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>

using namespace std;
#define ll long long

int main() {
ll n;
cin>>n;
ll sum=0;
for(ll i=1;i<=n;i++)
{
    ll t=n/i;
    sum+=((t*(t+1))/2)*i;
    
    
}
    cout<<sum<<endl;
    
    
    
    return 0;
}