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:
string=input()
stack=[]
arr=[]
for i in range(len(string)):
    f=True
    if stack:
        if string[stack[-1]]=='(' and string[i]==')':
            stack.pop()
            f=False
    if f:
        stack+=(i,)
stack=[-1]+stack+[len(string)]
for i in range(0,len(stack)-1):
    if stack[i+1]-stack[i]-1>0:
        arr+=(stack[i+1]-stack[i]-1,)
if len(arr)==0:
    print(0,1)
else:
    print(max(arr),arr.count(max(arr)))