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 = int(input())
s = input()
nums = []
for ch in s:
	if ch=="(":
		nums.append(1)
	else:
		nums.append(-1)
for i in range(1,n):
	nums[i]+=nums[i-1]
# print(*nums)
if nums[-1]==2 and all(i>=0 for i in nums):
	ans = 0
	for i in range(n-1,-1,-1):
		if nums[i]<2:break
		if s[i]=="(":
			ans+=1
	print(ans)
elif nums[-1]==-2 and min(nums)==-2:
	ans = 0
	for i in range(n):
		if s[i]==")":
			ans+=1
		if nums[i]<0:break
	print(ans)
else:
	print(0)