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()

d = [-1] * len(s)
e = [-1] * len(s)

stack = []
for i, c in enumerate(s):
    if(c == "("):
        stack.append(i)
    elif(stack):
        f = stack.pop()
        d[i] = f
        e[i] = f
        if(e[f - 1] != -1):
            e[i] = e[f - 1]

best = 0
count = 0
for i in range(len(s)):
    if(e[i] != -1):
        if(best < i - e[i] + 1):
            best = i - e[i] + 1
            count = 0
        if(best == i - e[i] + 1):
            count += 1

if(best == 0):
    print("0 1")
else:
    print(best, count)