Graph Theory Question

Let G=(V,E) be a graph with V={1,2,...,n}. We'll assume G has the following property:
For every $Y \subset V$ with $|Y| = n-2$ , there exist distinct sets $F_1 , F_2 \in E$ inducing the same subet of Y : $F_1 \cap Y = F_2 \cap Y$ (i.e.- $F_1,F_2$ have a common vertex).
Show that $|E| \ge \lceil 3(n-1)/2 \rceil$ .

I really need help in this one.