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>.
W,st = list(input().strip()),[]
arr,brr,mx =[-1]*len(W),[-1]*len(W),0

for i in range(len(W)):
	if W[i] == '(':
		st.append(i)
		arr[i]=-1
	elif W[i] == ')':
		if len(st):
			arr[i] = st.pop()
			if arr[i]-1 > 0:
				arr[i] = arr[i] if arr[arr[i]-1] == -1 else arr[arr[i]-1]
		else:
			arr[i] = -1
	if (arr[i]!=-1) :
		brr[i] = i-arr[i]+1
	mx = max(mx,brr[i])
print(mx,brr.count(mx)) if not mx==-1 else print(0,1)