#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main() {
    int N;
    string S;
    cin >> N >> S;

    vector<int> min_values;
    int total_sum = 0;
    int current_sum = 0;
    int current_min = 0;

    for (char c : S) {
        if (c == '(') {
            current_sum += 1;
            current_min = min(current_min, current_sum);
        } else {
            current_sum -= 1;
            current_min = min(current_min, current_sum);
        }
        min_values.push_back(current_min);
        total_sum += (c == '(' ? 1 : -1);
    }

    sort(min_values.rbegin(), min_values.rend());

    int max_min_sum = 0;
    int current = 0;
    for (int m : min_values) {
        current += m;
        if (current > max_min_sum) {
            max_min_sum = current;
        }
    }

    int result = N * (N + 1) / 2 - total_sum + 2 * max_min_sum;
    cout << result << endl;

    return 0;
}