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,l,num,flag=input(),0,1,0#flag 当前已经有几对括号
d,length=[],0
for i in s:
    if not flag:
        if i=='(':
           flag+=1
           length+=1
    else:
        if i=='(':
            flag+=1
        else:
            flag-=1
        length+=1
    if flag==0:
        d.append(length)
        length=0
for j in d:
    if j>l:
        l=j
        num=1
    elif j==l and j!=0:
        num+=1
print(l,num)



