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

seq = input()

ds = {}

cur = 0

ds[0] = -1

high = 0
count = 0

for ind,b in enumerate(seq):
    if b == '(':
        cur += 1
    else:
        del ds[cur]
        cur -= 1
    #print(cur)
    if cur in ds:
        if ind-ds[cur] > high:
            high = ind-ds[cur]
            count = 1
        elif ind-ds[cur] == high:
            count += 1
    else:
        ds[cur] = ind
#print(ds)

if high == 0:
    print(0,1)
else:
    print(high,count)