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:
RI = lambda : [int(x) for x in input().split()]
rw = lambda : [input().strip()]


s=list(input().strip())

stack=[]
index_stack=-1

stack.append(-1)
index_stack+=1

maxo=0
c=0
for i in range(len(s)):
    if(s[i]=='('):
        stack.append(i)
        index_stack+=1
    else:
        stack.pop()
        index_stack-=1

        if(len(stack)!=0):
            length_temp=i-stack[index_stack]
            if(length_temp>maxo):
                maxo=length_temp
                c=1
            elif(length_temp==maxo):
                c+=1
        else:
            stack.append(i)
            index_stack+=1
if(c!=0):
    print(maxo,end=" ")
    print(c)
else:
    print("0 1")