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:
inp,kol,max_len,pos=input(),1,0,[-1];
for i in range(len(inp)): 
  if(inp[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);
#the problem requires you to find the longest real bracket sequence and the number ofsuch other sequences that might exist WITH THE SAME MAXIMUM LENGHT.the lenght of the no of brackes bn any two points is the difference bn the last index and the one before the 1st index.