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
from sys import stdin, stdout
import collections
import math

N = int(input())

s = input()

level = 0
L = [0]*N

for i in range(N):
    if s[i]=='(':
        level += 1
    else:
        level -= 1
    L[i] = level
        
if level!=2 and level!=-2:
    print(0)
    quit()

mini = level
res = 0
if level==2:
    last = [0]*N
    front = [0]*N
    for i in range(N-1,-1,-1):
        mini = min(mini,L[i])
        last[i] = mini
        
    mini = L[0]
    for i in range(N):
        mini = min(mini,L[i])
        front[i] = mini
    
    for i in range(N):
        if front[i]>=0 and last[i]>=2 and s[i]=='(':
            res += 1
    #print(front,last)
    
if level==-2:
    last = [0]*N
    front = [0]*N
    for i in range(N-1,-1,-1):
        mini = min(mini,L[i])
        last[i] = mini
    mini = 0
    for i in range(N):
        front[i] = mini
        mini = min(mini,L[i])
    
    for i in range(N):
        if front[i]>=0 and last[i]>=-2 and s[i]==')':
            res += 1
    #print(front,last)
            
print(res)