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.*;
import java.math.*;

public class Solution implements Runnable
{
	Scanner scanner;
	PrintWriter pw;

	public void solve() throws Exception
	{
		String t = scanner.nextLine();
		int max = 0;
		int cnt = 1;

		int[] s = new int[t.length() + 1];
		s[0] = 0;

		int[] l = new int[t.length()];
		Arrays.fill(l, 0);

		for (int i = 0; i < t.length(); ++i)
		{
			if (t.charAt(i) == '(')
			{
				s[++s[0]] = i;
			}
			else if (s[0] > 0)
			{
				int j = s[s[0]];
				int len = i - j + 1;
				if (j > 0 && l[j - 1] > 0)
				{
					len += l[j - 1];
				}
				if (len > max)
				{
					max = len;
					cnt = 1;
				}
				else if (len == max)
				{
					++cnt;
				}
				l[i] = len;
                --s[0];
			}
		}

		pw.println(max + " " + cnt);
	}

	public static void main(String[] args) throws Exception
	{
		new Thread(new Solution()).start();
	}

	public void run()
	{
		try
		{
//			scanner = new Scanner(new BufferedReader(new FileReader("input.txt")));
			scanner = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
//			pw = new PrintWriter(new File("output.txt"));
			pw = new PrintWriter(new OutputStreamWriter(System.out));

			solve();

			pw.close();
		}
		catch(Exception e)
		{
			e.printStackTrace();
			pw.close();
			System.exit(1);
		}
	}
}