Let q in N be a prime number and let x $=\{$x$1,...,$ xn$\}.$ You are given black$-$box access to a

polynomial p$($x$)$ in Fq$[$x$]$ computed by an circuit of size poly$($n$).$ Your goal is to estimate the degree of p$($x$).$

Describe an algorithm that achieves this. Prove the correctness and running time of your algorithm.