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 PYTHON):

Solution:
s='('+raw_input()+')'
n=len(s)

def f(m):
    pred=[-1]*(2*n)
    x=0
    ln=0
    c=0
    for pos in xrange(n):
        if pred[x]!=-1:
            v=pos-pred[x]
            ln=max(ln,v)
            if v==m: c+=1
        if s[pos]=='(':
            pred[x+1]=pos+1
            x+=1
        else:
            pred[x] = -1
            x-=1
            if pred[x]==-1: pred[x]=pos+1
    return (ln,c if m else 1)

(ln,num)=f(f(0)[0])
print ln,num