For each of the following two problems, decide whether it is a P-problem or an NP-hard problem. If it is P ,name a polynomial time algorithm to solve it and justify your answer briefly. If it is NP-hard, Show it.

(1) Find a negative-weight cycle in a weighted directed graph G = (V, E)

(2) Find a negative-weight cycle with the most negative total weight (i.e. Negative but with the largest absolute value)