Let $S$ be the set of all real values of $\lambda$ such that a plane passing through the points $\left(-\lambda^2, 1,1\right)$, $\_\_\_\_$ $\left(1,-\lambda^2, 1\right)$ and $\left(1,1,-\lambda^2\right)$ also passes through the point $(-1,-1,1)$. Then $S$ is equal to
