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()
n = len(s)
dp = [0]*n
st = []
for i in range(n):
    if s[i]=='(':
        st.append(i)
    else:
        if len(st)!=0:
            he = st.pop()
            if he:
                dp[i] = dp[he-1]+i-he+1
            else:
                dp[i] = i+1
ans = 0
cnt = 1
for i in range(n):
    if dp[i]==ans:
        cnt += 1
    elif dp[i]>ans:
        ans = dp[i]
        cnt = 1
if ans==0:
    cnt = 1
print(ans,cnt)