Well-Formed Parentheses Checker

You are given a string s consisting solely of the characters (' and ')'. Your task is to determine whether the string is well-formed.

A string is considered well-formed if and only if:

• For every prefix of the string, the number of (' is greater than or equal to the number of ').
• The total number of (' equals the total number of '), i.e., $$ \#('(') = \#(')') $$.

For example, the string "()()" is well-formed while "(()" is not.

inputFormat

The input is read from stdin as a single line that contains the bracket sequence.

Constraints: The input string consists only of the characters '(' and ')'.

outputFormat

Print to stdout a single line: True if the sequence is well-formed, otherwise False.

()

True