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()
s1=0
s2=0
ans=[]
st=[]
c=0
for i in s:
    if(i=='('):
        s1+=1
        st.append(i)
    else:
        if(s1>0):
            c1=0
            while(st[-1]!='('):
                k=st.pop()
                c1+=k
            c1+=2
            st.pop()
            s1-=1
            st.append(c1)
        else:
            st.append(')')


ans=[]
c=0
kk=1
for i in st:
    if(i==')' or  i=='('):
        ans.append(c)
        c=0
    else:
        c+=i
        kk=0
ans.append(c)
if(kk==1):
    print(0,1)
else:
    print(max(ans),ans.count(max(ans)))