Valid Parenthesis Expression

Given a string S consisting only of the characters '(' and ')', determine whether it is a valid parenthesis expression.

A valid expression satisfies the following condition in LaTeX:

\( \text{For every prefix of the string, the number of '(' is not less than the number of ')', and the total counts are equal.} \)

You can think of it as checking if every opening bracket has a corresponding closing bracket in the correct order.

inputFormat

The input is read from standard input (stdin) and consists of a single line containing the string S, where S contains only '(' and ')'.

outputFormat

The output, written to standard output (stdout), should be a single line with either True if the string is a valid parenthesis expression, or False otherwise.

## sample

()

True

</p>