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>

int main()
{
    int n;
    std::cin >> n;
    long long ans = 0;
    for (int i=1; i<=n; ++i) {
        long num = n / i;
        ans += i * (num * (num + 1) / 2);
    }
    std::cout << ans << std::endl;
}