On minimal strongly connected congruences of a directed path

Let $G = (V, \alpha)$ be a directed graph. An equivalence relation $\theta\subseteq V\times V$ is called a strongly connected congruence of $G$ if the quotient graph $G/\theta$ is strongly connected. Minimal (under inclusion) strongly connected congruences of a directed path are described and the total amount of them is found ($2^{n-3}$ if the path has $n$ vertices).