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 <iostream>
using namespace std;

long long n, ans;

int main() {
    cin >> n;
    for(long long k = 1; k <= n; k++) {
        long long i = n/k;
        ans += k*i*(i+1)/2;
    }
    cout << ans;
}