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>.
string=input()
def isReg(string):
	if len(string)%2!=0:
		return False
	chert=[]
	for i in string:
		if i=="(":
			chert.append("(")
		else:
			chert.append(")")
		if chert[len(chert)-1]==")" and chert[len(chert)-2]=="(":
			chert.pop(len(chert)-1)
			chert.pop(len(chert)-1)
	if not chert:
		return True
	return False
high=0
substr=[]
for i in range(0,len(string)-1):
	if string[i]=="(" and string[i+1]==")":
		sa='()'
		sd=i-1
		for k in range(i+1,len(string)):
			sds=len(sa)
			if isReg(sa)  and sds>high:
				substr.append(sa)
				high=sds
			else:
				break
			sa=string[sd:k+2]
			sd-=1
ana=0
print(high,end=' ')
for i in substr:
	if len(i)==high:
		ana+=1
if high>0:
	print(ana)
else:
	print('1')