Balance Parentheses

You are given a string s consisting solely of the characters '(' and ')'. Your task is to determine the minimum number of parentheses that must be added in order to make the string balanced.

A balanced parentheses string is defined such that every opening parenthesis '(' has a corresponding closing parenthesis ')' in the correct order. Mathematically, if we let open_count be the number of unmatched '(' and close_count be the number of unmatched ')', then the answer is given by:

$$result = open\_count + close\_count$$

For example:

• For s = "(()", one ')' is needed.
• For s = ")))(((", three ')'s and three '('s (in order) are missing, so the answer is 6.
• For s = "()()", the string is already balanced, so the answer is 0.
• For s = ")()(", the answer is 2.

inputFormat

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

outputFormat

Output a single integer representing the minimum number of parentheses that must be added to make s balanced.

## sample

(()

1

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