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:
a = input()
brakets = []
q = -1
ansmax = 0
quantity = 1
k = 0
for i in range(len(a)):
    if a[i] == '(':
        brakets.append(i)
    elif brakets != []:
        brakets.pop()
        if brakets != []:
            k = i - brakets[-1]
        else:
            k = i - q
        if k > ansmax:
            ansmax = k
            quantity = 1
        elif k == ansmax:
            quantity += 1
    else:
        q = i
print()
print(ansmax, quantity)