Consider the fraction, ${\displaystyle \frac{n}{d}}$, where $n$ and $d$ are positive integers. If $n<d$ and $\mathrm{HCF}(n,d)=1$, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for $d\le 8$ in ascending order of size, we get: $$\frac{1}{8},\frac{1}{7},\frac{1}{6},\frac{1}{5},\frac{1}{4},\frac{2}{7},\frac{1}{3},\frac{3}{8},\frac{2}{5},\frac{3}{7},\frac{1}{2},\frac{4}{7},\frac{3}{5},\frac{5}{8},\frac{2}{3},\frac{5}{7},\frac{3}{4},\frac{4}{5},\frac{5}{6},\frac{6}{7},\frac{7}{8}$$

It can be seen that there are $21$ elements in this set.

How many elements would be contained in the set of reduced proper fractions for $d\le 1000000$?