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:
bs = input().strip()
n = len(bs)
prevs = [-1] * n
starts = [-1] * n

opens = []
for i, b in enumerate(bs):
	if b == '(':
		opens.append(i)
	else:
		if opens:
			j = opens.pop()
			prevs[i] = j
			if starts[j-1] == -1:
				starts[i] = j
			else:
				starts[i] = starts[j-1]

best = 0
best_count = 1

for i, s in enumerate(starts):
	if s != -1:
		l = i - s + 1
		if l > best:
			best = l
			best_count = 1
		elif l == best:
			best_count += 1

print(best, best_count)