import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

N = int(readline())
S = read().rstrip().decode()

L = '('
R = ')'

dp = [(0, 0)]
total_pair = 0
now_pair = 0
for x in S:
    a, b = dp[-1]
    if x == L:
        dp.append((a, b + 1))
    else:
        if b:
            now_pair += 1
            dp.append((a, b - 1))
        else:
            dp.append((a + 1, 0))
    total_pair += now_pair

dp.sort(key=lambda x: min(x))

left = []
right = []
for a, b in dp:
    if a <= b:
        left.append((a, b))
    else:
        right.append((a, b))

x = 0
y = 0
for a, b in left + right[::-1]:
    p = min(y, a)
    total_pair += p
    y -= p
    a -= p
    if not y:
        x, y = x + a, b
    else:
        x, y = x, y + b

print(total_pair * 2)