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.*;


public class Driver {

    public static void main(String[] args) throws IOException {
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        char[] sequence = br.readLine().toCharArray();

        int countX = 0;
        int countY = 0;
        int idx = -1;
        int longestSequence = 0;
        int longestIdx = 1;


        for (int i = 0; i < sequence.length; i++) {
            if (sequence[i] == '(') {
                countX++;
            }
            else {
                countY++;
            }

            if (countY == countX) {
                if (i - idx == longestSequence) {
                    longestIdx++;
                }
                if (i - idx > longestSequence) {
                    longestSequence = i - idx;
                    longestIdx = 1;
                }
            }
            else if (countY > countX) {
                idx = i;
                countX = 0;
                countY = 0;
            }
        }


        if (countY < countX) {
            idx = sequence.length;
            countX = 0;
            countY = 0;

            for (int i = sequence.length-1; i >= 0; i--) {
                if (sequence[i] == ')') {
                    countX++;
                }
                else {
                    countY++;
                }

                if (countY == countX) {
                    if (idx - i == longestSequence) {
                        longestIdx++;
                    }
                    if (idx - i > longestSequence) {
                        longestSequence = idx - i;
                        longestIdx = 1;
                    }
                }
                else if (countY > countX) {
                    idx = i;
                    countX = 0;
                    countY = 0;
                }
            }
        }

        if (longestSequence == 0) {
            System.out.println("0 1");
        }
        else {
            System.out.println(longestSequence + " " + longestIdx );
        }
    }
}