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:
s = raw_input()
ans, count = 0, 1
stk = [-1]
for i in range(len(s)):
    if(s[i] == '('):
        stk.append(i)
    elif(len(stk)>1):
        stk.pop()
        temp = i - stk[-1]
        if(temp>ans):
            ans, count = temp, 1
        elif(ans == temp):
            count += 1
    else:
        stk[0] = i
print ans, count