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 N;
  scanf("%ld",&N);
  long ans=0;
  for(long j=1;j<=N;j++){
    long X=N/j;
    ans+=(X*(X+1)/2)*j;
  }
  printf("%ld\n",ans);
}