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()
l = len(s)
stack = []
ans = 0
sub = 0
for i in range(l):
    if stack and stack[-1][0]=='(' and s[i]==')':
        del stack[-1]
    else:
        stack.append((s[i],i))
#print(stack)
if not stack:
    print(f'{l} 1')
else:
    if stack[0][1]!=0:
        stack = [(0,-1),]+stack
    if stack[-1][1]!=l-1:
        stack = stack+[(0,l),]
    stackl = len(stack)
    for i in range(1,stackl):
        ans = max(ans,stack[i][1]-stack[i-1][1]-1)
        if stack[i][1]-stack[i-1][1]-1:
            sub+=1
    if ans:
        print(ans,sub)
    else:
        print(ans,1)