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.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

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

    static class EAlmostRegularBracketSequence {
        public void solve(int testNumber, ScanReader in, PrintWriter out) {

            int n = in.scanInt();
            int Opre[] = new int[n + 5];
            int Cpre[] = new int[n + 5];
            int Osuf[] = new int[n + 5];
            int Csuf[] = new int[n + 5];


            int arr[] = new int[n + 1];
            String str = in.scanString();
            for (int i = 1; i <= n; i++) arr[i] = str.charAt(i - 1);
            boolean f = true;
            for (int i = 1; i <= n; i++) {
                if (arr[i] == '(') {
                    Opre[i] = 1 + Opre[i - 1];
                    Cpre[i] = Cpre[i - 1];
                } else {
                    Opre[i] = Opre[i - 1];
                    Cpre[i] = 1 + Cpre[i - 1];
                }
                if (!f) {
                    Opre[i] = -1;
                    Cpre[i] = -1;
                }
                if (Cpre[i] > Opre[i]) f = false;
            }
            f = true;


            for (int i = n; i >= 1; i--) {
                if (arr[i] == '(') {
                    Osuf[i] = 1 + Osuf[i + 1];
                    Csuf[i] = Csuf[i + 1];
                } else {
                    Osuf[i] = Osuf[i + 1];
                    Csuf[i] = 1 + Csuf[i + 1];
                }
                if (!f) {
                    Osuf[i] = -1;
                    Csuf[i] = -1;
                }
                if (Osuf[i] > Csuf[i]) f = false;
            }

            long ans = 0;
            for (int i = 1; i <= n; i++) {
                if (Cpre[i] != -1 && Csuf[i] != -1) {
                    if (arr[i] == '(' && (Opre[i] + Osuf[i + 1] - Cpre[i] - Csuf[i + 1]) == 2) ans++;
                    else if (arr[i] == ')' && (Cpre[i] + Csuf[i + 1] - Opre[i] - Osuf[i + 1]) == 2) ans++;
                }
            }
            out.println(ans);
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        public String scanString() {
            int c = scan();
            while (isWhiteSpace(c)) c = scan();
            StringBuilder RESULT = new StringBuilder();
            do {
                RESULT.appendCodePoint(c);
                c = scan();
            } while (!isWhiteSpace(c));
            return RESULT.toString();
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}

