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()
n = len(s)
stack = []
maxlen = 0
cnt = 0
curlen = 0
for i in range(0,n):
    if(s[i]=='('):
        stack.append(s[i])
    elif(s[i]==')'):
        if(len(stack)>0):
            stack.pop()
            curlen+=1
            if(len(stack)==0):
                if(curlen>maxlen):
                    maxlen = curlen
                    cnt = 1
                elif(curlen==maxlen):
                    cnt+=1
                curlen = 0
if(maxlen==0):
    print("0 1")
else:
    print(maxlen*2,cnt)