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()
n = len(s)
ss = []
mlen = 0
cnt = 0
f={0:1}
for i in s:
    if i =='(':
        ss.append(1)
    if ss!=[] and i ==')':
        ss.pop()
        cnt+=2
        if cnt in f:
            f[cnt]+=1
        else:
            f[cnt]=1
    if ss==[]:
        mlen=max(mlen,cnt)
        cnt = 0
print(mlen,f[mlen])