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:
ins, max_len, kol, pos=input(), 0, 1, [-1]
for i in range(len(ins)):
    if ins[i]=='(': pos.append(i)
    elif len(pos)>1:
        pos.pop()
        x=i-pos[-1]
        if max_len<x: max_len, kol = x, 1
        elif max_len==x: kol+=1
    else: pos[0]=i
print(max_len,kol)