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>.
def check(st):
	l=0
	c=0
	ans=0
	i=0
	count=0
	while i<len(st):
		if st[i]=='(':
			c+=1
		else:
			if c!=0:
				l+=2
				c-=1
		if c==0:
			if l==ans:
				count+=1
			ans=max(l,ans)
			l=0
			c=0
		i+=1
	if ans==0:
		count=1
	print(ans,count)
st=input()
check(st)