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>
#pragma GCC optimize ("O2")
int main(void)
{
  int K,div,N;long long a=0;K=scanf("%d",&N);
  while(K<=N){div=N/K;a+=1ll*K++*div*(div+1)/2;}
  return printf("%lld\n",a),0;
}