Bajtek has forgotten his phone password. He remembers that it consisted of three distinct positive integers $a < b < c$ separated by hashes. Additionally, the sum of these numbers was $n$, and for every pair of numbers (among $(a, b)$, $(a, c)$, and $(b, c)$), one of the numbers was a multiple of the other.

Help him count how many possible triples he must check so he can decide whether it is worth wasting time on it or if it is better to buy a new phone.

Input

The first and only line of input contains a single integer $n$ ($1 \le n \le 10^9$).

Output

Output a single integer – the number of such triples $(a, b, c)$.

Examples

Input 1

35

Output 1

2

Note

The two triples are $(1, 2, 32)$ and $(5, 10, 20)$.