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:
t = input()
a = [0] * (len(t) + 1)
m = n = k = 0
for i in range(len(t)):
    j = t[i]
    if j == '(':
        k += 1
        if k > 0:
            a[k] = i
    else:
        k -= 1
        if k < 0:
            k = 0
            a[k] = i + 1
            w = 0
        elif k == 0:
            w = i - a[k] + 1
        else:
            w = i - a[k]
        if w > m:
            m = w
            n = 1
        elif w == m:
            n += 1
    # print(a[:10])
if m == 0:
    n = 1
print(m, n)