Valid Parentheses Sequence

You are given a string s consisting solely of the characters ( and ). Your task is to determine whether the string is a valid parentheses sequence.

A parentheses sequence is called valid if it satisfies the following conditions:

• For every prefix of the string, the number of opening parentheses is greater than or equal to the number of closing parentheses.
• The total number of opening and closing parentheses is equal, i.e. \( \text{count}(\text{'('}) = \text{count}(\text{')'}) \).

If the sequence is valid, output YES; otherwise, output NO.

inputFormat

The input consists of a single line containing a string s with only the characters ( and ). The string may be empty.

outputFormat

Output a single line: YES if the given string is a valid parentheses sequence, and NO otherwise.

()

YES