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 = list(input())
n = len(s)
v = [0]*n

for i in range(1,n):
    if s[i]=="(":
        continue
    if s[i-1]=="(":
        if i-2>=0:
            v[i]=v[i-2]+2
        else:
            v[i]=2
    else:
        if v[i-1]>0:
            j = i-1-v[i-1]
            if j>=0 and s[j]=="(":
                if j==0:
                    v[i]=v[i-1]+2
                else:
                    v[i]=v[i-1]+2+v[j-1]

from collections import Counter
c = Counter(v)
m = max(v)

if m == 0:
    print(*(0,1))
else:
    print(*(m,c[m]))
