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:
def ii(): return int(input())
def si(): return input()
def mi(): return map(int,input().split())
def msi(): return map(str,input().split())
def li(): return list(mi())

s=si()
dp=[0]*(len(s)+1)
ocnt=0

for i in range(len(s)):
    if s[i]=='(':
        ocnt+=1
        
    else:
        if ocnt>0:
            ocnt-=1
            
            if s[i-1]==')':
                dp[i]=dp[i-1]+2
                
            else:
                if i>1:
                    if s[i-2]==')':
                        dp[i]=2+dp[i-2]
                        
                    else:
                        dp[i]=2
                        
                else:
                    dp[i]=2
                    
            dp[i]=dp[i]+dp[i-dp[i]]
            
if max(dp)==0:
    print(0,1)
    
else:
    print(max(dp),dp.count(max(dp)))