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()
n = len(s)
dp = []
stack = []
for i in range(n):
	if s[i]=="(":
		if len(stack)==0:
			dp.append(1)
			stack.append(1)
			continue
		dp.append(stack[-1]+1)
		stack.append(stack[-1]+1)
	else:
		if len(stack)==0:
			continue
		dp.append(stack[-1])
		stack.pop()

maxx = 0
count = 1
d = {}
for i in range(len(dp)):
	if dp[i] not in d:
		d[dp[i]] = i
	else:
		diff = i - d[dp[i]] + 1
		del d[dp[i]]
		if diff>maxx:
			maxx = diff
			count = 1
		elif diff==maxx:
			count += 1
print (maxx,count)