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 sys import stdin,stdout
input = stdin.readline

s = input()
s = s[:-1]
n = len(s)

substring = [None for i in range(n)]
ending = [None for i in range(n)]
frequency = [0 for i in range(n+1)]

stack = []

for index,character in enumerate(s):
    
    if(character == '('):
        stack.append(index)
        continue
    
    if(len(stack) == 0):
        continue
    
    ind = stack.pop()
    substring[index] = ind
    ending[index] = ind
    
    if(ind > 0):
        ind -= 1
        if(s[ind] == ')' and substring[ind] != None):
            ending[index] = ending[ind] 

    if(ending[index] != None):
        frequency[index - ending[index] + 1] += 1
    
mx,cnt = 0,1
for index,freq in enumerate(frequency):
    if(freq > 0 and index > mx):
        mx,cnt = index,freq

print(mx,cnt)