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>.
s = input()
mx = 0
cnt = 0
n = len(s)
stack = []
op = 0
curr = 0
for i in range(n):
    if(stack):
        if(s[i] == ")"):
            if(op):
                op-=1
                curr += 2
                if(mx < curr):
                    mx = curr
                    cnt = 1
                elif(mx == curr):
                    cnt += 1
            else:
                curr = 0
        else:
            stack.append(s[i])
            op+=1
    else:
        if(s[i] == "("):
            op += 1
        stack.append(s[i])
if(mx == 0):
    cnt = 1
print(mx, cnt)