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 LRegular {

    public static void main(String[] args) {
        Scanner sc = new Scanner (System.in);
        String str =  sc.nextLine();
        sc.close();
        Stack <Integer> stk = new Stack <> ();
        stk.push(-1);
        int max = 0, freq = 1;
        for(int i = 0; i < str.length(); i++) {
            char x = str.charAt(i);
            if(x == '(')
                stk.push(i);
            else {
                stk.pop();
                if(!stk.empty()) {
                    int c = i - stk.peek();
                    if(c > max) {
                        max  = c;
                        freq = 1;
                    }
                    else if(c == max)
                        freq++;
                }
                else
                    stk.push(i);
            }
        }
        System.out.println(max + " " + freq);
    }
}