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()
st = []
a = 0 
b = 0
c = 0
m = 0
n = 0
#print(s[82:])
for i in range(len(s)):
    if s[i]=='(':
        st.append(i)
    elif s[i]==')':
        if st:
            st.pop()
            if st == []:
                if c!=b:
                    a = c
                b = i + 1
                c = i + 1
                if i - a + 1 > m:
                    m = i - a + 1
                    n = 1
                elif i - a + 1 == m:
                    n+=1
        else:
            c = i + 1
    #print(a,b)
z = len(s)
while st :
    c = st.pop()
    #print(c)
    if z - c - 1 > m:
        m = z - c - 1
        n = 1
    elif z - c - 1 == m:
        n+=1
    z = c
if m == 0:
    n = 1
print(m,n)