# Is $MSB$ of permanent and certifying half number of witnesses easy?

1. Can there be a $$P$$ algorithm to decide if number of perfect matchings is at least $$(n!/2)+1$$ for a bipartite graph on $$n+n$$ vertices?

2. Can there be a $$P$$ algorithm to decide if number of witnesses exactly $$2^n$$ for a $$SAT$$ formula with $$2n$$ variables

At least are any of above problems in $$PH$$? Is there any consequence if they are so?