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()
# s = "()(())()"
st = []
ans = []

for i,c in enumerate(s):
    if c=="(":
        st.append(i)
    elif st:
        q = st.pop()
        cur = [q,i] 
        while True:
            if ans:
                x,y = ans[-1]
                if x==cur[0]+1 and y== cur[1]-1:
                    ans.pop()
                elif y==cur[0]-1:
                    ans.pop()
                    cur[0]=x
                else:
                    break
            else:
                break
        ans.append(cur)
mx = 0
mc = 1
for x,y in ans:
    if y-x+1>mx:
        mx = y-x+1
        mc = 1
    elif y-x+1==mx:
        mc+=1
print(mx,mc)