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
size = int(input())
seq = input()
offsets = []
if seq[0] == "(":
  offsets.append(1)
else:
  offsets.append(-1)
for char in seq[1:]:
  if char == "(":
    offsets.append(offsets[-1] + 1)
  else:
    offsets.append(offsets[-1] - 1)
min_offsets = [offsets[-1]]*size
for idx in range(size-2, -1, -1):
  min_offsets[idx] = min(min_offsets[idx+1], offsets[idx])
counter = 0
for idx, char in enumerate(seq):
  if idx >0:
    if offsets[idx-1] < 0:
      break
  proposed_offset = -2
  if char == ")":
    proposed_offset = 2
  if min_offsets[idx] + proposed_offset >= 0 and offsets[-1] + proposed_offset == 0:
    counter+=1
#     print(idx)
# print(offsets)
# print(min_offsets)
print(counter)