Balanced Parentheses Checker

You are given a string s that consists solely of the characters '(' and ')'. Your task is to determine whether the string is balanced.

A string is considered balanced if every opening parenthesis has a corresponding closing parenthesis and the pairs of parentheses are properly nested. In other words, at any point in the string, the number of closing parentheses should not exceed the number of opening parentheses.

The mathematical condition for balance can be expressed as: \( \forall i, \; balance(i) \ge 0 \) and \( balance(n) = 0 \), where \( balance(i) \) is the cumulative difference between '(' and ')' up to position \( i \), and \( n \) is the length of the string.

Read the input from stdin and output the result to stdout as either True or False.

inputFormat

The input consists of a single line, representing the string of parentheses s. The string may be empty and will contain only the characters '(' and ')'.

Example:

()()

outputFormat

Output a single line: True if the parentheses in the string are balanced, and False otherwise.

Example:

True

## sample

()()

True