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>.
ins, max_len, kol, pos=input(), 0, 0, [-1]
for i in range(len(ins)):
    if ins[i]=='(': pos.append(i)
    elif len(pos)>1:
        pos.pop()
        x=i-pos[-1]
        if max_len<x: max_len, kol = x, 1
        elif max_len==x: kol+=1
    else: pos[0]=i
print(max_len,kol)
