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:
    if l.count("(")>=l.count(")"):
        for i in range(len(l)):
            if l[i]=="(":
                ans.append(i+1)
            else:
                try:
                    ans.pop()
                except:
                    continue
    else:
        for i in range(1,len(l)+1):
            if l[-i]==")":
                ans.append(i)
            else:
                try:
                    ans.pop()
                except:
                    continue
    ans.insert(0,0)
    ans.append(len(l))
    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))))