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
# Created by nikita at 30/12/2018

n = int(input())
s = input()

prefBal = [0] * n
prefBal.append(0)
prefCan = [False] * n
prefCan.append(True)
suffBal = [0] * n
suffBal.append(0)
suffCan = [False] * n
suffCan.append(True)

currBal = 0
currCan = True
for i in range(n):
    if s[i] == '(':
        prefBal[i] = currBal + 1
    else:
        prefBal[i] = currBal - 1
    currBal = prefBal[i]
    prefCan[i] = currCan and (prefBal[i] >= 0)
    currCan = prefCan[i]

currBal = 0
currCan = True
for i in range(n-1, -1,- 1):
    if s[i] == ')':
        suffBal[i] = currBal + 1
    else:
        suffBal[i] = currBal - 1
    currBal = suffBal[i]
    suffCan[i] = currCan and (suffBal[i] >= 0)
    currCan = suffCan[i]

# print(prefBal)
# print(prefCan)
# print(suffBal)
# print(suffCan)

ans = 0
for i in range(n):
    if s[i] == '(':
        if prefCan[i-1] and suffCan[i+1] and prefBal[i-1] - 1 - suffBal[i+1] == 0:
            ans += 1
    if s[i] == ')':
        if prefCan[i-1] and suffCan[i+1] and prefBal[i-1] + 1 - suffBal[i+1] == 0:
            ans += 1

print(ans)