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)
ss = []
c = [-1 for j in range(n)]
d = [-1 for k in range(n)]
mlen = 0
cnt = 0
f={0:1}
for i in range(n):
    if s[i] =='(':
        ss.append(i)
    if ss!=[] and s[i] ==')':
        c[i] = ss.pop()
        d[i] = c[i] 
        if s[d[i]-1]==')' and c[d[i]-1]!=-1:
            c[i] = c[d[i]-1]
        
for i in range(len(c)):
    if c[i]!=-1:
        c[i]=i-c[i]+1
mx = max(c)
if mx == -1:
    print(mlen,f[mlen])
else:
    print(mx,c.count(mx))