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 deque
def solve(st):
    stack = deque()
    mx = 0
    for i in range(len(st)):
        if st[i] == "(":
            stack.append(i)
        else:
            if len(stack) == 0:
                S[i] = -1
                E[i] = -1
            else:
                ri = stack.pop()
                S[i] = ri
                E[i] = ri
                if ri > 0 and st[ri-1] == ")" and S[ri-1] >= 0:
                    E[i] = E[ri-1]
                l = i-E[i]+1
                F[l] += 1
                mx = max(mx, l)
    F[0] = 1
    print(mx, F[mx])


max_l = 1000001
F = [0 for i in range(max_l)]
S = [0 for i in range(max_l)]
E = [0 for i in range(max_l)]
s = input()
solve(s)