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.*;
public class C0005_LongestRegularBracketSequence {
	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int numMax = 1, NumMax = 0, open = 0, close = 0, maxLength = 0;
		String str = sc.next();
		sc.close();
		
		for (int i=0; i<str.length(); i++) {
			if (str.charAt(i)=='(')
				open++;
			if (str.charAt(i)==')')
				close++;
			if (close > open) {
				close = 0;
				open = 0;
				continue;
			}
			if (open==close) {
				if (open+close == maxLength)
					numMax++;
				else if (open+close > maxLength) {
					maxLength = open+close;
					numMax = 1;
				}
			}
		}
		open = 0;
		close = 0;
		for (int i=str.length()-1; i>=0; i--) {
			if (str.charAt(i)=='(')
				open++;
			if (str.charAt(i)==')')
				close++;
			if (open > close) {
				close = 0;
				open = 0;
				continue;
			}
			if (open==close) {
				if (open+close == maxLength)
					NumMax++;
				else if (open+close > maxLength) {
					maxLength = open+close;
					NumMax = 1;
				}
			}
		}
		numMax = Math.max(numMax, NumMax);
		System.out.println(maxLength + " " + numMax);
		
		
	}
}