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()
a=[]
n=len(s)
c=[-1 for i in range(n)]
d=[-1 for i in range(n)]
for i in range(len(s)):
    if s[i]=='(':
        a.append(i)
    else:
        if len(a)>0:
            d[i]=a[-1]
            c[i]=d[i]
            a.pop()
            if d[i]-1>-1:
                if c[d[i]-1] != -1:
                    c[i]=c[d[i]-1]
length=0
ans=0
for i in range(n):
    if c[i] is not -1:
        if length<(i-c[i]+1):
            length=(i-c[i]+1)
            ans =1
        elif length==(i-c[i]+1):
            ans += 1
if length==0:
    print(0,1)
else:
    print(length,ans)