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()
z=0
curl=0
maxl=0
kol=0
for x in s:
    if x==")":
        z-=1
        if z==-1:
            z=0
            if maxl<curl:
                maxl=curl
                kol=1
                curl=0
            else:
                if maxl==curl:
                    kol+=1
        else:
            curl+=1
    else:
        curl+=1
        z+=1
if z==0:
    if maxl<curl:
        maxl=curl
        kol=1
        curl=0
    else:
        if maxl==curl:
            kol+=1
if maxl==0:
    print("0 1")
else:
    print(str(maxl)+" "+str(kol))
