N = int(input())
S = input()

s_sum = 0
s_min = 0
P = []
for s in S:
    if s == "(":
        s_sum += 1
    else:
        s_sum -= 1
    s_min = min(s_min, s_sum)
    P.append((s_sum, s_min))

P.sort(key=lambda x: x[0] - x[1], reverse=True)
t_min = 0
t_sum = 0
for s, m in P:
    t_min = min(t_min, t_sum + m)
    t_sum += s

ans = N * (N + 1) // 2 - t_sum + 2 * t_min
print(ans)