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()
n=len(s)
d={}
d[0]=-1
d[1]=0
v=1
st=[]
m=0
c=1
st.append(s[0])
for i in range(1,n):
    if (s[i]==')') and (v>0) and (st[v-1]=='('):
        st.pop()
        v-=1
        if m==(i-d[v]):
            c+=1        
        elif m<(i-d[v]):
            m=i-d[v]
            c=1
        #d[v]=i
    else:
        v+=1
        d[v]=i
        st.append(s[i])
    #print(v,m,c)
    #input()
print(m,c)