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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;

public class E1095 {

	public static void main(String[] args) throws NumberFormatException, IOException {
//		BufferedReader br = new BufferedReader(new FileReader("F:/books/input.txt"));
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		Integer n = Integer.parseInt(br.readLine());
		String s1 = br.readLine();
		s1 = process(s1);
		System.out.println(solve(s1));
	}

	private static int solve(String s) {
		int ret = 0;
		if(s.equals("")) return ret;
		ArrayDeque<Character> st = new ArrayDeque<Character>();
		for(int i=0;i<s.length();i++) {
			char c = s.charAt(i);
			if(c=='(') {
				st.push(c);
				ret++;
			}
			else {
				if(st.isEmpty()) return 0;
				st.pop();
				if(st.size()<2) ret = st.size();
			}
		}
		return ret-1;
	}

	private static String process(String s1) {
		StringBuilder sb = new StringBuilder("");
		int cnt= 0;
		for (int i = 0; i < s1.length(); i++) {
			if(s1.charAt(i)=='(') cnt++;
		}
		int l = s1.length();
		if(Math.abs(l-2*cnt)!=2) return sb.toString();
		if(cnt>(l-cnt)) return s1;
		for(int i=l-1;i>=0;i--) 
			if(s1.charAt(i)=='(') sb.append(")");
			else sb.append("(");
		return sb.toString();
	}

}
