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(raw_input())
brackets = raw_input()

cnt_pre = [0 for _ in xrange(n)]
cum_min_pre = [0 for _ in xrange(n)]
for i in xrange(n):
    cnt_pre[i] += cnt_pre[i-1] if i > 0 else 0
    cnt_pre[i] += 1 if brackets[i] == '(' else -1
    cum_min_pre[i] = min(cum_min_pre[i-1], cnt_pre[i]) if i > 0 else cnt_pre[i]

cnt_suf = [0 for _ in xrange(n)]
cum_min_suf = [0 for _ in xrange(n)]
for i in xrange(n-1, -1, -1):
    cnt_suf[i] += cnt_suf[i+1] if i < n-1 else 0
    cnt_suf[i] += 1 if brackets[i] == ')' else -1
    cum_min_suf[i] = min(cum_min_suf[i+1], cnt_suf[i]) if i < n-1 else cnt_suf[i]

ans = 0
if n > 1:
    for i in xrange(n):
        if i == 0 and brackets[i] == ')': # cant for ( to )
            ans += 1 if cum_min_suf[i+1] >= 0 and cnt_suf[i+1] == 1 else 0
        elif i == n-1 and brackets[i] == '(': # cant for ) to (
            ans += 1 if cum_min_pre[i-1] >= 0 and cnt_pre[i-1] == 1 else 0
        elif 0 < i < n-1 and cum_min_pre[i-1] >= 0 and cum_min_suf[i+1] >= 0:
            if brackets[i] == ')':
                ans += 1 if -cnt_pre[i-1]-1+cnt_suf[i+1] == 0 else 0
            else: # '('
                ans += 1 if -cnt_pre[i-1]+1+cnt_suf[i+1] == 0 else 0
print ans