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
#from random import random, randint
from sys import stdout, stdin
import math

#n, k = map(int, input().split())
n = int(input())
s = input()

zuor = {'(':1, ')':-1}
arr = [zuor[c] for c in s]
obpos = [z == 1 for z in arr]

suma, sume = [], []
akt = 0
for z in arr:
    akt += z
    suma.append(akt)
akt = 0
for z in reversed(arr):
    akt -= z
    sume.append(akt)
sume = list(reversed(sume))

summe = sum(arr)

if min(suma) < -2 or min(sume) < -2:
    print(0)
elif summe==2:
    if min(suma)<0:
        print(0)
    else:
        letzte1 = len(suma) - 1 - suma[::-1].index(1)
        ok = [i>letzte1 for i in range(n)]
        print(sum((b1 and b2 for b1, b2 in zip(ok, obpos))))
elif summe==-2:
    if min(sume)<0:
        print(0)
    else:
        erste1 = sume.index(1)
        ok = [i<erste1 for i in range(n)]
        print(sum((b1 and not b2 for b1, b2 in zip(ok, obpos))))
else:
    print(0)







