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:
s = input()
m = [-1]*len(s)
e = [-1]*len(s)
f = [0]*len(s)
stack = []
l = 0
for i in range(len(s)):
    if s[i] == "(":
        stack.append(i)
    else:
        if len(stack) == 0:
            m[i] = -1
        else:
            p = stack.pop()
            m[i] = p
            if p == 0:
                e[i] = m[i]
            else:
                if (s[p-1] == ")") and (m[p-1]>=0):
                    e[i] = e[p-1]
                else:
                    e[i] = m[i]
            if (e[i] >= 0):
                c = (i-e[i])+1
                f[c-1] += 1
for k in range(len(f)):
    if f[k] > 0:
        l = k
if l > 0:
    print(l+1,f[l])
else:
    print(l,1)