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 defaultdict
t, r, p = input(), {'(': 1, ')': -1}, defaultdict(int)
l, k, s, x = 0, 1, 0, -1
for i, c in enumerate(t, 1):
    y = r[c]
    if x < 0:
        if p[s]:
            d = i - p[s]
            if d >= l:
                if d > l: l, k = d, 1
                else: k += 1
            if y < 0: p[s] = 0
        elif y > 0: p[s] = i
    elif y > 0: p[s] = i
    x = y
    s += y
if x < 0 and p[s]:
    d = len(t) + 1 - p[s]
    if d >= l:
        if d > l: l, k = d, 1
        else: k += 1
print(l, k)