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()
st=[]
count=0
maxV=0
flag=False
prev=0
for i,ch in enumerate(s):
    if ch==')' and not st:
        flag=True
        continue
    elif ch=='(':
        st.append(i)
    else:
        idx=st.pop()
        length=i-idx+1
        if not flag and not st:
            length+=prev
        if length==maxV:
            count+=1
        elif length>maxV:
            maxV=length
            count=1
        if not st:
            flag=False
        prev=length
if maxV==0:
    print('0 1')
else:
    print(str(maxV)+' '+str(count))





#   n,m,x,y=(map(int,input().split()))



