Splitting Natural Numbers

Fusu loves to split natural numbers. For a given positive integer \(n\), if \(n = i\times j\times k\) for some positive integers \(i, j, k\), we call the ordered triple \((i,j,k)\) an excellent splitting of \(n\). Note that the order matters, so for example, when \(n=2\), we have:

• \(2 = 1 \times 1 \times 2\)
• \(2 = 1 \times 2 \times 1\)
• \(2 = 2 \times 1 \times 1\)

Thus, if \(f(n)\) is the number of excellent splittings of \(n\), your task is to compute the sum \[ S = \sum_{n=1}^N f(n). \]

inputFormat

The input consists of a single line containing a positive integer \(N\). (\(1 \le N\))

outputFormat

Output a single integer, the value of \(\sum_{n=1}^N f(n)\).

sample

1

1