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
def main():
    count=int(input())
    string=input()
    front=[0]
    back=[0]
    for x in range(count):
        if string[x]=="(":
            front.append(front[-1]+1)
        else:
            front.append(front[-1]-1)
    for x in range(count-1,-1,-1):
        if string[x]==")":
            back.append(back[-1]+1)
        else:
            back.append(back[-1]-1)
    assert (back[-1])==-(front[-1])
    #print(front)
   # print(back)
    valid_front=[False for x in range(count+1)]
    valid_back=[False for x in range(count+1)]
    for x in range(count+1):
        if front[x]>=0:
            valid_front[x]=True
        else:
            break
    for x in range(count+1):
        if back[x]>=0:
            valid_back[x]=True
        else:
            break
    #print(valid_front,valid_back)
    tot=0
    for x in range(count):
        if valid_front[x] and valid_back[count-x-1]:
            if string[x]==")":
                if front[x]+1-back[count-x-1]==0:
                    tot+=1
                    #print(x)
            else:
                if front[x]-1-back[count-x-1]==0:
                    tot+=1
                    #print(x)
    print(tot)
main()
