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.Stack;
    
    public class C {
        // Codeforces Beta Round #5
        public static void main(String[] args) throws IOException {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            char[] word = br.readLine().toCharArray();
    
            int n = word.length;
            int[] d = new int[n], c = new int[n];
            int max = 0;
            Stack<Integer> stack = new Stack<Integer>();
            for (int i = 0; i < n; i++) {
                if (word[i] == '('){
                    stack.push(i);
                    d[i] = c[i] = -1;
                }else {
                    if (stack.isEmpty())
                        d[i] = c[i] = -1;
                    else {
                        d[i] = stack.pop();
                        if (d[i] - 1 > 0 && word[d[i] - 1] == ')' && c[d[i] - 1] != -1)
                            c[i] = c[d[i] - 1];
                        else
                            c[i] = d[i];
                    }
                }
            }
    
            for (int i = 0; i < n; i++)
                if (c[i] != -1)
                    max = Math.max(max, i - c[i] + 1);
    
            if (max == 0) {
                System.out.println("0 1");
            } else {
                int cnt = 0;
                for (int i = 0; i < n; i++)
                    if (c[i] != -1)
                        if (i - c[i] + 1 == max)
                            cnt++;
    
                System.out.println(max + " " + cnt);
            }
        }
    }