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:
def longestBracketSequence(S):
    stack = []
    pairIdxs = [-1 for _ in range(len(S))]
    extends = [-1 for _ in range(len(S))]
    frequence = [0 for _ in range(len(S)+1)]

    l = 0
    for i in range(len(S)):
        c = S[i]
        if c == "(":
            stack.append(i)
        else:
            if len(stack) > 0:
                idx = stack.pop()
                pairIdxs[i] = idx
                extends[i] = idx
                if idx > 0 and S[idx-1] == ")" and extends[idx-1] >= 0:
                    extends[i] = extends[idx-1]
                j = i-extends[i]+1
                frequence[j] += 1
                l = max(l, j)
    frequence[0] = 1
    print(l, frequence[l])


S = input()
longestBracketSequence(S)