import sys

# sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
# inf = (1 << 63)-1
inf = (1 << 31)-1
md = 10**9+7
# md = 998244353

n = II()
s = SI()
cs = [0]
cnt = cur = 0
for c in s:
    if c == "(":
        cs.append(cs[-1]+1)
        cur += 1
    else:
        cs.append(cs[-1]-1)
    cnt += cur

mn = [inf]
for s in cs[1:]:
    mn.append(min(mn[-1], s))
# pDB(cs)
# pDB(mn)

pos, neg = [], []
for s, m in zip(cs[1:], mn[1:]):
    if s >= 0:
        pos.append((s, m))
    else:
        neg.append((s, m))
pos.sort(key=lambda x: (-x[1], -x[0]))
neg.sort(key=lambda x: (x[1]-x[0], -x[0]))

# sm = [(s, m) for s, m in zip(cs[1:], mn[1:])]
# sm.sort(key=lambda x: (-x[0], x[1]))

now = 0
# loss = 0
for s, m in pos+neg:
    d = max(0, -now-m)
    now += s+d
    # pDB(s, m, now, loss)

ans = cnt-now
print(ans*2)