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>.
brckts = input()

stack = []
for i in brckts:
    flag = False
    if i == ")":
        su = 0
        while stack and stack[-1] != "(" and stack[-1] != ")":
            su += stack.pop()
        if stack != [] and stack[-1] == "(":
            # print(stack)
            flag = True
            stack.pop()
            while  stack and stack[-1] != "(" and stack[-1] != ")":
                su += stack.pop()
            su += 2
        if su != 0 :
            stack.append(su)
        if flag != True:
            stack.append(')')
    else:
        stack.append(i)

ma = 0
for i in stack:
    if i != "(" and i != ")":
        ma = max(i, ma)
c = 0
for i in stack:
    if i == ma:
        c += 1

if stack == []:
    print("0 1")
else:
# print(stack)
    print(ma, c)

#(()())()(())()()())())()((()(()(())()()())((()(())()(()()()()))()(())()(((()())()(()((())()(())(()))
