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
import sys
import math

data = sys.stdin.read().split()
data_ptr = 0

def data_next():
    global data_ptr, data
    data_ptr += 1
    return data[data_ptr - 1]

N = int(data_next())
S = list(data[1])

n_open = S.count('(')
n_closed = N - n_open
if n_open > n_closed:
    S.reverse()
    for i in range(N):
        if S[i] == '(':
            S[i] = ')'
        else:
            S[i] = '('

depth = 0
ans = 0
past_first_neg = False
for i in range(N):
    if S[i] == ')':
        depth -= 1
        if depth < -2:
            ans = 0
            break
        if not(past_first_neg):
            ans += 1
        if depth < 0:
            past_first_neg = True
    else:
        depth += 1
if depth != -2:
    ans = 0
print(ans)
