366. Valid Parenthesis String

0

Medium

You are 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 ')' or a single left parenthesis '(' or an empty string "".

Input Format

The string containing special characters.

Output Format

The boolean result as the string is valid or not

Example

Input

( *)

Output

true

Constraints

Length of s is less than 100
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