$n$ families, each with four members, a father, a mother, a son and a daughter, were invited to a restaurant. They were all seated at a large circular table with $4n$ seats such that men and women alternate.

Let $M(n)$ be the number of ways the families can be seated such that none of the families were seated together. A family is considered to be seated together only when all the members of a family sit next to each other.

For example, $M(1)=0$, $M(2)=896$, $M(3)=890880$ and $M(10)\equiv 170717180(\mathrm{mod}1000000007)$.

Let $S(n)={\displaystyle \sum _{k=2}^{n}M(k)}$.

For example, $S(10)\equiv 399291975(\mathrm{mod}1000000007)$.

Find $S(2021)$. Give your answer modulo $1000000007$.