There is an undirected graph G $=($V$,$ E$).$ You use an edge e $=($u$,$ v$)$ to indicate that u and v are $$attracted$$ to each other. $($If there is no edge connecting to two vertices u and v$,$ then we say that u and v are repellent to each other.$)$ Given a graph G $=($V$,$ E$),$ design an algorithm to find a subset of vertices V $0$ V so that any vertex in V $0$ has at least $10$ attracted vertices in V $0$ and at least $10$ repellent vertices in V $0.$ Your algorithm should maximize the size of $|$V $0|.$ Show your algorithm, its correctness, and its running time.