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=[-1]*len(s)
l=[0]*len(s)
q=[]
for i in range(len(s)):
    if s[i]=='(':q.append(i)
    elif q:
        x=q.pop()
        a[i]=x
        l[i]+=i-x+1
        if x>0:l[i]+=l[x-1]
m,c=0,1
for i in range(len(s)):
    if l[i]>m:m,c=l[i],1
    elif l[i]==m:c+=1
if m==0:c=1
print('%i %i' %(m,c))