Problems
Remove the parentheses
Remove the parentheses
Given a string consisting of parentheses.
Determine the minimum number of characters to be removed from this string, so that the remaining characters will form the correct bracket sequence.
Input data
One line consisting of no more than 10^5
parentheses.
Output data
Print the answer to the problem.
Examples
Input example #1
())(()
Output example #1
2
Input example #2
))(((
Output example #2
5
Input example #3
(()(()))
Output example #3
0