A unit fraction contains $1$ in the numerator. The decimal representation of the unit fractions with denominators $2$ to $10$ are given:

$$\begin{array}{rl}1/2& =0.5\\ 1/3& =0.(3)\\ 1/4& =0.25\\ 1/5& =0.2\\ 1/6& =0.1(6)\\ 1/7& =0.(142857)\\ 1/8& =0.125\\ 1/9& =0.(1)\\ 1/10& =0.1\end{array}$$

Where $0.1(6)$ means $0.166666\cdots$, and has a $1$-digit recurring cycle. It can be seen that $1/7$ has a $6$-digit recurring cycle.

Find the value of $d<1000$ for which $1/d$ contains the longest recurring cycle in its decimal fraction part.