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:
# Longest Regular Backet Sequencing
from collections import deque
def main():
    st = deque()
    s = input()
    S = [-1 for i in range(len(s))]
    E = [-1 for i in range(len(s))]
    F = [0 for i in range(len(s)+1)]
    F[0] = 1
    ma = 0
    for i in range(len(s)):
        if(s[i] == "("): 
            st.append(i)
        else:
            if(len(st)==0):
                S[i] = E[i] = -1
            else:
                idx = st.pop()
                S[i] = E[i] = idx
                if(idx > 0 and s[idx - 1] == ")" and S[idx - 1] >= 0):
                    E[i] = E[idx-1]
                l = i - E[i] + 1
                F[l] += 1
                ma = max(ma,l)
    print(ma,F[ma])
main()