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 {
    FastScanner in;
    PrintWriter out;

    void run() {
        in = new FastScanner();
        out = new PrintWriter(System.out);
        problem();
        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }

        public long nextLong() {
            return Long.parseLong(nextToken());
        }

        public double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }

    public static void main(String[] args) {
        new Main().run();
    }

    void problem() {
        int n = in.nextInt();
        String s = in.nextToken();

        LinkedList<Integer> q = new LinkedList<>();
        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == '(') {
                q.addFirst(i);
            } else {
                if (q.size() > 0 && s.charAt(q.getFirst()) == '(') {
                    q.removeFirst();
                } else {
                    q.addFirst(i);
                }
            }
        }

        if (q.size() != 2 || s.charAt(q.getFirst()) != s.charAt(q.getLast())) {
            out.println(0);
            return;
        }

        int res = 0;
        if (s.charAt(q.getFirst()) == '(') {
            for (int i = q.getFirst(); i < n; i++) {
                if (s.charAt(i) == '(') {
                    res++;
                }
            }
        } else {
            for (int i = 0; i <= q.getLast(); i++) {
                if (s.charAt(i) == ')') {
                    res++;
                }
            }
        }
        out.println(res);
    }
}
