# Problem C

Semi-prime H-numbers

This problem is based on an exercise of David Hilbert, who pedagogically suggested that one study the theory of $4n+1$ numbers. Here, we do only a bit of that.

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

As with regular integers, we partition the **H**-numbers into units, **H**-primes, and **H**-composites. $1$ is the only unit. An **H**-number $h$ is **H**-prime
if it is not the unit, and is the product of two **H**-numbers in only one way: $1 \cdot h$. The rest of the numbers
are **H**-composite.

For examples, the first few **H**-composites are: $5 \cdot 5 = 25$, $5 \cdot 9 = 45$, $5 \cdot 13 = 65$, $9 \cdot 9 = 81$, $5 \cdot 17 = 85$.

Your task is to count the number of **H**-semi-primes. An **H**-semi-prime is an **H**-number which can be written as the product of
exactly two **H**-primes. The two **H**-primes may be equal or different. Of the
examples above, all five numbers are **H**-semi-primes. $125 = 5 \cdot 5 \cdot 5$ is not an
**H**-semi-prime, because it is the product
of three **H**-primes.

## Input

Each line of input contains an **H**-number $h \le
1\, 000\, 001$. The last line of input contains
$0$ and this line should
not be processed. There are at most $10\, 000$ test cases.

## Output

For each **H**-number $h$ in the input, print a line with
$h$ followed by the number
of **H**-semi-primes between $1$ and $h$ inclusive, separated by one space
in the format shown in the sample.

Sample Input 1 | Sample Output 1 |
---|---|

21 85 789 0 |
21 0 85 5 789 62 |