A binary sequence is a sequence in which each term is equal to $$0$$ or $$1$$. A binary sequence is called friendly if each term is adjacent to at least one term that is equal to $$1$$. For example, the sequence $$0,1,1,0,0,1,1,1$$ is friendly. Let $$F_{n}$$ denote the number of friendly binary sequences with $$n$$ terms. Find the smallest positive integer $$n\geq 2$$ such that $$F_{n}>100$$.