Minimum path cover

You have n tasks (nodes 0..n-1) and a list of directed precedence edges forming a DAG; edge [u, v] means task u can be immediately followed by task v on the same worker. A worker processes a chain of tasks where each consumes the next via such an edge, and every task must be done by exactly one worker. Return the minimum number of workers needed so that each task is covered exactly once (the minimum number of vertex-disjoint paths that cover all nodes). Constraints: 1 <= n <= 60; the graph is a DAG with no self loops.