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:
l = input()
m = len(l)
max_d = 0
d = [-1]*m
c = [-1]*m
dis = [-1]*m
times = 1
stack = []
for i in range(m):
    if l[i] is '(':
        stack.append(i)
    else:
        if stack:
            d[i] = stack.pop()
            c[i] = d[i]
            dis[i] = i-c[i]+1
            if d[d[i]-1] != -1:
                c[i] = c[d[i]-1]
                dis[i] = i-c[i]+1
            if dis[i]>max_d:
                max_d = dis[i]
                times = 1
            elif dis[i]==max_d:
                times += 1
print(max_d,times)