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>.
l=input()
ans=[]
if "()" not in l:
    print("0 1")
else:

    for i in range(len(l)):
        if l[i]=="(":
            ans.append(i+1)
        else:
            if 1 not in list(map(lambda x:x>0,ans)):
                ans.append(-i-1)
            else:
                ans.pop()

    ans.insert(0,0)
    ans.append(len(l)+1)
    for k in range(len(ans)):
        if ans[k]<0:
            ans[k]=-ans[k]
    answer=[]

    for j in range(1,len(ans)):
        answer.append(ans[j]-ans[j-1]-1)
    print(str(max(answer)) + " " + str(answer.count(max(answer))))