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D - Together Square

Score : $400$ points

Problem Statement

You are given an integer $N$. Find the number of pairs $(i,j)$ of positive integers at most $N$ that satisfy the following condition:

• $i \times j$ is a square number.

Constraints

• $1 \le N \le 2 \times 10^5$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.

4

6

The six pairs $(1,1),(1,4),(2,2),(3,3),(4,1),(4,4)$ satisfy the condition.

On the other hand, $(2,3)$ does not, since $2 \times 3 =6$ is not a square number.

254

896