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C - ABC conjecture

Score : $300$ points

Problem Statement

You are given a positive integer $N$.

Find the number of triples of positive integers $(A, B, C)$ such that $A\leq B\leq C$ and $ABC\leq N$.

The Constraints guarantee that the answer is less than $2^{63}$.

Constraints

• $1 \leq N \leq 10^{11}$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.

4

5

There are five such triples: $(1,1,1),(1,1,2),(1,1,3),(1,1,4),(1,2,2)$.

100

323

100000000000

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