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<stdio.h>
int main()
{
  int i,num,N;i=scanf("%d",&N)+1;long ans=1l*N*(N+1)-1;
  while(i*i<=N){num=N/i;ans+=i*(1l*num*num-i*i+num);i++;}
  return printf("%ld\n",ans),0;
}