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())
s = input()
open = s.count('(')
close = s.count(')')

counter = 0
for i in range(n):
    if s[i] == '(':
        counter += 1
    else:
        counter -= 1
    if counter <= -3:
        print(0)
        exit()

if open - close == 2:
    ans = 0
    ansFound = False
    for i in reversed(range(n)):
        if s[i] == '(':
            if not ansFound:
                ans += 1
            if counter <= 2:
                ansFound = True
            counter -= 1
        else:
            counter += 1
        if counter < 0:
            print(0)
            exit()
    print(ans)

elif close - open == 2:
    counter = 0
    ans = 0
    for i in range(n):
        if s[i] == '(':
            counter += 1
        else:
            counter -= 1
            ans += 1
        if counter < 0:
            break
    print(ans)
else:
    print(0)