You are given a bracket sequence s consisting of n opening '(' and closing ')' brackets.

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

You can change the type of some bracket s_i. It means that if s_i =  ')' then you can change it to '(' and vice versa.

Your task is to calculate the number of positions i such that if you change the type of the i-th bracket, then the resulting bracket sequence becomes regular.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 10^6) — the length of the bracket sequence.

The second line of the input contains the string s consisting of n opening '(' and closing ')' brackets.

Output

Print one integer — the number of positions i such that if you change the type of the i-th bracket, then the resulting bracket sequence becomes regular.

Examples

Input


6
(((())


Output


3


Input


6
()()()


Output


0


Input


1
)


Output


0


Input


8
)))(((((


Output


0
n = int(input())
sequence = input()

moreopen = 0
moreclosed = 0
small = 0

stack = 0
stop = False
completestop = False
for i in range(n):
    if sequence[i] == '(':
        stack+=1 
    else:
        stack-=1 
    #moreopen
    if stack >= 2 and sequence[i] == '(':
        moreopen+=1
    if stack <= 1:
        moreopen = 0
    #moreclosed
    if stack >= -2 and not stop and sequence[i] == ')':
        moreclosed+=1 
    if stack < 0:
        stop = True
    if stack < -2:
        completestop = True
        break;
if completestop:
    print(0)
elif stack == 2 and not stop:
    print(moreopen)
elif stack == -2:
    print(moreclosed)
else:
    print(0)
    
    
    
    
    