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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.*;


public class C
{
	BufferedReader in;
	PrintStream out;
	StringTokenizer tok;
	public C() throws NumberFormatException, IOException
	{
		in = new BufferedReader(new InputStreamReader(System.in));
		//in = new BufferedReader(new FileReader("in.txt"));
		out = System.out;
		run();
	}
	boolean isClosed(char c)
	{
		return c==')';
	}
	int max = 0;
	int cnt = 1;
	void run() throws NumberFormatException, IOException
	{
		char[] s = nextToken().toCharArray();
		Stack<Integer> pos = new Stack<Integer>();
		Stack<Character> stack = new Stack<Character>();
		int last = 0;
		for(int i = 0; i < s.length; i++)
		{
			if(!isClosed(s[i]))
			{
				stack.add(s[i]);
				pos.add(i);
			}
			else
			{
				if(stack.size()>0)
				{
					stack.pop();
					pos.pop();
					int k;
					if(pos.size()>0)
						k = i - pos.peek();
					else k = i-last+1;
					if(k>max)
					{
						max = k;
						cnt = 1;
					}
					else if(max==k)cnt++;
				}
				else last = i+1;
			}
		}
		out.println(max+" "+cnt);
	}
	public static void main(String[] args) throws NumberFormatException, IOException 
	{
		new C();
	}
	String nextToken() throws IOException
	{
		if(tok ==null || !tok.hasMoreTokens()) tok = new StringTokenizer(in.readLine());
		return tok.nextToken();
	}
	int nextInt() throws NumberFormatException, IOException
	{
		return Integer.parseInt(nextToken());
	}
	long nextLong() throws NumberFormatException, IOException
	{
		return Long.parseLong(nextToken());
	}
	double nextDouble() throws NumberFormatException, IOException
	{
		return Double.parseDouble(nextToken());
	}
}