Given an integer N as input you need to tell whether N can be expressed in the form a₁^b₁ * a₂^b₂ * a₃^b₃ .....a_T^b_T where a_i > a_i+1 and all a_is and b_is are prime .If the number could be expressed in the above form you need to ouput "YES" followed by value of expression a₁^b₁+1 * a₂^b₂+1 * a₃^b₃+1 .....a_T^b_T+1 modulo 1000000007 on the same line or otherwise output "NO" .
T = Total number of distinct prime factors of N .

CONSTRAINTS
1<=N<=10^18

INPUT
An Integer N as given in the problem

OUPUT
"YES" followed by the value of expression modulo 1000000007 or "NO"