Misha and Permutation

Misha is an expert on combinatorics, so he knows a lot about permutations. Recently, he learned the definition of a convex polygon and invented too many new problems involving permutations. Please help him solve one of them. Let's define a function on a set a with size k: F(a1, a2, ... , ak). Imagine that we have sticks of lengths a1, a2, ... , ak. F(a1, a2, ... , ak) = 1, if and only if a conv