A student of pepcoding has recently found out about groupings of brackets (sequences of parenthesis). A balanced parenthesis sequence follows the following definition: 1. An empty sequence is balanced. 2. If R is a balanced sequence, then (R) is also balanced. 3. If M and N represent two balanced sequences, then their concatenation MN is also balanced. the sequences (), ()() and (())() are balanced, while ()) and ))() are unbalanced. Now, you need to find the length of longest unbalanced subsequence of the given string (String only contains parenthesis).
Input Format
The only line contains a string containing '(' and ')' only.
Output Format
Output a line containing answer to the corresponding query.
Constraints
1<= length of string <= 10^5
Example
Input
)
Output
1