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

s = input()
stack = deque()
ls = [0]*1000000
ans = -1

for i in range(len(s)):
    if s[i] == ')':
        if stack:
            r = stack.pop()
            ls[i] = ls[r-1] + (i-r+1)
    else:
        stack.append(i)
    # print(ls, stack)

f_ans = max(ls)
count = ls.count(f_ans)

if f_ans <= 0:
    print(0, 1)
else:
    print(f_ans, count)