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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Vadim
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        E solver = new E();
        solver.solve(1, in, out);
        out.close();
    }

    static class E {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.ni();
            String s = in.ns();
            int b = 0;
            int[] suffix = new int[n];
            Arrays.fill(suffix, -100);
            for (int i = n - 1; i >= 0; i--) {
                if (s.charAt(i) == ')') {
                    b++;
                } else {
                    b--;
                }
                if (b < 0)
                    break;
                suffix[i] = b;
            }

            int c = 0;
            int ans = 0;
            for (int i = 0; i < n; i++) {
                b = 0;
                if (i < n - 1)
                    b = suffix[i + 1];
                if (s.charAt(i) == ')') {
                    b--;
                    if (c >= 0 && b >= 0 && b == c)
                        ans++;
                    c--;
                } else {
                    b++;
                    if (c >= 0 && b >= 0 && b == c)
                        ans++;
                    c++;
                }
                if (c < 0)
                    break;
            }
            out.println(ans);

        }

    }

    static class InputReader extends BufferedReader {
        public InputReader(InputStream st) {
            super(new InputStreamReader(st));
        }

        public String readLine() {
            try {
                return super.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        private int readByte() {
            try {
                return read();
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }

        public int ni() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = num * 10 + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public String ns() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

    }
}

