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C - Four Variables

Score : $300$ points

Problem Statement

You are given a positive integer $N$.
Find the number of quadruples of positive integers $(A,B,C,D)$ such that $AB + CD = N$.

Under the constraints of this problem, it can be proved that the answer is at most $9 \times 10^{18}$.

Constraints

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

Input

The input is given from Standard Input in the following format:

$N$

Output

Print the answer.

4

8

Here are the eight desired quadruples.

• $(A,B,C,D)=(1,1,1,3)$
• $(A,B,C,D)=(1,1,3,1)$
• $(A,B,C,D)=(1,2,1,2)$
• $(A,B,C,D)=(1,2,2,1)$
• $(A,B,C,D)=(1,3,1,1)$
• $(A,B,C,D)=(2,1,1,2)$
• $(A,B,C,D)=(2,1,2,1)$
• $(A,B,C,D)=(3,1,1,1)$

292

10886

19876

2219958