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.util.Scanner;

/**
 * Longest Regular Bracket Sequence
 * CodeForces - 5C
 *
 * @author coderWu
 */
public class Main {

    public static boolean[] visited = new boolean[1000001];

    public static int count;

    public static void main(String[] args) {

        Scanner input = new Scanner(System.in);
        String string = input.next();
        count = 0;
        char c;
        for (int i = 0, l = string.length(); i < l; ++i) {
            c = string.charAt(i);
            if (c == '(') {
                count++;
            }
            if (c == ')') {
                if (count > 0) {
                    visited[i] = true;
                }
                count--;
            }
            if (count < 0) {
                count = 0;
            }
        }
        count = 0;
        for (int i = string.length() - 1; i >= 0; --i) {
            c = string.charAt(i);
            if (c == ')') {
                count++;
            }
            if (c == '(') {
                if (count > 0) {
                    visited[i] = true;
                }
                count--;
            }
            if (count < 0) {
                count = 0;
            }
        }
        count = 0;
        //最长长度
        int max = 0;
        //数量
        int number = 0;
        for (int i = 0, l = string.length(); i < l; ++i) {
            if (visited[i]) {
                count++;
            } else {
                count = 0;
            }
            if (count > max) {
                max = count;
                number = 1;
            } else if (count == max) {
                number++;
            }
        }
        if (max == 0) {
            number = 1;
        }
        System.out.println(max + " " + number);
    }

}