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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Stack;
import java.io.File;
import java.io.FileNotFoundException;
import java.util.Vector;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author zodiacLeo
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        FastPrinter out = new FastPrinter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC
    {
        private final static char OPEN = '(';

        public void solve(int testNumber, FastScanner in, FastPrinter out)
        {
            char[] s = in.next().toCharArray();
            int n = s.length;
            int[] match = new int[n];
            Stack<Integer> stack = new Stack<>();
            for (int i = 0; i < n; i++)
            {
                if (s[i] == OPEN)
                {
                    stack.push(i);
                } else
                {
                    if (!stack.isEmpty())
                    {
                        int start = stack.pop();
                        int end = i;
                        match[start] = match[end] = 1;
                    }
                }
            }
            int max = 0;
            int count = 1;
            for (int i = 0, sum = 0; i < n; i++)
            {
                if (match[i] == 0)
                {
                    sum = 0;
                } else
                {
                    sum++;
                    if (sum > max)
                    {
                        max = sum;
                        count = 1;
                    } else if (sum == max)
                    {
                        count++;
                    }
                }
            }
            out.println(max + " " + count);

        }

    }

    static class FastScanner
    {
        public BufferedReader br;
        public StringTokenizer st;

        public FastScanner(InputStream is)
        {
            br = new BufferedReader(new InputStreamReader(is));
        }

        public FastScanner(File f)
        {
            try
            {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e)
            {
                e.printStackTrace();
            }
        }

        public String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                String s = null;
                try
                {
                    s = br.readLine();
                } catch (IOException e)
                {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

    }

    static class FastPrinter extends PrintWriter
    {
        public FastPrinter(OutputStream out)
        {
            super(out);
        }

        public FastPrinter(Writer out)
        {
            super(out);
        }

    }
}