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:
"""

"""
a1 = 0 #store the max of len(substring)
a2 = 1 #store the found same length substring
b1 = [-1]

for i1, i2 in enumerate(raw_input()):
    if i2 == '(':
        b1.append(i1)

    elif len(b1) > 1:
        b1.pop()
        c1 = i1 - b1[-1] #calculate the len of current longest substring found
        if a1 < c1: #if previously found is not longest, update the counters
            a1 = c1
            a2 = 1
        elif a1 == c1:
            a2 += 1
    else:
        b1[0] = i1

print a1, a2