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 defaultdict

s = input()


n = len(s)
stack = [ ]
dct   = defaultdict(int)
_max  = 0
i = 0


while(i<n):
    while(i<n and s[i]==')'):
        i+=1

    length = 0
    while(i<n):
        if(s[i]=='('):
            stack.append(i)
            i+=1

        elif(stack!=[ ]):
            length = i-stack.pop() + 1
            dct[length]+=1
            _max = max(length,_max)
            i+=1
        
        else:
            break

if(_max==0):
    print(0,1)
else:
    print(_max,dct[_max])

