Problem $5(20$ pts$)$ Give a deterministic $O(n^2)$ time algorithm to detect a square $($a length $4$ cycles$)$ in an undirected graph $G$ with $n$ vertices. $[$Hint: in any square there are two distinct paths between pairs of diagonal vertices. As an example, for the square $($uvxy$),$ we can go from $u$ to $x$ using either $v$ or $y.]$