Semi-prime H-numbers

This problem is based on an exercise proposed by David Hilbert, who suggested studying the theory of numbers of the form $4n+1$. Here we explore only a small part of it.

An H-number is a positive integer that is one more than a multiple of four: $1, 5, 9, 13, 17, 21, \dots$ are the H-numbers. For this problem we pretend that these are the only numbers. The H-numbers are closed under multiplication.

Just as with the ordinary integers, we partition the H-numbers into units, H-primes, and H-composites. $1$ is the only unit. An H-number $h$ is an H-prime if it is not the unit and can be written as a product of two H-numbers in exactly one way, namely $1 \times h$. All remaining H-numbers are H-composites.

For example, the first few H-composites are $5 \times 5 = 25$, $5 \times 9 = 45$, $5 \times 13 = 65$, $9 \times 9 = 81$, and $5 \times 17 = 85$.

Your task is to count the H-semi-primes. An H-semi-prime is an H-number that is the product of exactly two H-primes; the two H-primes may be equal or different. In the example above, all five numbers are H-semi-primes. By contrast, $125 = 5 \times 5 \times 5$ is not an H-semi-prime, because it is the product of three H-primes.

Each line contains an H-number $h$ with $1 \le h \le 1000001$. The final line contains $0$ and must not be processed.

For each input H-number $h$, print a single line containing $h$ and the number of H-semi-primes between $1$ and $h$ inclusive, separated by a single space.