## Goal

You might know Fermat’s small theorem:

If `n` is prime, then for any integer `a`, we have `a^n` ≡ `a` mod `n`, that means that `a^n` and `a` have the same remainder in the euclidian division by `n`.

There are numbers, called Carmichael numbers, that are not prime but for which the equality remains true for any integer `a`.

For example, 561 is a Carmichael numbers because for any integer `a`, `a^561` ≡ `a` mod `561`. It’s in fact the smallest Carmichael number.

You have to tell if the given number is a Carmichael number or not. Beware, you might be given a prime number.
Output

YES if `n` is a Carmichael number, or NO if it’s not.