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:
arr = raw_input()
arr = list(arr)

stack = []
max_length = 0
max_occ = 1

shape = [0] * len(arr)
for index, brac in enumerate(arr):
    if brac == "(":
        stack.append(index)
    else:
        if len(stack) > 0:
            closed_index = stack.pop()
            shape[closed_index] = index

pointer = 0
while pointer < len(arr):
    if shape[pointer] > 0:
        last_pointer = shape[pointer]
        for i in range(pointer, last_pointer+1):
            shape[i] = True
        pointer = last_pointer + 1
    else:
        shape[pointer] = False
        pointer += 1

current_length = 0
for item in shape:
    if item:
        current_length += 1
    else:
        if current_length > max_length:
            max_length = current_length
            max_occ = 1
        elif current_length == max_length:
            max_occ += 1
        current_length = 0

if current_length > max_length:
    max_length = current_length
    max_occ = 1
elif current_length == max_length:
    max_occ += 1

if max_length == 0:
    max_occ = 1

print "{} {}".format(max_length, max_occ)