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.ArrayList;

public class FiveC {
    public static void main(String[] args) throws IOException {
        BufferedReader readInput = new BufferedReader(new InputStreamReader(System.in));
        String sequence = readInput.readLine();
        ArrayList<Integer> parens = new ArrayList<Integer>();
        parens.add(-1);

        int len = 0;
        int numSubStrings = 0;

        for(int i = 0; i < sequence.length(); i++) {

            char currentParen = sequence.charAt(i);
            if(currentParen == '(') {
                parens.add(i);
            }
            else {
                if(parens.size() <= 1) {
                    parens.set(0, i);
                }
                else {
                    parens.remove(parens.size()-1);
                    int t = i - parens.get(parens.size() - 1);
                    if(t > len) {
                        len = t;
                        numSubStrings = 1;
                    }
                    else if(t == len) {
                        numSubStrings += 1;
                    }
                }
            }
        }
        System.out.println(len == 0 ? "0 1" : len + " " + numSubStrings);
    }
}