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 PYTHON):

Solution:
#!/usr/bin/python

import fileinput

# Read in data
string = fileinput.input()[0]

# Define a stack
stk = [ { 'i': -1, 'c': ')'} ]

# Solve the max length
maxlen = 0
start = 1
count = 1
for i in range(0, len(string)):
	if string[i] == '(':
		stk.append( {'i': i, 'c': string[i]} )
	elif string[i] == ')':
		peak = stk[-1]
		if (peak['c'] == '('):
			stk.pop()
			peak = stk[-1]
			nowlen = i - peak['i']
			if nowlen > maxlen:
				maxlen = nowlen
				count = 1
			elif nowlen == maxlen:
				count += 1
		else:
			stk.append( {'i': i, 'c': string[i]} )

print maxlen, count