Problem Description

This problem is translated from PA 2018 Trial Round PIN.

Bytie forgot the phone PIN. He remembers it consists of three distinct positive integers $a < b < c$. The sum of these numbers is $n$. Also, for every pair of numbers (among $(a, b)$, $(a, c)$, and $(b, c)$), one number is a multiple of the other.

Help him compute the number of possible triples he needs to check, so that he can decide whether it is worth wasting time trying PINs.

Input Format

One line contains a positive integer $n$.

Output Format

Output one integer, the number of valid triples.

35

2

Hint

Explanation for Sample 1

There are two feasible triples: $(1,2,32)$ and $(5,10,20)$.

Constraints

This problem uses bundled testdata.

For $100\%$ of the data, it is guaranteed that $1 \le n \le 10^9$.

Translated by ChatGPT 5