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:
from collections import deque, defaultdict
s = input()
mp = defaultdict(int)
stack = deque([-1])
_max = 0
for i,c in enumerate(s):
    if c == '(':
        stack.append(i)
    else:
        last = stack.pop()
        if len(stack) == 0:
            stack.append(i)
        else:
            curr =  i - stack[-1]
            if curr > _max:
                _max = curr

            mp[curr] += 1

if _max == 0:
    print(0, 1)
else:
    print(_max, mp[_max])