475. Minimize String's Cost

0

Medium

Given a string s consisting of lowercase English characters, '(' and ')', your task is to remove parentheses in any positions to make the resulting string valid. The cost of a string is defined as the total number of deletions required to make it valid. Minimize the cost of the string.

Input Format

The first line contains a string s.

Output Format

An integer representing the cost of the string.

Example

Input

Codin(g(Bl)o)cks)

Output

1

Constraints

1 <= s.length <= 10^4
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