Marcin's class has a very important math test tomorrow! Marcin's friends have sneakily found out that the only thing they will need to do on the test is to calculate the sum:

$$S_n = d(1) + d(2) + \dots + d(n)$$

for various values of $n$, where $d(i)$ denotes the number of divisors of the number $i$. Unfortunately, his friends forgot to tell Marcin exactly which values of $n$ will appear on the test. Since Marcin (and especially his parents) cares a lot about a good grade in math, Marcin decided to take a palmtop to the test, which will automate his work and ensure he gets an 'A', even if very large numbers $n$ appear on the test. Unfortunately, Marcin does not know how to program, so he asked you for help. Will your program enable him to get an 'A'?

Task

Write a program that: reads the number $n$, calculates the value of the sum $S_n$, * prints the result.

Input

The first and only line contains a single integer $n$ ($1 \le n \le 10^{12}$).

Output

The first and only line of output should contain a single integer — the value of the sum $S_n$. Remember that Marcin's grade depends on the correctness of your program!

Examples

Input 1

5

Output 1

10