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:
line = raw_input()
vmax = 0;count = 1
stk = [1]
for kh in line:
    if kh == '(':
        stk.append(1)
    else:
        if len(stk) < 2:
            stk[0] = 1
        else:
            stk[-1] += 1
            stk[-2] += stk[-1]
            stk.pop()
            if stk[-1]-1 > vmax:
                vmax = stk[-1]-1
                count = 1
            elif stk[-1]-1 == vmax:
                count += 1

            
print vmax, count