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(input())
cnt = [1] * (n + 1)
tot = 1
for i in xrange(2, n + 1):
    for j in xrange(i, n + 1, i):
        cnt[j] += 1
    tot += i * cnt[i]
print tot