After barely passing Algebra I, Parsa swore to take revenge on the unit. After much plotting, he's now ready to present his problem to the professor.
Parsa defines a sequence of natural numbers d_1, d_2, ..., d_k to be n-Abelian if all the following conditions are satisfied:
1. Every number in the sequence must be greater than 1. In other words, for every i, we have d_i > 1.
2. The product of all the numbers in the sequence must be equal to n, i.e., d_1 * d_2 * ... * d_k = n.
3. If the sequence has more than one element, each number must divide the next one: d_1 | d_2, d_2 | d_3, ..., d_{k-1} | d_k~.
Given n, tell Parsa how many n-Abelian sequences exist.

Input Format:

The first line an integer n.

Output:

Output the number of different sequences.

Sample Input:

8

Sample Output:

3