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>.
string=input()
stack=[]
arr=[]
for i in range(len(string)):
    f=True
    if stack:
        if string[stack[-1]]=='(' and string[i]==')':
            stack.pop()
            f=False
    if f:
        stack+=(i,)
stack=[-1]+stack+[len(string)]
for i in range(0,len(stack)-1):
    if stack[i+1]-stack[i]-1>0:
        arr+=(stack[i+1]-stack[i]-1,)
if len(arr)==0:
    print(0,1)
else:
    print(max(arr),len(arr))
