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Write a function that takes a string of parentheses, and determines if the order of the parentheses is valid. The function should return true if the string is valid, and false if it's invalid.

Examples

"()"              =>  true
")(()))"          =>  false
"("               =>  false
"(())((()())())"  =>  true

Constraints

0 <= input.length <= 100

Along with opening (() and closing ()) parenthesis, input may contain any valid ASCII characters. Furthermore, the input string may be empty and/or not contain any parentheses at all. Do not treat other forms of brackets as parentheses (e.g. [], {}, <>).