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>.
string = input()
stack = []
t = 0
r = 0
maxt = 0
for i in range(len(string)):
    if string[i] == '(':
        stack.append('(')
        if i == len(string) - 1:
            if t >= maxt:
                maxt = t
            if t != 0:
                r += 1
    else:
        if len(stack) != 0:
            stack.pop(-1)
            t += 2
            if i == len(string) - 1:
                if t >= maxt:
                    maxt = t
                if t != 0:
                    r += 1
        else:
            if t >= maxt:
                maxt = t
            if t != 0:
                r += 1
            t = 0
if r == 0:
    print(0, 1)
else:
    print(maxt, r)







