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()
n=len(s)
arr=[None for x in range(n)]
stack=[]
countarr=[0 for x in range(n+1)]

for i in range(n):
    if s[i]=="(":
        stack.append(i)
    else:
        if stack:
            arr[i]=stack.pop()
maxlen=0;count=1
for i in range(n):
    if arr[i]!=None and arr[i]!=0:
        preindex=arr[i]-1

        if arr[preindex]!=None:
            arr[i]=arr[preindex]

for i in range(n):
    if arr[i]!=None:
        countarr[i-arr[i]+1]+=1
for i in range(n+1):
    if countarr[i]!=0:
        count=countarr[i]
        maxlen=i

print(maxlen,count)


