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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class e {

	public static void main(String[] args) throws IOException {
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		int n = in.nextInt();
		int[] arr = new int[n];
		String str = in.next();
		for (int i = 0; i < n; i++) {
			if (str.charAt(i) == '(') {
				arr[i] = 1;
			} else {
				arr[i] = -1;
			}
		}
		int[] pres = new int[n];
		boolean[] goodPres = new boolean[n];
		goodPres[0] = true;
		int[] sufs = new int[n];
		boolean[] goodSufs = new boolean[n];
		goodSufs[n - 1] = true;
		for (int i = 1; i < n; i++) {
			pres[i] = pres[i - 1] + arr[i - 1];
			goodPres[i] = goodPres[i - 1] && pres[i] >= 0;
		}
		for (int i = n - 2; i >= 0; i--) {
			sufs[i] = sufs[i + 1] + arr[i + 1];
			goodSufs[i] = goodSufs[i + 1] && sufs[i] <= 0;
		}
		int ans = 0;
		for (int i = 0; i < n; i++) {
			if (goodPres[i] && goodSufs[i] && pres[i] + sufs[i] - arr[i] == 0) {
				ans++;
			}
		}
		out.println(ans);
		
		out.close();
	}
	
	static class FastScanner {
	    BufferedReader br;
	    StringTokenizer st;
		
	    public FastScanner(InputStream i) {
	        br = new BufferedReader(new InputStreamReader(i));
	        st = new StringTokenizer("");
	    }
				
	    public String next() throws IOException {
	        if(st.hasMoreTokens())
	            return st.nextToken();
	        else
	            st = new StringTokenizer(br.readLine());
	        return next();
	    }

	    public int nextInt() throws IOException {
	        return Integer.parseInt(next());
	    }
	    //#
	    public long nextLong() throws IOException {
	        return Long.parseLong(next());
	    }
	    public double nextDouble() throws IOException {
	        return Double.parseDouble(next());
	    }
	    //$
	}
}
