Tessellate S.T.E.M.S (2019) - Computer Science - College - Set 1 - Objective Problem 1

Consider a directed graph on $n$ vertices (with $n \geq 4$ ) where for any $u \neq v$ there is either an edge from $u$ to $v$ or from $v$ to $u$ .

What is the smallest value of $k$ below that will make the following statement correct?

There exists a vertex $v$ such that for all $u$ there is a path of length $\leq k$ from $v$ to $u$ .

This problem is a part of Tessellate S.T.E.M.S (2019)