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:


"""
ai             aj
bi             bj


1              2
2              1

1  how many pairs 
2
"""



import collections
n = int(raw_input())
mem = [0] * (n + 1)
mem[1] = 1
primes = [True] * (n + 1)
posprimes = []
d= 2
while( d <= n):
	if primes[d] is True:
		posprimes.append(d)
		k = 2
		while(k * d <= n):
			primes[k * d] = False
			k += 1
	d+=1
def f(k):
	if primes[k] is True:
		mem[k] = 2 if k > 1 else 1
		return mem[k]
	for pos in posprimes:
		if k % pos == 0:
			count = 0
			q = k
			while(q % pos == 0):
				q /= pos
				count += 1

			mem[k] = (count + 1) * mem[q]
			return mem[k]



s = 0
k = 1
while (k<= n):
	s += k * f(k)
	k += 1
print s




#2 4 6 8 10 12 14 16 18
#    6      12       18