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.*;
import java.io.*;
public class EdB {

	public static void main(String[] args) throws Exception{
		int num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
//	 		String input1 = bf.readLine().trim();
//	 		String input2 = bf.readLine().trim();
	 	char[] input = bf.readLine().trim().toCharArray();
	 	int[] d = new int[input.length];
	 	int[] c = new int[input.length];
 		Stack<Integer> stack = new Stack<Integer>();
 		for(int i = 0;i<input.length;i++){
 			if (input[i] == '('){
 				c[i] = -1;
 				d[i] = -1;
 				stack.push(i);
 			}
 			else{
 				if (stack.size() != 0){
 					int index = stack.pop();
 					d[i] = index;
 					c[i] = index;
 					if (d[i]-1 >= 0 && input[d[i]-1] == ')' && c[d[i]-1] != -1)
 						c[i] = c[d[i]-1];
 					
 				}
 				else{
 					d[i] = -1;
 					c[i] = -1;
 				}
 			}
 		}
 		int max = 0;
 		int maxcount = 0;
 		for(int i = 0;i<input.length;i++){
 			if (c[i]!= -1){
 				if (i-c[i]+1 > max){
 					max = i-c[i]+1;
 					maxcount = 1;
 				}
 				else if (i-c[i]+1 == max)
 					maxcount++;
 			}
 		}
 		if (max == 0)
 			out.println("0 1");
 		else
 			out.println(max + " " + maxcount);
	 		
 		out.close();
 		
 		
 		
 	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is