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.*;
public class Longestrbs {

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