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.io.*;
import java.util.Stack;
public class Main{
    public static void main(String[] args)throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int[] d=new int[1000000];
        int[] c=new int[1000000];
        for(int i=0;i<1000000;i++){
            c[i]=-1;
        }
        char[] ch=br.readLine().trim().toCharArray();
        Stack<Integer> stack=new Stack<>();
        for(int i=0;i<ch.length;i++){
            if(ch[i]=='('){
                stack.push(i);
            }
            else{
                if(stack.isEmpty()){
                    d[i]=-1;c[i]=-1;
                }
                else{
                    int td=stack.pop();
                    int tc=td;
                    if((td-1)>=0 && ch[td-1]==')' && c[td-1]!=-1){
                        c[i]=c[td-1];
                    }
                    else{
                        c[i]=td;
                    }
                    d[i]=td;
                }
            }
        }
        int max_len=0, count=1;
        for(int i=0;i<1000000;i++){
            if(c[i]>=0){
                int len=i-c[i]+1;
                if(len>max_len){
                    max_len=len;
                    count=1;
                }
                else if(len==max_len){
                    count++;
                }
            }
        }
        System.out.println(max_len+" "+count);
    }
}