ACdream原创群赛(13)のwuyiqi退役专场

H - Salmon And Cat

Time Limit: 2000/1000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

SubmitStatus

Problem Description

Math is very important, for those who are also in school, make sure you will learn more about math.

Salmon and Cat are good friends.Today Salmon ask Cat to help her judge whether a number is perfect or not. Perfect number is a kind of number defined by like this.

First, 1 and 3 are perfect number.Then if a and b are perfect numbers, 2+ab+2a+2b is also a perfect number.For example, 1 and 1 are perfect numbers,  so 2+1+2+2 = 7 is perfect number.

If Cat can't help Salmon,  Salmon will be sad and Cat will be much more sad. So Cat must solve the problem to maintain their friendship. Can you help Cat to solve the problem?

Input

This problem contains multiple test cases.

Each test case contains one line.

Each line contains an interger n, 1 <= n <= 10^9.

Output

For each test case, if n is a perfect number, output “Yes”, otherwise output “No”.

Sample Input

3
7
8

Sample Output

Yes
Yes
No

Hint

建议使用scanf printf

意解:易知偶数不是完美数;
          假设c为完美数,则c = 2+ab+2a+2b;
          c + 2 = 2+ab+2a+2b + 2 = (a + 2) * (b + 2);
          因为一开始只有1和3为完美数,所以完美数类似于 c + 2 = (3 ^ x) * (5 ^ y)这种形式.
AC代码:
          

/*
* this code is made by eagle
* Problem: 1115
* Verdict: Accepted
* Submission Date: 2014-09-25 19:57:34
* Time: 28MS
* Memory: 1676KB
*/
#include <iostream>
#include <cstdio>
 
using namespace std;
 
 
int main()
{
    int n;
    while(~scanf("%d",&n))
    {
        if(n % 2 == 0) puts("No");
        else
        {
            n += 2;
            while(n % 15 == 0) n /= 15;
            while(n % 3 == 0) n /= 3;
            while(n % 5 == 0) n /= 5;
            if(n == 1) puts("Yes");
            else puts("No");
        }
    }
    return 0;
}