "1357"

ar = itertools.permutations(alphabet, 5)

arl = []

for e in ar:

arl.append(list(e))

count = 0

for e in arl:

flag = True

for i in range(len(e)-1):

if (e[i] in cet and e[i+1] in cet) or (e[i] in necet and e[i+1] in necet) or e[0] == '0' or e.count('1') != 0:

flag = False

if flag:

count += 1

print(count)

from itertools import *

word = '0234567'

count = 0

for i in permutations(word,5):

x = ''.join(i)

if x[0] != '0':

x = x.replace('7','1').replace('5','1').replace('3','1').replace('6','0').replace('4','0').replace('2','0')

if ('00' not in x) and ('11' not in x):

count += 1

print(count)

from itertools import*

s = permutations('01234567',5)

cnt = 0

for i in s:

p=''.join(i)

if p[0]!='0' and p.count('1')==0:

if int(p[0])%2 != int(p[1])%2 and int(p[1])%2 != int(p[2])%2 and int(p[2])%2 != int(p[3])%2 and int(p[3])%2 != int(p[4])%2:

cnt += 1

print(cnt)

cnt = 0

for i in range(1, 100000):

i = str(oct(i)[2:])

if len(i) == 5 and '1' not in i:

p = [int(d) for d in i]

if len(set(p)) == 5:

if all(p[i]%2 != p[i+1]%2 for i in range(4)):

cnt += 1

print(cnt)