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()
n = len(s)

def solve(s, n):
   
    left = 0
    right = 0
    maxlength = 0
    exist = 0
    
    for i in range(n):

        if (s[i] == '('):
            left += 1
        else:
            right += 1

       
        if (left == right):
            exist += 1
            maxlength = max(maxlength, 2 * right)

        
        elif (right > left):
            left = right = 0

    left = right = 0
    
    return maxlength, exist


r, p = solve(s, n)
if r == 0  and p == 0:
    print("0 1")
else:
    print(r, p)
