Acdream 1115--to find the law--salmon and Cat

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

Salmon and Cat are good friends. Today Salmon ask Cat to help her judge whether a number are 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 were perfect numbers, 2+ab+2a+2b is also a perfect number. For example, 1 and 1 were perfect numbers, so 2+1+2+2 = 7 is perfect number.

If Cat can ' t help Salmon, Salmon'll be sad and Cat'll 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 is contains one line.

Each line contains an interger N, 1≤n≤109.

Output

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

Sample Input

378

Sample Output

Yesyesno

Hint

/*   Find Patterns   . All numbers are the product of 3 or 5 */#include <cstdio> #include <cstring>using namespace Std;int main () {    int n;    while (~SCANF ("%d", &n)) {        n + = 2;        while (n% 3 = = 0) n/= 3;        while (n% 5 = = 0) n/= 5;        if (n = = 1) printf ("yes\n");        else printf ("no\n");    } return 0;}            

　　

Acdream 1115--to find the law--salmon and Cat