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()
c=0
pointer=0
fs=-1
for i in range(len(s)):
    if s[i]=="(":
        if c==0:
            pointer=i
        c+=1
    else:
        c-=1
    if c<0:
        c=0
    elif c==0:
        fs=max(i-pointer+1,fs)
cc=0
c=0
pointer=0
for i in range(len(s)):
    if s[i]=="(":
        if c==0:
            pointer=i
        c+=1
    else:
        c-=1
    if c<0:
        c=0
    elif c==0:
        if i-pointer+1==fs:
            cc+=1
if fs==-1:
    print(0,1)
else:
    print(fs,cc)