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Valid Parentheses String Solution

Problem Statement

Given a string `s` containing only the characters '(', ')', and '*', determine if the string is valid. A string is valid if and only if: 1. Any left parenthesis '(' must have a corresponding right parenthesis ')'. 2. Any right parenthesis ')' must have a corresponding left parenthesis '('. 3. Left parenthesis '(' must go before the corresponding right parenthesis ')'. 4. '*' can be treated as a single right parenthesis ')', a single left parenthesis '(', or an empty string "".

Example 1

Input

()

Output

true

Explanation: The string is valid. The '(' has a matching ')' and they appear in the correct order.

Example 2

Input

(*)

Output

true

Explanation: The '*' can be treated as an empty string, making the string '()', which is valid.

Example 3

Input

(*))

Output

true

Explanation: The first '*' can be treated as '(', making the string '(())', which is valid. Alternatively, the first '*' can be an empty string, and the second ')' matches the '('. So the string becomes '()', which is valid.

Example 4

Input

)(

Output

true

Explanation: The ')' appears before the '(', violating the order rule.

Constraints

1 <= s.length <= 100
s[i] is either '(', ')', or '*'.

Valid Parentheses String Solution

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