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:
from collections import defaultdict

s = input()

stack = [ ]
dct   = defaultdict(int)

n  = len(s)
d  = [-1 for i in range(n)]
c  = [-1 for i in range(n)]

i = 0
while(i<n):
    if(s[i]=='('):
        stack.append(i)
    elif(stack==[]):
        None
    else:
        d[i] = stack.pop()
        
        if(c[d[i]-1]!=-1):
            c[i] = c[d[i]-1]
        else:
            c[i] = d[i]
    i+=1

# print(d)
# print(c)
_max  = 0
count = 1

for i in range(n):
    if(c[i]!=-1):
        temp =(i-c[i]+1)
        if(temp>_max):
            _max = temp
            count =1
        elif(temp==_max):
            count+=1

print(_max,count)