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())
a=list(input())
k=0
st=[]
for i in range(n):
    if a[i]==')' and len(st)>0 and st[-1][0]=='(':
        k+=2
        st.pop()
    else:
        st.append([a[i],i+1])
if n%2==1 or len(st)==0:
    print(0)
elif len(st)==2 and st[0][0]==st[1][0]:
    if st[0][0]=='(':
        print((n-st[1][1])//2+1)
    else:
        print(st[0][1]//2+1)
else:
    print(0)