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 tG{
    public static void main(String[] args) {
        Scanner in=new Scanner(System.in);
        String s=in.next();
        int length=s.length();

        int[] dp1=new int[length];
        int[] dp2=new int[length];

        for(int i=0;i<dp2.length;i++)
            dp1[i]=dp2[i]=-1;

        Stack<Integer> stack=new Stack<Integer>();

        for(int i=0;i<length;i++){
            if(s.charAt(i)=='(')
                stack.push(i);

            else if(!stack.isEmpty()){
                    dp1[i]=dp2[i]=stack.pop();
                    if(dp2[i]!=0&&s.charAt(dp2[i]-1)==')'&&dp1[dp2[i]-1]!=-1)
                        dp1[i]=dp1[dp2[i]-1];
            }
        }

        int max=Integer.MIN_VALUE,count=0;

        for(int i=0;i<dp1.length;i++){
            if(dp1[i]!=-1){
                if(i-dp1[i]+1>max) { max=i-dp1[i]+1; count=1;}
                else if(i-dp1[i]+1==max) count++;
            }
        }


        if(max==Integer.MIN_VALUE)
            System.out.println(0+" "+1);
        else
            System.out.println(max+" "+count);
    }
}