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.Scanner;

public class E {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        String s = in.next();
        char[] brs = s.toCharArray();
        int opens = 0;
        for (char br: brs) {
            if (br == ')') {
                opens--;
            } else {
                opens++;
            }
        }

        if (opens == 2) {
            int med = brs.length/2;
            for (int i = 0; i < med; i++) {
                char temp = brs[i];
                brs[i] = (brs[brs.length - i - 1] == ')' ? '(' : ')');
                brs[brs.length - i - 1] = (temp == ')' ? '(' : ')');
            }
        } else if (opens != -2) {
            System.out.println("0");
            return;
        }

        opens = 0;
        int result = 0;
        boolean canChange = true;
        for (int i=0; i<brs.length; i++) {
            if (brs[i] == ')') {
                opens--;
            } else {
                opens++;
            }
            if (opens < -2) {
                System.out.println("0");
                return;
            } else if (canChange && brs[i] == ')') {
                result++;
                if (opens<0) {
                    canChange = false;
                }
            }
        }

        System.out.println(result);
    }
}
