Score : $300$ points

问题描述

你已知一个正整数 $N$。

找出满足条件 $A\leq B\leq C$ 且 $ABC\leq N$ 的正整数三元组 $(A, B, C)$ 的数量。

约束条件保证答案小于 $2^{63}$。

以上为通义千问 qwen-max 翻译，仅供参考。

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.

Sample Input 1

4

Sample Output 1

5

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

Sample Input 2

100

Sample Output 2

323

Sample Input 3

100000000000

Sample Output 3

5745290566750

update @ 2024/3/10 09:57:04