AT_abc480_e [ABC480E] Product-Bounded Arithmetic Sequences

A sequence of positive integers $ A=(A_1,\dots,A_{|A|}) $ is called a **good sequence** if it satisfies all of the following conditions. - $ |A|\geq 3 $ - $ A $ is an arithmetic progression; that is, $ A_{i+1}-A_{i}=A_2-A_1 $ for all $ 1 \leq i \leq |A|-1 $ . - $ A_2-A_1 > 0 $ Find the number of good sequences such that the product of all elements is at most $ N $ . It can be proved that the answer is at most $ 10^{18} $ under the constraints.

The input is given from Standard Input in the following format: > $ N $

Print the answer.

### Sample Explanation 1 There are $ 4 $ good sequences whose product is at most $ 24 $ : $ (1,2,3),(1,2,3,4),(1,3,5),(2,3,4) $ . ### Constraints - $ 1 \leq N \leq 10^{18} $ - $ N $ is an integer.