544. Score of Parentheses

0

Medium

Given a **balanced parentheses** string `s`, calculate and output the score of the string.
The **score of a balanced parentheses** string is determined by the following rules:
* The score of "()" is 1.
* The score of AB is equal to the sum of the scores of A and B, where A and B are balanced parentheses strings.
* The score of (A) is equal to 2 times the score of A, where A is a balanced parentheses string.

Input Format

The input consists of a single line containing a string s.

Output Format

Print the score of the given balanced parentheses string.

Example

Input

()((()))

Output

5

Constraints

1<= s.length <= 100

`s` consists of only '(' and ')'.

`s` is a balanced parentheses string.

`s` consists of only '(' and ')'.

`s` is a balanced parentheses string.

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