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;
#define pi 2*asin(1.0)
 
int main() {

int N;
cin>>N;
long Answer=0;
long A;
for(int i=1;i<N+1;i++){
A=N/i;
Answer+=i*A*(A+1)/2;
}


cout<<Answer<<endl;

}