Problem: 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.

Input

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

Output

Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

Examples

Input

)((())))(()())


Output

6 2


Input

))(


Output

0 1

Solution (in PYTHON3):

Solution:
import sys
inp = sys.stdin.readlines()
inp1 = inp[0]
leninp1 = len(inp1) - 1 
stack = [0]*(leninp1 + 1)
# print(stack)
top = -1
repetetion = [0]*(leninp1+1)
maxCount = 0
stack[0] = -1
top+=1


for i in range(leninp1):
	if inp1[i]=='(':
		stack[top+1] = i
		top+=1
	else:
		top-=1
		if top==-1:
			stack[top+1]= i
			top+=1
		else:
			# print(stack)
			# print(top)
			maxCount = max(maxCount,i-stack[top])
			repetetion[i-stack[top]]+=1


if maxCount!=0:
	print(str(maxCount)+" "+str(repetetion[maxCount]))
else:
	print("0 1")