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 case1(s:str, n:int):
    val = 0
    count = 0
    for i in range(n):
        if s[i] == '(': val += 1
        else: val -= 1
        if val < 0: return 0
        elif val == 0 or val == 1: count = 0
        elif s[i] == '(': count += 1;
    return count

def case2(s:str, n:int):
    val = 0
    count = 0
    for i in range(n):
        if s[i] == '(': val += 1
        else: val -= 1
        if val == -1:
            val += 2
            for j in range(i+1, n):
                if s[j] == '(': val += 1
                else: val -= 1
                if val < 0: return 0
            return count + 1
        elif s[i] == ')': count += 1
    return count

n = int(input())
s = input()
l = 0
r = 0
for i in range(n):
    if s[i] == '(': l += 1
    else: r += 1
if l - r == 2: print(case1(s, n))
elif l - r == -2: print(case2(s, n))
else: print(0)