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E - Fraction Floor Sum

Score : $500$ points

Problem Statement

Given is a positive integer $N$. Find the value $\displaystyle\sum_{i=1}^N \left[ \frac{N}{i} \right]$.

Here, for a real number $x$, $[x]$ denotes the largest integer not exceeding $x$.

Constraints

• $1 \leq N \leq 10^{12}$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.

3

5

We have $\left[ \frac{3}{1} \right]+\left[ \frac{3}{2} \right]+\left[ \frac{3}{3} \right]=3+1+1=5$.

10000000000

231802823220

Note that the input and output may not fit into a $32$-bit integer type.