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>
#include<algorithm>

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