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:
import sys

s = sys.stdin.readline().rstrip()

balance = 0
balanceRecord = {0: -1}
minBalance = 0
maxLen = 0
maxCount = 1

for i in range(len(s)):
    if s[i] == '(':
        balance += 1
    else:
        balance -= 1
    if balance < minBalance:
        minBalance = balance
        balanceRecord = {}
    
    if balance in balanceRecord:
        balanceRecord.pop(balance+1)
        newLen = i - balanceRecord[balance]
        if newLen > maxLen:
            maxLen = newLen
            maxCount = 1
        elif newLen == maxLen:
            maxCount += 1
    else:
        balanceRecord[balance] = i

print(str(maxLen) + ' ' + str(maxCount))