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?
This problem contains multiple test cases.
Each test case contains one line.
Each line contains an interger n, 1 ≤ n ≤ 109.
For each test case, if n is a perfect number, output “Yes”, otherwise output “No”.