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.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class A {
	public static void main(String[] args) throws NumberFormatException, IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt();
		char [] c = sc.next().toCharArray();
		int [] pre = new int[n];
		for (int i = 0; i < pre.length; ++i) {
			pre[i] = c[i] == '('?1:-1;
			if(i > 0)
				pre[i] += pre[i-1];
		}
		int [] suff = new int[n];
		suff[n-1] = pre[n-1];
		for (int i = suff.length-2; i >= 0; --i) {
			suff[i] = Math.min(suff[i+1], pre[i]);
		}
		int ans = 0;
		for (int i = 0; i < suff.length; ++i) {
			if(c[i] == '('){
				if(suff[i] >= 2 && pre[n-1] == 2)
					++ans;
			}
			else{
				if(suff[i] >= -2 && pre[n-1] == -2)
					++ans;
			}
			if(pre[i] < 0)
				break;
		}
		out.println(ans);
		out.close();
	}
	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

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

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}
		public long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}
	}

}
