Problem Description

The Tenka1 Magic Power Plant is a power plant that can generate electricity using a mysterious magic.

The fuel used for magic power generation is a string $ S $ consisting of ( and ), and the length of $ S $ is even.

By rewriting this string into a balanced string using the Tenka1 Word Processor, the magic power generation is successful.

A balanced string is defined as follows:

• () is a balanced string.
• If T is a balanced string, then (T) is also a balanced string.
• If T and U are balanced strings, then TU is also a balanced string.

The Tenka1 Word Processor has the following four operations:

Initially, the cursor points to the first character of $ S $.

1. Move the cursor to the right (it does not move if the cursor is already at the end).
2. Move the cursor to the left (it does not move if the cursor is already at the beginning).
3. If the character pointed by the cursor is (, change it to ).
4. If the character pointed by the cursor is ), change it to (.

For example, if $ S $ is the following string:

```
())(()))

By performing operations 1 and 4, we can change it to:

 ```
(()(()))

which is a balanced string.

Fude-kun, the responsible person at the power plant, wants to rewrite the string into a balanced string with the fewest operations possible.

Given $ S $, find the minimum number of operations required to rewrite it into a balanced string.

Input Format

The input is given from the standard input in the following format:

$ S $

Output Format

Output the minimum number of operations required to rewrite the string into a balanced string. End the output with a newline.

Sample Input and Output

Sample Input #1

())(()))

Sample Output #1

2

Sample Input #2

((((

Sample Output #2

5

Sample Input #3

)))(((

Sample Output #3

9

Notes/Hints

Constraints

• The length of $ S $, $ |S| $, is even.
• $2 \leq |S| \leq 100$

见题面 Input 部分

见题面 Output 部分