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
def read(type = 1):
    if type:
        file = open("input.dat", "r")
        n = int(file.readline())
        a = file.readline()
        file.close()
    else:
        n = int(input().strip())
        a = input().strip()
    return n, a


def solve():
    sol = 0
    vs = []
    v = 0
    for i in range(n):
        if a[i] == "(":
            v += 1
        else:
            v -= 1
        vs.append(v)
    mins = [10000000 for i in range(n)]
    last = n
    for i in range(n):
        if i:
            mins[n-i-1] = min(vs[n-i-1], mins[n-i])
        else:
            mins[n-i-1] = vs[n-i-1]
        if vs[n-i-1] < 0:
            last = n-i-1
    for i in range(n):
        if a[i] == "(" and vs[n-1] == 2:
            if i:
                if mins[i] >= 2:
                    sol += 1
        if a[i] == ")" and vs[n-1] == -2:
            if i != n-1:
                if mins[i] >= -2:
                    sol += 1
        if i == last:
            break
    return sol


n, a = read(0)
sol = solve()
print(sol)