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 Counter as cr
st=input()
c=0
s=[]
ans=[]
for i in st:
    if i=='(':
        if len(s)==0:
            ans.append(c)
            c=0
        s.append(i)
    else:
        if len(s)!=0:
            c+=2
            s.pop()
        else:
            ans.append(c)
            c=0
            ans.append(')')
ans.append(c)
t=[0]
for i in ans:
    if i==')':
        t.append(0)
    else:
        t.append(i+t[-1])
m=cr(t)
c=max(t)
if c==0:
    print("0 1")
else:
    print(c,m[c])
