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 PYTHON):

Solution:
exp=str(raw_input())
st=[-1]
ans=[]
for i in range(0,len(exp)):
    if exp[i]=="(":
        st.append(i)
    else:
        val=st.pop()
        if len(st)==0:
            st.append(i)
        else:
            ans.append(i-st[-1])
if len(ans)==0:
    print 0,1 
else:
    print max(ans) ,ans.count(max(ans))