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()
stack = []
ans = [0 for i in range(len(s))]
for i,l in enumerate(s):
	if l=="(": stack.append(i)
	elif stack:
		p = stack.pop()
		ans[i]=ans[p-1]+i-p+1
print(max(ans),ans.count(max(ans)) if max(ans)>0 else 1)
