Problem: 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

Solution (in CPP):

Solution:
#include <iostream>
 
int main()
{
    long long N;
    std::cin >> N;
    long long ans = 0;
    for (long long i=1; i<N+1; i++)
    {
        long long n = N/i;
        ans += i*(n*(n+1))/2;
    }
    std::cout << ans;
}