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 g(x) ((x*(x+1))/2)

int main(){
    int N;
    cin >> N;
    long long s=0;
    for(int i=1; i<=N; i++){
        s += i*g((long long)N/i);
    }
    cout << s << endl;
}