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()
ans = dict()

stack = [-1]
res = 0
for i in range(len(s)):
    c = s[i]
    if c == ')' and stack[-1] != -1 and s[stack[-1]] == '(':
        stack.pop()
        ans[i-stack[-1]] = ans.get(i-stack[-1],0)+1
        res = max(i-stack[-1], res)
    else:
        stack.append(i)

if res not in ans.keys():
    print('0 1')
else:
    print(" ".join([str(res),str(ans[res])]))