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()

f=0
b=0
l=[]
for i in range(n):
    l.append(f-b)
    if s[i]=="(":
        f=f+1
    else:
        b=b+1

f=0
b=0
r=[]
for i in range(n-1,-1,-1):
    r.append(b-f)
    if s[i]=="(":
        f=f+1
    else:
        b=b+1

r=r[::-1]
# print(l)
# print(r)

fl=[False]*n
i=0
while i<n:
    if l[i]<0:
        break
    i=i+1

for j in range(i+1,n):
    fl[j]=True

fr=[False]*n
i=n-1
while i>=0:
    if r[i]<0:
        break
    i=i-1

for j in range(i-1,-1,-1):
    fr[j]=True


cnt=0
for i in range(n):
    if s[i]=="(":
        if l[i]-r[i]==1 and l[i]>0 and r[i]>=0 and fl[i]==False and fr[i]==False:
            cnt=cnt+1
    else:
        if r[i]-l[i]==1 and r[i]>0 and l[i]>=0 and fl[i]==False and fr[i]==False:
            cnt=cnt+1
    # print(i,cnt)
print(cnt)



