Sum of Divisors

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

inputFormat

Input

Input is given from Standard Input in the following format:

N

outputFormat

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

样例

4

23