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 defaultdict
inpu = sys.stdin.readline
prin = sys.stdout.write
s = inpu().rstrip('\n')
stack = []
l = 0
ans = defaultdict(int)
for i in s :
    if i == "(" :
        stack.append(i)
        l += 1
    else :
        if len(stack) != 0:
            stack.pop()
            if len(stack) == 0:
                ans[2*l] += 1
                l = 0
if len(ans) == 0:
    prin("0 1")
else :
    m = max(ans.keys())
    prin(str(m) + ' ' + str(ans[m]) + '\n')
