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 PYTHON):

Solution:
from collections import Counter
r=raw_input().strip()
n=len(r)
dp=[0]*(n)
d=Counter()
ans=0

for i in range(1,n):
    if r[i]==')' and i-dp[i-1]-1>=0 and r[i-dp[i-1]-1]=='(':
        dp[i]=dp[i-1]+2
        if i-dp[i-1]-2>=0:
            dp[i]+=dp[i-dp[i-1]-2]
        d[dp[i]]+=1
        ans=max(ans,dp[i])
if ans==0:
    d[ans]=1

print ans,d[ans]