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 *
s=input()
score=0
stack=[]
al=defaultdict(int)
val=0
temp=[]
saver=defaultdict(list)
saver[0].append(0)
for i in range(len(s)):
    if(s[i]==')'):
        if(score==0):
            stack=[]
            val=0
            saver=defaultdict(list)
            saver[0].append(i+1)
        else:
            stack.pop()
            score-=1
            al[i-(saver[score][-1])+1]+=1
        
    else:
        stack.append('(')
        score+=1
        
        saver[score].append(i+1)
    temp.append(val)
    
if(len(al)):
    print(max(al),al[max(al)])
else:
    print(0,1)