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 sys
from collections import Counter
inpu = sys.stdin.readline
prin = sys.stdout.write
s = inpu().rstrip('\n')
check = [0]*len(s)
stack = []
ind = []
for i, j in enumerate(s) :
    if (len(stack) == 0) and (j == ')') :
        continue
    if j == '(' :
        stack.append(j)
        ind.append(i)
    if j == ')' :
        stack.pop()
        check[ind.pop()] = 1
        check[i] = 1
ans = [0]*len(s)
for i in range(len(s)) :
    if check[i] == 1:
        ans[i] = 1 + ans[i - 1]
c = Counter(ans).most_common()
if c[-1][0] == 0:
    prin("0 1\n")
else:
    prin(' '.join(map(str, c[-1])) + '\n')