Sum of Distinct Prime Factors

Given an integer $N$, compute the sum of its distinct prime factors. If a prime factor appears more than once in the prime factorization of $N$, it should be included only once. Since the computed sum might be very large, output the result modulo $10^9+7$.

For example, if $N = 28$, its prime factorization is $2^2 \times 7$, so the distinct prime factors are $2$ and $7$, and the answer is $2 + 7 = 9$.

inputFormat

The input consists of a single integer $N$ ($1 \le N \le 10^9$) provided via standard input.

outputFormat

Output a single integer representing the sum of the distinct prime factors of $N$, modulo $10^9+7$, to standard output.## sample

28

9