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 PYTHON):

Solution:
N = int(raw_input())

ans = 0
for i in range(1, N+1):
  # i + 2i + 3i + ... + (N/i)*i
  q = N/i
  ans += (i * q * (q+1))/2
print ans