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:
"""
Codeforces
5C - Longest Regular Bracket Sequence
http://codeforces.com/contest/5/problem/C

Héctor González Belver
../07/2018
"""
import sys


def main():
  pattern = sys.stdin.readline().strip()

  max_length = 0
  substring_counter = 1
 
  ##longest substring!! --> stack ==> O(n)
  #-->the first element: index before the beginning of the next valid substring
  #-->store indexes of previous starting brackets
  stack = [-1]
  for i, c in enumerate(pattern):
    if c == '(':
      stack.append(i)
    else:
      stack.pop()

      if stack:
        if i - stack[-1] > max_length:
          max_length = i - stack[-1]
          substring_counter = 1
        elif i - stack[-1] == max_length:
          substring_counter += 1
      else:
        stack.append(i)

  
  sys.stdout.write(str(max_length) + ' ' + str(substring_counter) + '\n')

if __name__ == '__main__': 
  main()