Let G be an directed acyclic graph with vertex set V and edge set E$.$

Design a $($recursive$)$ backtracking algorithm that counts the number of topological orderings of the vertices in V$.$

$($Hint: use an array indexed by vertices that keeps track of the indegree of each vertex.$)$

$[$high level description or pseudocode of algorithm. Proof of correctness. $($No runtime analysis necessary.$)]$