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.util.*;
public class E529D3 {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int n =sc.nextInt();
		String s = sc.next();
		int sum = 0;
		for(int i=0; i<n; i++) {
			if(s.substring(i, i+1).equals("(")) {
				sum += 1;
			} else {
				sum -= 1;
			}
		}
		if(sum != 2 && sum != -2) {
			System.out.println(0);
		} else if(sum == -2) {
			int curr = 0;
			int count = 0;
			boolean flag = false;
			boolean p = true;
			for(int i=0; i<n; i++) {
				if(s.substring(i,i+1).equals(")")) {
					if(curr >=0 && !flag) {
						count++;
					}
					curr--;
				} else {
					curr++;
				}
				if(curr <0) {
					flag = true;
				}
				if(curr <-2) {
					p = false;
				}
			}
			count = p? count : 0;
			System.out.println(count);
		} else if(sum == 2) {
			int curr = 0;
			int count = 0;
			boolean p = true;
			for(int i=0; i<n; i++) {
				if(s.substring(i,i+1).equals("(")) {
					if(curr >0) {
						count++;
					}
					curr++;
				} else {
					curr--;
				}
				if(curr <= 1) {
					count = 0;
				}
				if(curr <0) {
					p = false;
				}
			}
			count = p? count: 0;
			System.out.println(count);
		}
	}
}
