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)
sa=[-1]*n
f=[0]*(n+1)
ex=[-1]*n
arr=[]
for i in range(n):
    if s[i]=='(':
        arr.append(i)
    else:
        if len(arr)!=0:
            p=arr.pop()
            sa[i]=p
            ex[i]=p
            if s[p-1]==')' and sa[p-1]!=-1:
                ex[i]=ex[p-1]
            d=i-ex[i]+1
            f[d]+=1
flag=False
for i in range(len(f)-1,-1,-1):
    if f[i]!=0:
        print(i,f[i])
        flag=True
        break
if flag==False:
    print(0,1)