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>.
import math

def slove():
    a = str(input())
    dp = [0]*(len(a)+1)
    pd = 0
    c = len(a)
    maxx=-1
    for i in range(1,c+1):
        if a[i-1]==")":
            if pd!=0:
                pd-=1
                dp[i]=dp[i-1]+2
        else:
            dp[i-1]=dp[i-2]
            pd+=1
        maxx=max(maxx,dp[i-1])    
    if maxx==0:
        print(0,1)
    else:
        
        ans = 0
        for i in range(len(dp)):
            if dp[i]==maxx:
                ans+=1
        print(maxx,ans-1)        




    
    




if __name__=='__main__':
    
        slove()