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 PYTHON):

Solution:
from collections import defaultdict
def ans (s):
    balance, maxlen, curlen = 0, 0, 0
    cnt = defaultdict (int)
    for i in s:
        balance += 1 if i == '(' else -1
        curlen += balance >= 0
        if balance < 0:
            curlen, balance = 0, 0
        if balance == 0:
            maxlen = max (curlen, maxlen)
            cnt[curlen] += 1
            
    cnt[0] = 1
    return maxlen, cnt[maxlen]
S = raw_input ()
print ' '.join (map (str, max (ans (S), ans (S[::-1].replace ('(', '1').replace (')', '2').replace ('1', ')').replace ('2', '(')))))