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 REP(i, n) for(long i=1; i<=(long)(n); i++)
int main(){
long N, ans=0; cin >> N; 
REP(i, N){ ans+=(i*(N/i)*(1+N/i))/2; }
cout << ans << "\n";
}