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>.
tot,start,maxi,to=0,[],-1,0
for i,c in enumerate(input()):
    if c=='(':  
        start.append(i-1)
        to+=1
    else:
        if to>0:
            to-=1
            if maxi<(i-start[to]): maxi,count = i-start[to],1
            elif maxi==(i-start[to]): count+=1
            start.pop()
if maxi==-1:    print("0 1")
else: print(maxi,count)