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 $h\le 1000001$. The last line of input contains $0$ and this line should not be processed. There are at most $10000$ 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.

21
85
789
0

21 0
85 5
789 62