Numerical Methods: Euler to Runge–Kutta · Superchallenge problem

The symplectic Euler method for $x' = y$, $y' = -x$ updates $x_{n+1} = x_n + h\,y_n$, then $y_{n+1} = y_n - h\,x_{n+1}$. For suitable step sizes the computed orbit is exactly periodic. What is the smallest $h > 0$ for which every orbit returns to its starting point after exactly $8$ steps (and not sooner)?