Consider the Clique$-$IS problem:

Input: Graph G$=($V$,$E$)$ and integer k$.$

Output: Sets of vertices S and T where S is a clique in G and T is an independent set in G$,$ S and T are disjoint, and $$S$=$k$,$T$=$k; or NO if none exist.

Prove that Clique$-$IS is NP$-$complete.