Your older brother is an amateur mathematician with lots of
experience. However, his memory is very bad. He recently got
interested in linear algebra over finite fields, but he does
not remember exactly which finite fields exist. For you, this
is an easy question: a finite field of order $q$ exists if and only if $q$ is a prime power, that is,
$q = p^ k$ holds for some
prime number $p$ and some
integer $k \geq 1$.
Furthermore, in that case the field is unique (up to
isomorphism).
The conversation with your brother went something like
this:
Input
The input consists of one integer $q$, satisfying $1 \leq q \leq 10^9$.
Output
Output “yes” if there exists a
finite field of order $q$.
Otherwise, output “no”.
Sample Input 1 
Sample Output 1 
1

no

Sample Input 2 
Sample Output 2 
37

yes

Sample Input 3 
Sample Output 3 
65536

yes
