#!/usr/bin/python

# -*- coding: utf-8 -*-

from collections import deque

from math import log10

def permute(seq, index):

   seqc = seq[:]

   seqn = [seqc.pop()]

   divider = 2

   while seqc:

     index, new_index = divmod(index,divider)

     seqn.insert(new_index, seqc.pop())

     divider += 1

   return seqn

def z62():

    #0~7八个数放到正方体的八个顶点上,每个面的四个数之和都相等

    a=[0, 1, 2, 3, 4, 5, 6, 7]

    n=sum(a)

    if n%2==1:

        return

    else:

        n/=2

    for i in range(0,40320):

        v1=permute(a,i)

        if (v1[0] + v1[1] + v1[2] + v1[3] == n and

            v1[0] + v1[1] + v1[4] + v1[5]== n and

            v1[0] + v1[2] + v1[4] + v1[6] == n and

            v1[0] + v1[4] + v1[4]+ v1[7] == n and

            v1[0] + v1[1] > n / 2 and v1[5] > v1[7]):

            print v1

    return

def z58():

    #构造拉丁方：拉丁方是指n*n方阵其中每行每列1到n这些数字,只出现一次

    ss=6

    d = deque(range(1,ss+1))

    for i in range(ss):

        d.rotate(1)

        print list(d)

    return

def z59():

    '''答案如

    1 2 3

    4 5 6

    其中每一列右大于左

    每一行  下大于上

    填入1~6    6个数字 '''

    t=range(2,6)

    for i in t:

        for j in t:

            for m in t:

                n=14-i-j-m

                if i!=j!=m!=i and j>i and n>m and n>i:

                    print [1,i,j]

                    print [m,n,6]

    return

def iss(n):

    s=''.join(map(str,n))

    t=set(s)

    m=len(s)

    return len(t)==m and '' not in t

def z60():

    '''如192，384，576

    384数第二数是192的二倍

    576数第二数是192的三倍

    同时各位数是1~9'''

    for i in range(111,333):

       t=[i,2*i,3*i]

       if iss(t):print t

def z61():

    #如361，529，784,他们三数是完全平方,如361=19*19同时各位数是1~9

    ge=[x*x for x in range(11,31)]

    for i in ge:

        for j in ge:

            for m in ge:

                t=[i,j,m]

                if i<j<m and iss(t):print t

def zz68(n):

    if n==2 :return filter(lambda x: x%2==0,range(11,99))

    t=[]

    p=zz68(n-1)

    for j in p:

        for i in range(10):

            nn=j*10+i

            if iss([nn]) and nn%n==0:

                t.append(nn)

    return t

def z66():

    '''除式还原

    ~          x7x

    ~  xx /--------

    ~    /   xxxxx

    ~        x77

    ~      ------

    ~         x7x

    ~         x7x

    ~         ----

    ~          xx

    ~          xx

    ~          ---

    ~           0

    '''

    for i in range(1,10):

        for j in range(11,100):

            m2 = i * j

            m3 = 7 * j

            if ((m2 % 100 == 77 and m2 >100) and (m3 / 10 % 10 == 7 and m3 > 100)):

                for k in range(1,10):

                    if k*j<100:

                        print [i*100+70+k,j]

    return

def z67():

    '''除式还原2

    ~            x7xxx

    ~  xxx /-----------

    ~     /   xxxxxxxx

    ~         xxxx

    ~        ------

    ~          xxx

    ~          xxx

    ~        -------

    ~           xxxx

    ~            xxx

    ~         ---------

    ~             xxxx

    ~             xxxx

    ~          ---------

    ~                0

    '''

    g=lambda x,y:map(lambda a,b=x:int(log10(a*b))+1,y)==[4,3,3,4]

    t=[8,9]

    for i in range(100,142):

        for j in t:

            for m in t:

                for n in t:

                    n1=j * 10000+7000+m * 100+n

                    e=[j,7,m,n]

                    if g(i,e) and (m * 100+n)*i/10000==10:

                        print n1,i,n1*i

    return

def z68():

    #个数由123456789组成,其中前两位如12 可以被2 整除,123可以被3 整除,

    #前n位可以被n 整除,问他是多少

    print zz68(9)

def z63():

    '''减式还原

    ~        PEAR

    -         ARA

    -----------------

    ~         PEA

    其中不同的字母代表不同的数字'''

    t=range(0,10)

    for i in t:

        for j in t:

            for k in t:

                a,b,c= 100+k * 10+i,1000+k * 100+i * 10+j,i * 100+j * 10+i

                if a==b-c:

                    print [a,b,c]

def z64():

    '''乘式还原

    其中 a代表0~9前五个数字

    z代表0~9后五个数字

    ~      AZA

     *     AAZ

    -----------------

    ~     AAAA

    ~    AAZZ

    ~    ZAA

    -----------------

    ~    ZAZAA'''

    g=lambda y:''.join(map(lambda x:x> '' and '' or '' ,str(y)))

    t=range(1,5)

    m=range(5,10)

    t1=filter(lambda y:g(y)=='',range(100,500))

    for i in t1:

        for j in filter(lambda y,x=i:g(y*x)=='',t):

            for k in filter(lambda y,x=i:g(y*x)=="",t):

                for mm in filter(lambda y,x=i:g(y*x)=="",m):

                    jj =j *100+k *10+mm

                    if g(jj*i)=='':

                        print i,jj

    return

def z65():

    ''' 乘式还原2

    ~      PPP

     *      PP

    -----------

    ~     PPPP

    ~    PPPP

    -------------

    ~    PPPPP

    其中18个p的位置上全是素数2，3，5，7'''

    def g(n):

        t=str(n)

        return len(filter(lambda x: int(x) in (2,3,5,7),t))==len(t)

    for i in range(222,778):

        for j in range(11,78):

            if g(i) and g(j) and g(i*j)  and g(j%10*i)and g(int(j/10)*i):

                print i,j,i*j

if __name__ == '__main__':

    s=""

    for i in range(58,69):

        s+='z'+str(i)+'()\n'

    exec(s)