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
n=int(stdin.readline().strip())
s=input()
if n==1:
    print(0)
    exit(0)

dp1=[0 for i in range(n)]
dp2=[0 for i in range(n)]
v1=[True for i in range(n)]
v2=[True for i in range(n)]
for i in range(n):
    if s[i]=='(':
        dp1[i]=dp1[i-1]+1
    else:
        dp1[i]=dp1[i-1]-1
if s[n-1]=="(":
    dp2[n-1]=1
else:
    dp2[n-1]=-1
for i in range(n-2,-1,-1):
    if s[i]=='(':
        dp2[i]=dp2[i+1]+1
    else:
        dp2[i]=dp2[i+1]-1
for i in range(n):
    if dp1[i]<0:
        v1[i]=False
    if i>0 and v1[i-1]==False:
        v1[i]=False
for i in range(n-1,-1,-1):
    if dp2[i]>0:
        v2[i]=False
    if i<=(n-2) and v2[i+1]==False:
        v2[i]=False
ans=0
for i in range(1,n-1):
    if s[i]=="(":
        if (dp1[i-1]-1+dp2[i+1])==0 and v1[i-1] and v2[i+1]:
            ans+=1
    else:
        if (dp1[i-1]+1+dp2[i+1])==0 and v1[i-1] and v2[i+1]:
            ans+=1
if s[0]==")" and dp2[1]==-1 and v2[1]:
    ans+=1
if s[n-1]=="(" and dp1[n-2]==1 and v1[n-2]:
    ans+=1
print(ans)
