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 java.io.*;
import java.util.*;
public class Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            String s=input.next();
            Stack<Pair> st=new Stack<>();
            for(int i=0;i<n;i++)
            {
                if(s.charAt(i)==')')
                {
                    if(st.isEmpty() || st.peek().c==')')
                    {
                        st.push(new Pair(')',i));
                    }
                    else
                    {
                        st.pop();
                    }
                }
                else
                {
                    st.push(new Pair('(',i));
                }
            }
            if(st.size()!=2)
            {
                out.println(0);
            }
            else
            {
                Pair p1=st.pop();
                Pair p2=st.pop();
                if(p1.in>p2.in)
                {
                    Pair temp=p1;
                    p1=p2;
                    p2=temp;
                }
                if(p1.c==')' && p2.c=='(')
                {
                    out.println(0);
                }
                else if(p1.c=='(' && p2.c=='(')
                {
                    int count=0;
                    for(int i=p2.in;i<n;i++)
                    {
                        if(s.charAt(i)=='(')
                        {
                            count++;
                        }
                    }
                    out.println(count);
                }
                else
                {
                    int count=0;
                    for(int i=p1.in;i>=0;i--)
                    {
                        if(s.charAt(i)==')')
                        {
                            count++;
                        }
                    }
                    out.println(count);
                }
            }
        }
        out.close();
    }
    static class Pair
    {
        char c;
        int in;
        Pair(char c,int in)
        {
            this.c=c;
            this.in=in;
        }
    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt()
        {
            return Integer.parseInt(next());
        }
        long nextLong()
        {
            return Long.parseLong(next());
        }
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
        String nextLine()
        {
            String str="";
            try
            {
                str=br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}