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:
import sys
br=raw_input()
n=len(br)
a=[0]*(n+1);b=[0]*(n+1);cnt=0;b[0]=1;a[cnt]=-1;ma=0
for i in xrange(0,n):
    if br[i]=='(':
        cnt=cnt+1
        a[cnt]=i
    else:
        if cnt > 0: 
            cnt=cnt-1
            #print cnt,i-a[cnt]
            b[i-a[cnt]]=b[i-a[cnt]]+1
            ma=max(i-a[cnt],ma)
        else:
            a[0]=i
    #print i,br[i],cnt,a[cnt],i-a[cnt],b[i-a[cnt]]
print ma, b[ma]