Let $$\mathcal{P}$$ be a convex polygon with $$50$$ vertices. A set $$\mathcal{F}$$ of diagonals of $$\mathcal{P}$$ is said to be minimally friendly if any diagonal $$d\in\mathcal{F}$$ intersects at most one other diagonal in $$\mathcal{F}$$ at a point interior to $$\mathcal{P}$$. Find the largest possible number of elements in a minimally friendly set $$\mathcal{F}$$.