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:
def main():
    string=input()
    arr=list(string)
    maximum=0
    freq=1
    store=[]
    for x in range(len(arr)):
        if arr[x]=="(":
            if len(store)==0:
                store.append(x-1)
            store.append(x)
        else:
            if len(store)>0:
                del store[-1]
                if len(store)>0:
                    test=x-store[-1]
                    #print(store,x)
                    if test>maximum:
                        maximum=test
                        freq=1
                    elif test==maximum:
                        freq+=1
    print(maximum,freq)
            
            


main()