Problem Statement

For a positive integer X, let f(X) be the number of positive divisors of X.
Given $a positive integer N, find \sum_{K=1}^N K\times f(K)$.

Input

Input is given from Standard Input in the following format:
N

Output

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

Constraints

• $1 \leq N \leq 10^7$

Sample Input 1

4

Sample Output 1

23

We have f(1)=1, f(2)=2, f(3)=2, and f(4)=3, so the answer is $1\times 1 + 2\times 2 + 3\times 2 + 4\times 3 =23$.

Sample Input 2

100

Sample Output 2

26879

Sample Input 3

10000000

Sample Output 3

838627288460105

Watch out for overflows.

见题面 Input 部分

见题面 Output 部分