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.IOException;
import java.util.ArrayList;
import java.util.Stack;

public class Main {

    public void solve() throws IOException {

        ArrayList<Integer> arr = new ArrayList<Integer>();
        Stack<Integer> braces = new Stack<Integer>();
        int i;
        int count = 0;
        int max = 0;
        int maxCount = 1;
        while ((i = System.in.read()) != -1) {
            if (i == '(') {
                braces.push(count);
                arr.add(0);
            }
            if (i == ')') {
                if (!braces.isEmpty()) {
                    int open = braces.pop();
                    int cur = count + 1 - open;
                    if (open > 0) {
                        cur += arr.get(open - 1);
                    }
                    arr.add(cur);
                    if (cur == max) {
                        maxCount++;
                    }
                    if (cur > max) {
                        max = cur;
                        maxCount = 1;
                    }
                }
                else {
                    arr.add(0);
                }
            }
            count++;
        }
        System.out.println(max + " " + maxCount);
    }

    public void run() throws IOException {
        solve();
    }

    public static void main(String[] arg) throws IOException {
        new Main().run();
    }
}