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
n=int(input())
s=str(input())
arr1=[]
arr11=[]
count=0
flag=0
for i in range(len(s)):
    if(s[i]=='('):
        count+=1
    else:
        count-=1
    if(count<0):
        flag=1
    if(flag==0):
        arr11.append(1)
    else:
        arr11.append(-1)
    arr1.append(count)
arr2=[0]*n
arr22=[0]*n
count2=0
flag=0
for i in range(len(s)-1,-1,-1):
    if(s[i]=='('):
        count2+=1
    else:
        count2-=1
    if(count2>0):
        flag=1
    if(flag==0):
        arr22[i]=1
    else:
        arr22[i]=-1
    arr2[i]=count2
#print(arr1,arr11)
#print(arr2,arr22)
ans=0
for i in range(n):
    if(i==0):
        if(s[i]==')' and i<n-1 and arr2[i+1]==-1 and arr22[i+1]==1):
            ans+=1
    elif(i==n-1):
        if(s[i]=='(' and i>0 and arr1[i-1]==1 and arr11[i-1]==1):
            ans+=1
    else:
        if(s[i]=='('):
            if(arr1[i-1]+arr2[i+1]==1 and arr11[i-1]==1 and arr22[i+1]==1):
                ans+=1
        else:
            if(arr1[i-1]+arr2[i+1]==-1 and arr11[i-1]==1 and arr22[i+1]==1):
                ans+=1
print(ans)