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()
l=len(s)
lst=[]
arr=[]
for i in range(l):
    if(s[i]=="("):
        lst.append(i)
    else:
        if(len(lst)!=0):
            j=lst[-1]
            del lst[-1]
            m=2
            if(len(arr)!=0):
                last=arr[-1]
                if(last[0]<i and last[0]>j):
                    m=m+last[-1]
                    del arr[-1]
                    if(len(arr)!=0):
                        last = arr[-1]
                if(j-last[1]==1):
                    m=m+last[-1]
                    del arr[-1]
            arr.append([j,i,m])


if(len(arr)==0):
    print(0,1)
else:

    ct=0
    mx=-1
    for i in arr:
        if(i[-1]>mx):
            ct=1
            mx=i[-1]
        elif(i[-1]==mx):
            ct+=1
    print(mx,ct)

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