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=input()
a=[]
for i in s:
    if i=='(':
        a.append(-1)
    else:
        a.append(1)
#print (a)
b=[0]*(n);b[0]=a[0]
for i in range(1,n):
    b[i]=a[i]+b[i-1]
e=[];c=d=0
for i in range(n-1,-1,-1):
    if b[i]>=-1:
        c+=1
    if b[i]>=3:
        d+=1
    e.append((c,d))
e=e[::-1];g=0;ans=0
for i in range(n):
    if a[i]==-1:
        if e[i][0]==0 and (b[-1]+2)==0 and g==0:
            ans+=1
    else:
        if e[i][1]==0 and (b[-1]-2)==0 and g==0:
            ans+=1
    if b[i]>0:
        g+=1
#print (b)
#print(e)
print (ans)
