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 = input()
s = input()
r = []

r.append(1 if s[0] == '(' else -1)
for p in s[1:]:
  r.append(r[-1] + (1 if p == '(' else -1))

m = min(r)

if m < -2 or r[-1] != 2 and r[-1] != -2 or r[-1] == 2 and m < 0:
  print(0)
else:
  res = 0
  if r[-1] == 2:
    for i in range(len(r) - 1, -1, -1):
      if r[i] == 1:
        break
      if s[i] == '(':
      	  res += 1
  else:
    for i in range(len(r)):
      if r[i] == -1:
        break
      if s[i] == ')':
        res += 1
    res += 1
  print(res)
