You are given a string expr containing:

• lowercase letters
• parentheses '(' and ')'

Some parentheses may be misplaced.

A string is valid if every opening '(' has a matching closing ')' in the correct order. Your task is to remove the minimum number of parentheses so that the resulting string is valid.

Return all unique valid strings that can be formed with the minimum removals.

You may return the answers in any order.

Function Requirement

Write a function that takes a string expr and returns a list of all valid strings with minimum removals.

• Examples

• Constraints

• Hint