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:
mem = {}
def f(n):
	if n in mem:
		return mem[n]
	ans,b = 0, 1
	while(b <= n):
		k = n / b
		ans += b *k * (k + 1) / 2  
		b +=1
	mem[n] = ans
	return ans
print f(int(raw_input()))