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:
exp=input()
n=len(exp)
Pair=[-30]*(n+1)
S=[0]*n
cnt=-1
for i in range(n):
    if exp[i]=='(':
        cnt+=1
        S[cnt]=i
    elif exp[i]==')':
        if cnt>=0:
            Pair[S[cnt]]=i
            cnt-=1

Max=0
cnt=1
last=-100
i=0
while i<n:
    tmp=Pair[i]-i+1
    if tmp>0:
        i+=tmp
        tmp=max(tmp,tmp+last)
    else:
        i+=1
    last=tmp
    if tmp>Max:
        Max=tmp
        cnt=1
    elif tmp==Max:
        cnt+=1
print(Max,cnt)