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:
s = input()
ans, current = 0, 0
res = {}
stack = []
left = 0
for i in range(len(s)):
    if s[i] == '(':
        stack.append(-1)
    else:
        flag = False
        while len(stack) > 0 and stack[-1] != -2:
            if stack[-1] == -1:
                stack.pop()
                current += 2
                flag = True
                break
            else:
                current += stack[-1]
                stack.pop()
        stack.append(current)
        current = 0
        if not flag:
            stack.append(-2)

current = 0
while len(stack) > 0:
    if stack[-1] > 0:
        current += stack[-1]
    stack.pop()
    if len(stack) == 0 or stack[-1] < 0:
        if current in res:
            res[current] += 1
        else:
            res[current] = 1
        ans = max(ans, current)
        current = 0


if ans == 0:
    print('0 1')
else:
    print('%d %d' %(ans, res[ans]))