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 javax.sound.midi.SysexMessage;
import java.io.*;
import java.util.*;

public class Main {
    static class InputReader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        static void init(InputStream input) {
            reader = new BufferedReader(new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
            return tokenizer.nextToken();
        }

        static int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        static String nextLine() throws IOException {
            return reader.readLine();
        }
    }

    public static void main(String[] args) throws IOException {
        String whichInputToUse = "System.in";
//        String whichInputToUse = "input.txt";
        InputReader.init("System.in".equals(whichInputToUse) ? System.in : new FileInputStream(whichInputToUse));
        String parenthesisSequence = InputReader.nextLine();
        int length = parenthesisSequence.length();
        int longestRegularSequence = 0;
        int numberOfRegularSequences = 0;
        int[] parenPairs = new int[length];

        for (int i = length - 2; i >= 0; i--) {
            if (parenthesisSequence.charAt(i) == '(') {
                int previousLength = i + parenPairs[i + 1] + 1;
                if (previousLength < length) {
                    if (parenthesisSequence.charAt(previousLength) == ')') {
                        parenPairs[i] = parenPairs[i + 1] + 2;
                        if (previousLength + 1 < length) {
                            parenPairs[i] += parenPairs[previousLength + 1];
                        }
                    }
                }
            }
        }

        for (int i : parenPairs) {
            if (i > longestRegularSequence) {
                longestRegularSequence = i;
                numberOfRegularSequences = 1;
            } else if (i == longestRegularSequence) {
                numberOfRegularSequences++;
            }
        }

        if (longestRegularSequence == 0) {
            longestRegularSequence = 0;
            numberOfRegularSequences = 1;
        }

        System.out.println(longestRegularSequence + " " + numberOfRegularSequences);
    }
}