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(void){
    long N;
    std::cin >> N;
    long sum=0;
    for(long i=1; i<=N; i++){
        sum+=i*(N/i)*(N/i+1)/2;
    }
    std::cout << sum << std::endl;    
    return 0;
}