import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Scanner;

public class Main {

	void run() {
		Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();
		String str = sc.next();
		long ans = N * (N + 1) / 2;
		long sum = 0;
		long min = 0;
		long[][] a = new long[(int) N][2];
		for (int i = 0; i < N; ++i) {
			sum += (str.charAt(i) == '(' ? 1 : -1);
			ans -= sum;
			min = Math.min(min, sum);
			a[i][0] = sum;
			a[i][1] = min;
		}
		Arrays.sort(a, new Comparator<long[]>() {
			@Override
			public int compare(long[] o1, long[] o2) {
				return -Long.compare(Math.min(o1[1], o1[0] + o2[1]), Math.min(o2[1], o2[0] + o1[1]));
			}
		});
		sum = 0;
		min = 0;
		for (int i = 0; i < N; ++i) {
			min = Math.min(min, a[i][1] + sum);
			sum += a[i][0];
		}
		System.out.println(ans + 2 * min);
	}

	public static void main(String[] args) {
		new Main().run();
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

}