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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Stack;

public class KnapSack
{
    public static void main(String[]args) throws IOException 
    {
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    	char[] arr = br.readLine().toCharArray();
    	int[] ans = new int[1+(int)1e6];
    	Stack<String> stak = new Stack<String>();
    	int max = 0;
    	for (int i = 0; i < arr.length; i++) {
    		if(arr[i]=='(')
    		{
    			stak.push(arr[i]+"");
    		}
    		else
    		{
    			int cur = 2;
    			while(!stak.isEmpty() && !stak.peek().equals("("))
    				cur += Integer.parseInt(stak.pop());
    			if(stak.isEmpty())
    			{
    				continue;
    			}
    			stak.pop();
    			while(!stak.isEmpty() && !stak.peek().equals("("))
    				cur += Integer.parseInt(stak.pop());
    			stak.push(cur+"");
    			max = Math.max(max, cur);
    			ans[cur]++;
    		}
		}
    	for(int i = ans.length-1;i>=0;i--)
    	{
    		if(ans[i]>0)
    		{
    			System.out.println(i+" "+ans[i]);
    			return;
    		}
    	}
    	System.out.println("0 1");
    }
}