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.FileReader;
import java.io.InputStreamReader;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {

	static final String FILENAME = "";

	public static void main(String[] args) throws Exception {

		SC scan = new SC();

		int n = scan.nextInt();
		char[] c = scan.nextLine().toCharArray();
		Stack<Integer> s = new Stack<>();
		for(int i = 0; i < n; i++) {
			if(s.isEmpty())
				s.push(i);
			else if(c[i] == '(')
				s.push(i);
			else if(c[s.peek()] == '(')
				s.pop();
			else
				s.push(i);	
		}
		if(s.size() != 2 || c[s.get(0)] != c[s.get(1)]) {
			System.out.println(0);
			return;
		}
		if(c[s.peek()] == '(')
			System.out.println((n - s.get(1) - 1) / 2 + 1);
		else
			System.out.println(s.get(0) / 2 + 1);
	}
	

	static class SC {

		BufferedReader br;
		StringTokenizer st;

		public SC() throws Exception {
			if (FILENAME.equals(""))
				br = new BufferedReader(new InputStreamReader(System.in));
			else
				br = new BufferedReader(new FileReader(FILENAME));
			st = new StringTokenizer("");
		}

		public String nextLine() throws Exception {
			return br.readLine();
		}

		public String next() throws Exception {
			while (!st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws Exception {
			return Integer.parseInt(next());
		}

		public long nextLong() throws Exception {
			return Long.parseLong(next());
		}

		public double nextDouble() throws Exception {
			return Double.parseDouble(next());
		}
	}

}