n = int(input())
s = input()

mod = 998244353
#ans = 1
ans = 1
lt = 0
tmp = 1
for i in range(n):
    if s[i] == "(":
        lt += 1
    else:
        if lt > 1:
            tmp *= lt*2
        tmp %= mod
        lt -= 1
        if lt == 0:
            if tmp == 1:
                tmp = 2
            else:
                tmp += 2
            ans *= tmp
            ans %= mod
            tmp = 1

print(ans%mod)