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 = raw_input()
c = 0
cnt = []
for i in range(n):
	if s[i] == '(':
		c += 1
	else:
		c -= 1
	if c < -2:
		print 0
		exit()
	cnt.append(c)
if cnt[-1] not in [-2,2]:
	print 0
	exit()
p_rightmost_lt_2 = n-1
p_leftmost_lt_0 = 0
while cnt[ p_rightmost_lt_2 ] >= 2:
	p_rightmost_lt_2 -= 1
while p_leftmost_lt_0 < n and cnt[ p_leftmost_lt_0 ] >= 0:
	p_leftmost_lt_0 += 1
ans = 0
for i in range(n):
	if s[i] == '(' and cnt[-1] == 2 and i > p_rightmost_lt_2 and i <= p_leftmost_lt_0:
		ans += 1
	elif s[i] == ')' and cnt[-1] == -2 and i <= p_leftmost_lt_0:
		ans += 1
print ans