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>.
def main():
    string=input()
    arr=list(string)
    for x in range(len(arr)):
        if arr[x]=="(":
            arr[x]=1
        else:
            arr[x]=-1
    bo=True
    maximum=0
    freq=1
    for x in range(len(arr)):
        if bo:
            count=0
            length=0
            count+=arr[x]
            length+=1
            bo=False
        else:
            count+=arr[x]
            length+=1
        if count<0:
            bo=True
        elif count==0:
            if length>maximum:
                maximum=length
                freq=1
            elif length==maximum:
                freq+=1
            bo=True
    print(length,freq)
main()
