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:
inp = list(raw_input())

stack = []

maxLen = 0
maxCount = 1

last = -1
for i in xrange(0, len(inp)):
    c = inp[i]
    if c == ')':
        if stack:
            stack.pop()
            if stack:
                l = i - stack[-1]
            else:
                l = i - last
            if maxLen < l:
                maxLen = l
                maxCount = 1
            elif maxLen == l:
                maxCount += 1
        else:
            last = i
    elif c == '(':
        stack.append(i)

print "%s %s" % (maxLen, maxCount)