The hacker Michael develops breakthrough password manager, which is called
KEK (Keeper of Encrypted Keys). A distinctive feature of KEK is excellent
security. To achieve this, Michael had to develop innovative encryption
scheme. For example, in the well-known RSA scheme the sum of prime powers
in the factorization is equal to 2, whereas in Michael’s scheme this
sum is equal to 20!
However, the current version of the KEK runs very slow. Michael has found
out that the problem is in the function of checking a modulus for
correctness. This function should take the number n and answer, whether
the sum of prime powers included in the factorization of n is equal to
20. Can you do this quickly?
Remember that the factorization of an integer is the representation of it in
the form like p1α1 · p2α2 · ... ·
pkαk, where pi are prime numbers, and αi > 0. It is
known that such representation is unique. Then the sum of powers looks
like α1 + α2 + ... + αk.
The only line contains an integer n (1 ≤ n ≤ 1018).
If the sum of prime powers, included in the factorization of n,
is equal to 20, then output “Yes”, otherwise output “No”.
Problem Author: Vladimir Leskov
Problem Source: Ural FU Junior Championship 2016