B. Pluto Discovery!
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Pluto has just been named a planet! However, one of NASA's satellites thinks that in $$$n$$$ $$$(1 \leq n \leq 10^5$$$) years, an asteroid will come and destroy the planet. In order to save Pluto, NASA needs to calculate the sum of all remainders when $$$n$$$ is divided by every number from 1 to $$$n$$$, inclusive.

Input

The first and only line of input will contain $$$n$$$ $$$(1 \leq n \leq 10^5$$$).

Output

Output a single integer, denoting the number that NASA needs you to calculate.

Example
Input
5
Output
4