For a positive integer X, let f(X) be the number of positive divisors of X.

Given $a positive integer N, find \sum_{K=1}^N K\times f(K)$.

Constraints

• $1 \leq N \leq 10^7$

Input

Input is given from Standard Input in the following format:

N

Output

Print the value $\sum_{K=1}^N K\times f(K)$.

Examples

Input

4

Output

23

Input

100

Output

26879

Input

10000000

Output

838627288460105

见题面

见题面