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 int long long
signed main(){
  int N;
  cin>>N;
  int k=0;
  for(int j=1;j<=N;j++)
    for(int i=1;i*j<=N;i++)
      k+=i*j;
  cout<<k<<endl;
}