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
_ = input()
s = list(input())

def regular(s):
    k = 0
    for c in s:
        if c == '(': k += 1
        elif c == ')': k -= 1
        if k < 0: return False
    return k == 0

def regular_sums(s):
    k = 0
    ks = []
    for c in s:
        if c == '(': k += 1
        elif c == ')': k -= 1
        ks.append(k)
    return ks

sums = regular_sums(s)

if sums[-1] == 2:
    # x <= ia
    ia = 0
    while ia < len(sums) and sums[ia] >= 0:
        ia += 1

    # x > ib
    ib = len(s) - 1
    while ib >= 0 and sums[ib] >= 2:
        ib -= 1

    k = 0
    for i in range(max(ib + 1, 0), min(ia + 1, len(s))):
        if s[i] == '(':
            k += 1
    print(k)
elif sums[-1] == -2:
    # x <= ia
    ia = 0
    while ia < len(sums) and sums[ia] >= 0:
        ia += 1

    # x > ib
    ib = len(s) - 1
    while ib >= 0 and sums[ib] >= -2:
        ib -= 1

    k = 0
    for i in range(max(ib + 1, 0), min(ia + 1, len(s))):
        if s[i] == ')':
            k += 1
    print(k)
else:
    print(0)
