Minimum Additions to Make Parentheses Valid

You are given a string s composed only of the characters '(' and ')'. The task is to determine the minimum number of parentheses that must be added to make the string valid. A valid string is defined such that every opening parenthesis has a corresponding closing parenthesis and vice versa.

Mathematically, if we denote the number of unmatched opening parentheses as $\text{open\_needed}$ and unmatched closing parentheses as $\text{close\_needed}$, then the answer is given by:

[ \text{result} = \text{open_needed} + \text{close_needed} ]

Example: For input s = ")))((()", the output should be 2.

inputFormat

The input consists of a single line containing the string s (which only includes the characters '(' and ')').

outputFormat

The output is an integer representing the minimum number of parentheses needed to be added so that the string s becomes valid.

()))((

4