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 JAVA):

Solution:
import java.util.*;

public class Main
{
    public static void main(String[] args) {
        Scanner cin=new Scanner(System.in);
        String str=cin.next();
        int len=str.length(),i,ans=0,cnt=1;
        int dp[]=new int[1000001];
        Stack<Integer> s=new Stack<Integer>();
        while(!s.empty())
            s.pop();
        for(i=0;i<len;i++)
        {
            if(str.charAt(i)=='(')
            {
                s.push(i);
                dp[i]=0;
            }
            else
            {
                if(s.empty())
                continue;
                int temp=s.pop();
                if(temp>0)
                {
                    dp[i]=dp[temp-1]+i-temp+1;
                }
                else
                {
                    dp[i]=i-temp+1;
                }
                if(dp[i]>ans)
                {
                    ans=dp[i];
                    cnt=1;
                }
                else if(ans==dp[i])
                {
                    cnt++;
                }
            }
        }
        System.out.println(ans+" "+cnt);
        cin.close();
    }
}