Sereja and Permutations 3

Let p be a permutation of integers 1, ..., N. Lets call p good if there is at least one pair of indices (i,j) such that i and p[i] > j, p[j] > i. Sereja is interested in the number of permutations p of 1, ..., N that are good. This might seem easy at first, but Sereja is only interested in permutations that obey a list of M additional rules. Rule number i (1 ≤ i ≤ M) in Sereja's list says p(Xi) s