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.
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 10<sup class="upper-index">6</sup>.
s = input()
num_left = 0
num_right = 0
max_num = 0
max_num_start = 0
k = 0
k_start = 0
length = len(s)
for i in range(length):
    if num_left < num_right:
        if k > max_num:
            max_num = k - 1
            max_num_start = k_start
            k_start = i + 1
            k = 0
            num_left, num_right = 0, 0

    if s[i] == '(':
        num_left = num_left + 1
    else:
        num_right = num_right + 1
    k = k + 1
if max_num == 0:
    max_num_start = 1
print(max_num, ' ', max_num_start)