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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.Reader;
import java.util.*;
public class E {
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        int N = scanner.nextInt();
        int cnt = 0;
        char[] seq = scanner.next().toCharArray();
        int[] pref = new int[N];
        int[] suff = new int[N];
        for(int i = 0; i < N; i++) {
            if (seq[i] == '(') cnt++;
            else cnt--;
            pref[i] = cnt;
        }
        suff[N-1] = pref[N-1];
        for(int i = N-2; i>=0; i--) {
            suff[i] = Math.min(pref[i], suff[i+1]);
        }
        int ret = 0;
        int min = Integer.MAX_VALUE;
        for(int i = 0; i < N; i++) {
            if(seq[i] == ')' && min >= 0) {
                if (suff[i]>=-2 && cnt == -2) {
                    ret++;
                }
            }
            else if (seq[i] == '(' && min >= 0) {
                if (suff[i] >= 2 && cnt == 2) {
                    ret++;
                }
            }
            min = Math.min(min, pref[i]);
        }
        System.out.println(ret);
    }
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        public FastScanner() {
            this(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 readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }
    }
}
