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 Counter as cr
st=input()
s=[]
ans=[0,0]
for i in st:
    if i=='(':
        ans.append(0)
        s.append(i)
    else:
        if len(s)!=0:
            x=ans.pop()
            ans.append(x+2)
            s.pop()
            x=ans.pop()
            y=ans.pop()
            ans.append(x+y)
        else:
            ans.append(0)
m=cr(ans)
c=max(ans)
if c==0:
    print("0 1")
else:
    print(c,m[c])
# (()())()(())()()())())()((()(()(())()()())((()(())()(()()()()))()(())()(((()())()(()((())()(())(()))