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:
# -*-coding:utf-8 -*-
line=input()
s=[-1]
max_len=0
max_num=1
l=len(line)
for i in range(l):
    if line[i]=='(':
        s.append(i)
    elif len(s)>1:
        s.pop()
        n=i-s[-1]
        if max_len<n:
            max_len,max_num=n,1
        elif max_len==n:
            max_num+=1
    else:
        s[0]=i
print(str(max_len)+' '+str(max_num))