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:
'''input
()))()(())
'''
s = input().lstrip(')')
max_len = 0
num_max = 1
count = 0
start_pos = {}

for i, c in enumerate(s):
    if c == '(':
        count += 1
        if count not in start_pos:
            start_pos[count] = i
    else:
        count -= 1
        if count < 0:
            count = 0
            start_pos = {}
        if count + 2 in start_pos:
            del start_pos[count + 2]
        if count + 1 in start_pos:
            l = i - start_pos[count + 1] + 1
            if l > max_len:
                max_len = l
                num_max = 1
                # print(i, start_pos[count + 1])
            elif l == max_len:
                num_max += 1

print(max_len, num_max)