Valid Parenthesis String

Given a string s containing only three types of characters: '(', ')', and '*', return true if s is valid.

The following rules define a valid string:

  • Any left parenthesis '(' must have a corresponding right parenthesis ')'.
  • Any right parenthesis ')' must have a corresponding left parenthesis '('.
  • Left parenthesis '(' must go before the corresponding right parenthesis ')'.
  • '*' could be treated as a single right parenthesis ')', a single left parenthesis '(', or an empty string "".
Example 1
Inputs = "()"
Outputtrue
The string already contains a matching pair of parentheses.
Example 2
Inputs = "(*)"
Outputtrue
The * can be treated as an empty string, leaving a valid pair of parentheses.

Constraints

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

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