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()
p = 0
good = [0]*(n+1)
options = [0]*(n)
for i in range(n):
    if s[i] == '(':
        p += 1
        options[i] = p
        good[i+1] = good[i]+1
    else:
        p -= 1
        options[i] = p
        good[i+1] = good[i]
options2 = list(reversed(options))

if abs(p) != 2:
    print(0)
else:
    small = min(options)
    if p == 2:
        if small >= 2:
            print(good[n])
        elif small < 0:
            print(0)
        else:
            index = -1
            while options[index] >= 2:
                index -= 1
            print(good[n]-good[index])
    elif p == -2:
        if small < -2:
            print(0)
        elif small == -2:
            x = options.index(-1)
            print(x+1-good[x+1])
