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:
s = input()
st = list()
c  = 0
x  = 0
max = 0
st.append(-1)
for i in range(len(s)):
    if s[i] == '(':
        st.append(i)
    else:
        st.pop()
        if st :
            c = i-st[-1]
            if c > max:
                max = c
                x   = 1
            elif c >= 1 and c == max:
                x+=1
        else:
            st.append(i)
if x >= 1:
    print(str(max)+' '+ str(x))
else:
    print('0 1')