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

inp = raw_input()
stack = [-1] 
ret = 0
count = 1
for i in range(len(inp)):  
   if inp[i] == '(': 
      stack.append(i) 
   else:
      stack.pop()
      if len(stack) != 0: 
         if i-stack[len(stack)-1]>ret:
            ret =i-stack[len(stack)-1] 
            count =1
         elif i-stack[len(stack)-1]==ret:
            count+=1
      else: 
         stack.append(i) 
print ret, count