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>
#define rep(i,n) for(int i=1;i<(int) (n);i++)
using namespace std;
int main(){
  int64_t n,c=0;
  cin >> n;
  rep(i, n+1){
    int64_t y=n/i;
    c+=(y*(y+1)*i)/2;
  }
  cout << c << endl;
}