-A number n is perfect if the sum of its factors (except n itself) sum to exactly n. For example, 28 is perfect, since its factors (1,2,4,7,14) sum to 28. But 12 is not perfect: its factors (1,2,3,4,6) sum to 16, which is not 12. The PERFECT decision problem has as its input a number n written in binary and should output yes exactly when n is perfect. -Show that PERFECT is in NP. Is PERFECT in P? If yes, give a polynomial-time algorithm to check if a given integer n is perfect.