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 bisect
import collections
import copy
import functools
import heapq
import itertools
import math
import sys
import string
sys.setrecursionlimit(99999)

s = input()
# s = "))("
st = []
ans = []

for i,c in enumerate(s):
    if c=="(":
        st.append(i)
    elif st:
        q = st.pop()
        if ans:
            x,y = ans[-1]
            if x==q+1 and y== i-1:
                ans.pop()
                ans.append([q,i])
            elif y==q-1:
                ans.pop()
                ans.append([x,i])
            else:
                ans.append([q,i])
        else:
            ans.append([q,i])
mx = 0
mc = 1
for x,y in ans:
    if y-x+1>mx:
        mx = y-x+1
        mc = 1
    elif y-x+1==mx:
        mc+=1
print(mx,mc)
