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>.
from collections import deque
e=[None]*1000001
s=[None]*1000001
f=[0]*1000001
st=input()
stack=[]
max1=0
for i in range (len(st)):
    if(st[i]=='('):
        stack.append(i)
    else:
        if(len(stack)==0):
            s[i]=-1
            e[i]=-1
        else:
            idx=stack.pop()
            s[i]=idx
            e[i]=idx
            if(idx>0 and st[idx-1]==')' and s[idx-1]>=0):
                e[i]=e[idx-1]
            l=i-e[i]+1
            f[l]+=1
            max1=max(max1,l)
f[0]=1
print(max1,' ',f[max1])
