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 
# # For getting input from input.txt file 
# sys.stdin = open('inputf.in', 'r')  
# # Printing the Output to output.txt file 
# sys.stdout = open('outputf.in', 'w') 

# started at 16:27

mx, cnt, st = 0,1,[-1]
for i,w in enumerate(input().strip()):
	if w=='(': st.append(i)
	elif len(st)>1: 
		st.pop()
		_t = i - st[-1]
		if _t>mx: mx,cnt = _t,1
		elif _t==mx: cnt+=1
	else: st[0]=i
print(mx,cnt)


# submitted 17:17