Given an integer number n. Get all divisor of n then count number of prime factor in each divisor.

Divisor of n is all numbers that divide n.

Prime factor of N is number of primes in N. For example, 12 is 2^2 * 3^1 so 12 has 3 prime numbers 2, 2, 3.

Note: 1 is not prime.

Input

input contain one integer N where 1 <= N <= 10000

Output

Print number of prime factors for all divisor of N.

Print endl after the test case

Example

Input:
6

Output:
4

Explanation

Divisors of 6 are 1, 2, 3, 6.

• 1 contains 0 prime.
• 2 contains 1 prime.
• 3 contains 1 prime.
• 6 contains 2 prime.