Consider the fraction, `n/d`, where n and d are positive integers. If `n<d` and `HCF(n,d)=1`, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for `d <= 8` in ascending order of size, we get:

~~~
1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
~~~

It can be seen that there are 3 fractions between `1/3` and `1/2`.

How many fractions lie between `1/3` and `1/2` in the sorted set of reduced proper fractions for `d <= 12,000`?