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.*;
import java.io.*;

public class Main {
    
    static final int MAXN = 1000010;
    int[] sta = new int[MAXN];
    
    public void run() {
        //String str = cin.next();
        char[] s = cin.next().toCharArray();
        int top = 0;
        int maxLen = 0, num = 1;
        for (int i = 0; i < s.length; ++i) {
            if (s[i] == '(') sta[++top] = 0;
            else if (s[i] == ')') {
                if (top != 0) {
                    sta[top-1] += sta[top] + 2;
                    --top;
                } else {
                    if (sta[top] > maxLen) {
                        maxLen = sta[top];
                        num = 1;
                    } else if (sta[top] != 0 && sta[top] == maxLen) {
                        ++num;
                    }
                    sta[top] = 0;
                }
            }
        }
        while (top != -1) {
            if (sta[top] > maxLen) {
                maxLen = sta[top];
                num = 1;
            } else if (sta[top] != 0 && sta[top] == maxLen) {
                ++num;
            }
            --top;
        }
        out.println(maxLen + " " + num);
    }

    public static void main(String[] args) throws IOException {
        Main sloved = new Main();
        sloved.run();
        sloved.out.close();
    }

    Scanner cin = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
}