Leetcode 2450. Number of Distinct Binary Strings After Applying Operations

Given an initial binary string and a set of allowed operations that can be applied any number of times, count how many distinct binary strings can be produced. The core challenge is to model the operations as transformations (often linear over GF(2) or as component-wise constraints), determine the independent degrees of freedom (rank or independent components), and compute the number of reachable states (typically 2^r).