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 = ''.join(input().strip().split())
l = len(s)
stack = []
ans = 0
sub = 0
for i in range(l):
    if stack and stack[-1][0]=='(' and s[i]==')':
        del stack[-1]
    else:
        stack.append((s[i],i))
stackl = len(stack)
if not stack:
    print(f'{l} 1')
elif l==stackl:
    print('0 1')
else:
    if stack[0][1]!=0:
        stack = [(0,-1),]+stack
    if stack[-1][1]!=l-1:
        stack = stack+[(0,l),]
    stackl = len(stack)
    for i in range(1,stackl):
        if ans == stack[i][1]-stack[i-1][1]-1:
            sub+=1
        elif ans<stack[i][1]-stack[i-1][1]-1:
            ans = stack[i][1]-stack[i-1][1]-1
            sub=1
    print(ans,sub)