This is yet another problem dealing with regular bracket sequences.

We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not. 

You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 10<sup class="upper-index">6</sup>.
s=input()
n=len(s)
dp=[0]*(n)
for i in range(1,n):
    if s[i]==")":
    
        if s[i-1]==")":
            if i-dp[i-1]-1>=0:
                if s[i-dp[i-1]-1]=='(':
                    dp[i]=2+dp[i-1]
                    if i-dp[i-1]-2>=0:
                        dp[i]+=dp[i-dp[i-1]-2]


                else:dp[i]=0

        else:
            if i>=2:

                dp[i] = 2+dp[i-2]

m=max(dp)
if m==0:
    print(0,1)
else:print(m,dp.count(m))


        

