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
import sys
n=int(sys.stdin.readline())
s=sys.stdin.readline()[:-1]
pre=[0 for _ in range(n+2)]
suf=[0 for _ in range(n+2)]
for i in range(1,n+1):
    if s[i-1]==')':
        if pre[i-1]==0:
            pre[i]=float('inf')
        else:
            pre[i]=pre[i-1]-1
    else:
        pre[i]=pre[i-1]+1
#print(pre,'pre')
for i in range(n,0,-1):
    if s[i-1]=='(':
        if suf[i+1]==0:
            suf[i]=float('inf')
        else:
            suf[i]=suf[i+1]+1
    else:
        suf[i]=suf[i+1]-1
#print(suf,'suf')
ans=0
for i in range(1,n+1):
    if s[i-1]==')':
        x=pre[i-1]
        y=suf[i+1]
        if x+y+1==0:
            ans+=1
    else:
        x=pre[i-1]
        y=suf[i+1]
        if x+y-1==0:
            ans+=1
print(ans)
