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.io.PrintWriter;
import java.util.*;


public class LongestRegularBracketSequence {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		String str = br.readLine();
		
		int index = 0;
		int currlongest = 0;
		int maxlongest = 0;
		int longestCount = 1;
		int balance = 0;
		int start = 0;
		while(index<str.length()){
			if(str.charAt(index)=='(')
				balance++;
			else //if (str.charAt(index)==')')
				balance--;
			
			if(balance==0){
				currlongest = index - start +1;
				if(currlongest>maxlongest){
					maxlongest = currlongest;
					longestCount = 1;
				}
				else if(currlongest == maxlongest){
					longestCount++;
				}
			}
			else if(balance<0){
				start = index +1;
				balance = 0;
			}
			index++;
		}
		if(balance>0){
			index = str.length() - 1;
			currlongest = 0;
			balance = 0;
			start = index;
			while(index>=0){
				if(str.charAt(index)==')')
					balance++;
				else //if (str.charAt(index)==')')
					balance--;
				
				if(balance==0){
					currlongest = start - index+1;
					if(currlongest>maxlongest){
						maxlongest = currlongest;
						longestCount = 1;
					}
					else if(currlongest == maxlongest){
						longestCount++;
					}
				}
				else if(balance<0){
					start = index -1;
					balance = 0;
				}
				index--;
			}
		}
		pw.println(maxlongest+" "+ longestCount);
		pw.flush();
	}
}