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:
st=input()
b=[]
for j in st:
    b.append(j)
n=len(b)
arr=[]
dp=[0]*(n)
j=0
while(j<n):
    if b[j]==")":
        if arr==[]:
            pass
        else:
            if arr[-1][0]==b[j]:
                pass
            else:
                p=arr.pop()
                dp[j] = j - p[1] + 1
                if (p[1]-1)>=0 and b[p[1]-1]==")":
                    dp[j]+=dp[p[1]-1]


    else:
        arr.append([b[j],j])
    j+=1

p=dp.count(max(dp))
if max(dp)==0:
    print(0, 1)
else:
    print(max(dp), p)