n = int(input())
mod = 998244353
ans = 1
count = 0
dp = [1]
for v in input():
    if v == "(":
        dp.append(dp[-1])
        for i in range(len(dp)-2, 0, -1):
            dp[i] = (dp[i-1]+dp[i])%mod
        count += 1
    else:
        for i in range(len(dp)-1):
            dp[i] = (dp[i]+dp[i+1])%mod
        dp.pop()
        count -= 1
    if count == 0:
        ans = ans*dp[0]%mod
        dp = [1]
print(ans)