A unit fraction contains $1$ in the numerator. The decimal representation of the unit fractions with denominators $2$ to $10$ are given:
$$\begin{align} 1/2 &= 0.5\\ 1/3 &=0.(3)\\ 1/4 &=0.25\\ 1/5 &= 0.2\\ 1/6 &= 0.1(6)\\ 1/7 &= 0.(142857)\\ 1/8 &= 0.125\\ 1/9 &= 0.(1)\\ 1/10 &= 0.1 \end{align}$$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 $d \lt 1000 \times 4^N$ for which $1/d$ contains the longest recurring cycle in its decimal fraction part.