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

        int[] d=new int[length];
        int[] c=new int[length];

        for(int i=0;i<d.length;i++){
            c[i]=d[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()){
                    d[i]=stack.pop();
                    c[i]=d[i];
                    if(d[i]!=0&&s.charAt(d[i]-1)==')'&&c[d[i]-1]!=-1){
                        c[i]=c[d[i]-1];
                    }
                }
            }
        }

        int max=Integer.MIN_VALUE,count=0;

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

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

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