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:
# http://codeforces.com/problemset/problem/5/C


from sys import stdin


best = 0
cnt = 1
s = stdin.readline().strip()
d = [-1] * len(s)
c = [-1] * len(s)
stack = []

for i, e in enumerate(s):
    if e == ')':
        if len(stack) == 0:
            c[i] = -1
            d[i] = -1
        else:
            d[i] = stack[-1]
            c[i] = d[i]
            pos = d[i] - 1
            if pos >= 0 and c[pos] != -1 and s[pos] == ')':
                c[i] = c[d[i] - 1]
            stack.pop()
            rr = i - c[i] + 1
            if rr == best:
                cnt += 1
            if rr > best:
                cnt = 1
                best = rr
    else:
        stack.append(i)

print str(best) + " " + str(cnt)