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 collections

exp = input()
stack = []
n = len(exp)
dp = [0]*n
length = 0
cnt =0
for i in range(n):
    c = exp[i]
    if c =='(':
        stack.append(i)
        continue

    if not stack:
        continue
    j = stack.pop()
    dp[i]=i-j+1
    if j>=1:
        dp[i]+=dp[j-1]
    if dp[i]>length:
        length = dp[i]
        cnt = 1
    elif dp[i]==length:
       cnt+=1
if length ==0:
    print(0,1)
else:
    print(length,cnt)
