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().strip()
stack = []
oc = 0
cc = 0
maxi = 0
_hash = {}
_hash[0]=1
for i in range(len(s)):
    c = s[i]
    if c == ')':
        cc+=1
    else:
        oc+=1
    if cc > oc:
        #inbaalanced
        cc = 0
        oc = 0
        continue
    if cc == oc:
        maxi = max(maxi,cc+oc)
        if maxi in _hash.keys():
            _hash[maxi]+=1
        else:
            _hash[maxi]=1
print(maxi,_hash[maxi])
