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 int long long
signed main() {
    int n;
    cin >> n;
    int i;
    int sum = 0;
    for(i=1;i<=n;i++)
        sum+=(i*(n/i)*((n/i)+1)/2);
    cout << sum;    
}