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())
A=[1]*(n+1)
A[1]=1
for i in range(2,n+1):
    for j in range(i,n+1,i):
        A[j]+=1
A[1]=1
sum=0
for i in range(1,n+1):
    sum+=i*A[i]
print(sum)