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:
# cook your dish here
s = input()

st = []
p = len(s)
for i in range(p):
    if st != [] and s[i] == ')' and s[st[-1]] == '(':
        st.pop()
    else:
        st.append(i)
        
if len(st) == p:
    print("0 1")
else:
    st.append(p)
    d = [0]*(1000000 + 7)
    k = -1
    ma = 0
    for i in st:
        if i - k - 1 >= ma:
            ma  = i - k -1
            d[i-k-1] += 1
        k = i
    print(ma,d[ma])