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()
count = 0
val = 0
maxi = 0
maxc = 1
for i in s:
    
    if i == "(":
        count = count + 1
    else:
        count = count - 1
    
    if count == -1:
        if val > maxi:
            maxi = val
            maxc = 1
        if val == maxi:
            maxc = maxc + 1
        count = 0
        val = 0
        val = val - 1
    val = val + 1
    
if val > maxi and count ==0:
    maxi = val
if maxi == 0:
    print(0,end=" ")
    print(1)
else:
    print(maxi,end=" ")
    print(maxc)
