#include <cstdio>
int n, d, mn, ca[100009], cb[100009]; long long sum, curl, depl, curr, depr; bool fa[100009], fb[100009]; char s;
int main() {
	scanf("%d\n", &n);
	for (int i = 0; i < n; ++i) {
		s = getchar();
		d += (s == '(' ? 1 : -1);
		sum += d;
		mn = (mn < d ? mn : d);
		if (d >= 0) ca[-mn] += d, fa[-mn] = true;
		else cb[d - mn] -= d, fb[d - mn] = true;
	}
	for (int i = 0; i <= n; ++i) {
		if (fa[i]) depl = (depl < curl - i ? depl : curl - i);
		curl += ca[i];
	}
	for (int i = 0; i <= n; ++i) {
		if (fb[i]) depr = (depr < curr - i ? depr : curr - i);
		curr += cb[i];
	}
	printf("%lld\n", 1LL * n * (n + 1) / 2 + (depl < depr + sum ? depl : depr + sum) * 2 - sum);
	return 0;
}