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>.
if __name__ == "__main__":
	tmp = str(input())
	local_max = 0
	how_many = 1
	for i in range(len(tmp)):
		if tmp[i]=="(":
			j=i+1
			count = 1
			while(j<len(tmp)):
				#print("J:",j)
				if tmp[j]=="(":
					count+=1
					j+=1
				elif tmp[j]==")":
					count-=1
					j+=1
					if(count<=0):
						break
				else:
					print("wrong chr:",tmp[i])
					break
				#print("Count:",count)
			if count==0:
				#print("OK Find",j-i)
				if j-i>local_max:
					local_max =  j-i
					how_many = 1
				elif j-i==local_max:
					how_many+=1
	print(local_max,how_many)
			
