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
for _ in range(1):
    n=int(input())
    st=list(input().strip())
    rt=st[::]
    count=0
    add=0
    store_f=-1
    store_b=-1
    if n%2==1:
        print(0)
        continue
    for i in range(n):
        if st[i] =="(":
            add+=1
            continue
        add-=1
        if add <0:
            count+=1
            add+=2
            st[i] ="("
            store_f=i
    sub=0
    for i in range(n-1,-1,-1):
        if st[i] ==")":
            sub+=1
            continue
        sub-=1

        if sub <0:
            count+=1
            sub+=2
            st[i] =")"
            store_b=i
    if count >=2 or count==0:
        print(0)
        continue
    if count ==1 and ((add==0 and sub==0) or (add==2 and sub ==0)):
        if store_b==-1:
            print(rt[:store_f+1].count(")"))
        else:
            print(rt[store_b:].count("("))