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:
line = input()

all_pair = []
stack = []
for (i, ch) in enumerate(line):
    if ch == '(':
        stack.append(i)
    else:
        if len(stack):
            left = stack.pop()
            all_pair.append((left, i))

all_pair.sort()

left = -2
right = -2
res = [0, 1]
for pair in all_pair:
    if pair[0]==right+1:
        right = pair[1]
    elif right+1 < pair[0]:
        left, right = pair
    else:
        continue

    length = right-left+1
    if length > res[0]:
        res = [length, 1]
    elif length == res[0]:
        res[1] += 1

print(res[0], res[1])