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:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Sep  1 15:49:49 2018

@author: all_blue
"""

sequence = [char for char in input().strip()]
stack = []

max_seq = 0
num_max_seq = 1
open_braces_idx = -1

for idx in range(len(sequence)):
    if sequence[idx] == "(":
        stack.append(idx)
    elif stack:
        stack.pop()
        curr_seq = idx - stack[-1] if stack else idx - open_braces_idx
        if curr_seq > max_seq:
            max_seq = curr_seq
            num_max_seq = 1
        elif curr_seq == max_seq:
            num_max_seq += 1
    else:
        open_braces_idx = idx

print(max_seq, num_max_seq)