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()
stack = [-1]
mx = 0
cnt = 1
for i in range(len(s)):
    elem = s[i]
    if elem=='(':
        stack.append(i)
    else:
        stack.append(i)
        if len(stack) >= 3:
            if s[stack[-2]] == '(' and s[stack[-1]] ==')':
                stack.pop()
                stack.pop()
                curr = i-stack[-1]
                if curr > mx:
                    mx = curr
                    cnt = 1
                elif curr == mx:
                    cnt += 1
print(mx,cnt)