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
import sys


def main():
    _ = sys.stdin.readline()
    s = sys.stdin.readline().strip()
    prefix = [0] * (len(s) + 1)
    canPrefix = [True] * (len(s) + 1)
    count = 0
    for i, c in enumerate(s):
        count = count+1 if c == '(' else count-1
        isPossible = True if count >= 0 and canPrefix[i] else False
        prefix[i+1] = count
        canPrefix[i+1] = isPossible
    sufix = [0] * (len(s) + 1)
    canSuffix = [True] * (len(s) + 1)
    count = 0
    for i, c in enumerate(reversed(s)):
        count = count + 1 if c == ')' else count - 1
        isPossible = True if count >= 0 and canSuffix[len(s) - i] else False
        sufix[len(s)-1-i] = count
        canSuffix[len(s)-1-i] = isPossible
    ans = 0
    for i, c in enumerate(s):
        if canPrefix[i] == False or canSuffix[i+1] == False:
            continue
        elif c == '(' and prefix[i] - 1 - sufix[i+1] == 0:
            ans += 1
        elif c == ')' and prefix[i] + 1 - sufix[i+1] == 0:
            ans += 1
    print(ans)


if __name__ == "__main__":
    main()
