Let $M$ be a smooth n dimensional manifold. The foliation values of $M$, denoted by $F(M)$, is defined as

\begin{equation} F(M)=\{ 1\leq k\leq n\mid \text{there exist an smooth $k$ dimensional foliation of M} \}\end{equation}

Question:

For $n\in \mathbb{N}$, What is $F(S^{n})$?