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:
x = input()
ex=[-1]*len(x);m=0;
f=[0]*len(x);ans1=-1;s=[]
for index,i in enumerate(x):
    if i=='(':
        s.append(index)     
    else:
        if len(s) > 0 :
            p = s.pop()
            ex[index] = p
            if  p > 0  and   ex[p-1] > -1 :
                ex[index] = ex[p-1]  
            f[index-ex[index]]+=1
            ans1 = max(ans1,index-ex[index])

print(ans1+1,max(1,f[ans1]))