The vertices $V$ of a centrally symmetric hexagon in the complex plane are given by $V=\sqrt{2}i,-\sqrt{2}i,\frac{1}{\sqrt{8}}(1+i),\frac{1}{\sqrt{8}}(-1+i),\frac{1}{\sqrt{8}}(1-i),\frac{1}{\sqrt{8}}(-1-i)$. For each $j$, $1\le j\le 18$, an element $z_j$ is chosen from $V$ at random, independently of the other choices. Let $P={\prod }_{j=1}^{18}{z}_j$ be the product of the 18 numbers selected. What is the probability that $P=1$?