**Problem Statement:**
Given the required input arguments, write an efficient algorithm to solve the **Minimum Remove to Make Valid Parentheses** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge.
**Hint / Expected Approach:**
Stack for indices; collect invalid + rebuild
**Edge Cases to Consider:**
- (1) No parentheses
- (2) All balanced
- (3) Nested unmatched