Fix the bracket sequence
Given a string s of opening and closing brackets, you are allowed to change some opening brackets to closing ones and some closing to opening ones. At least how many operations are necessary to obtain a valid sequence of brackets?
Input
The only line of the input contains the string s (1 ≤ |s| ≤ ). It’s guaranteed that the length of s is even.
Output
The program should print the least amount of modifications needed to make the sequence valid.
Examples
Input | Output |
|---|---|
()(( | 1 |
)( | 2 |
()() | 0 |
((() | 1 |
Explanation
()(( → ()() ⇒ 1 modification
)( → () ⇒ 2 modifications
()() ⇒ no modifications needed
((() → ()() ⇒ 2 modifications
Constraints
Time limit: 2 seconds
Memory limit: 512 MB
Output limit: 1 MB