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<bits/stdc++.h>
using namespace std;
int main(){
long long n,i,j=0,p=0;
cin>>n;
for(i=1;i<=n;i++){j=n/i;
p=p+(((j)*(j+1))/2)*i;

}cout<<p<<endl;
return 0;
}