Maximum Profit from Valid Topological Order in DAG

Given a DAG with node scores, find a topological ordering that maximizes the sum of score[i] * position(i) (positions are 1-based) while respecting all edge precedence constraints. With n ≤ 22 the core challenge is optimizing the order under partial-order constraints—typically solved by bitmask DP that schedules higher-score nodes as late as possible subject to dependencies.