# Cantor

Cantor

The ternary expansion of a number is that number written in base 3. A number can have more than one ternary expansion. A ternary expansion is indicated with a subscript 3. For example, 1 = 13 = 0.222...3, and 0.875 = 0.212121...3.

The Cantor set is defined as the real numbers between 0 and 1 inclusive that have a ternary expansion that does not contain a 1. If a number has more than one ternary expansion, it is enough for a single one to not contain a 1.

For example, 0 = 0.000...3 and 1 = 0.222...3, so they are in the Cantor set. But 0.875 = 0.212121...3 and this is its only ternary expansion, so it is not in the Cantor set.

Your task is to determine whether a given number is in the Cantor set. The input consists of several test cases.

Each test case consists of a single line containing a number x written in decimal notation, with 0 <= x <= 1, and having at most 6 digits after the decimal point.

The last line of input is END. This is not a test case.

For each test case, output MEMBER if x is in the Cantor set, and NON-MEMBER if x is not in the Cantor set.

``````0
1
0.875
END
``````

``````MEMBER
MEMBER
NON-MEMBER
``````

``````#include<stdio.h>
#include<string.h>
#include<stdlib.h>
int main()
{
int i,t;
double x;
char a;
while(gets(a),strcmp(a,"END"))
{
x=atof(a);
t=0;
if(x==0||x==1)
printf("MEMBER\n");
else
{
i=13;
while(i--)
{
x=(x-(int)x)*3;
if((int)x==1)
{
printf("NON-MEMBER\n");
t++;
break;
}
}
if(t==0)
printf("MEMBER\n");
}
}
return 0;
}``````

``````#include <iostream>
#include <set>
#include <cstring>
#define INF 100000
#define LNF 1000000
#define MAX 666667
using namespace std;
void om()
{
cout<<"MEMBER"<<endl;
}
int main()
{
char n;
char end[]="END";
while(cin>>n)
{
if(strcmp(n,end)==0)break;
int len=strlen(n);
if(len==1)
{
om();
continue;
}
int num=0;
int i;
set<int> st;
for(i=2;i<len;i++)
{
num=num*10+n[i]-'0';
}
int count=0;
while(num<INF)
{
if(count++>=5)break;
num*=10;
}
if(num==0)
{
om();
continue;
}
bool achive=false;
while(1)
{
while(num<LNF)num*=3;
if(st.count(num))break;
st.insert(num);
if(num/LNF==1)
{
achive=true;
break;
}
num%=LNF;
}
if(!achive)om();
else cout<<"NON-MEMBER"<<endl;
}
return 0;
}
``````