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:
#!/usr/bin/env python
s = raw_input()
f = [0]
for i in range(1, len(s)):
    if s[i] == '(':
        k = 0
    else:
        if s[i-1] == '(':
            if i == 1:
                k = 2
            else:
                k = f[i-2]+2
        else:
            if (f[i-1] == i) or s[i-1-f[i-1]] == ')':
                k = 0
            else:
                if i-1-f[i-1] == 0:
                    k = f[i-1] + 2
                else:
                    k = f[i-2-f[i-1]] + f[i-1] + 2
    f.append(k)
ans = max(f)
if ans == 0:
    print 0, 1
else:
    print ans, f.count(ans)