Leetcode 3577. Count the Number of Computer Unlocking Permutations

Count the number of permutations of [0..n-1] (mod 1e9+7) starting with computer 0 unlocked, such that every other index i appears only after at least one previously placed index j<i with complexity[j] < complexity[i]; equivalently, count valid orders consistent with the unlocking precedence induced by index and complexity.