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 {
	
	private static BufferedReader br;
	
	private static void initReader() {
		br = new BufferedReader(new InputStreamReader(System.in));
	}

	private static void printPairs(int [] pairs) {
		for(int i=0;i<pairs.length; i++)
			System.out.print(i+ " ");
		System.out.println();
		for(int i=0;i<pairs.length; i++)
			System.out.print(pairs[i]+ " ");
		System.out.println();
	}
	
	private static void printMaxAndCount(int [] pairs) {
		int count = 0;
		int max = -1;
		int length = 0;
		int currLength;
		for(int i=0;i<pairs.length; i++) {
			if(pairs[i] != -1) {
				currLength = Math.abs(pairs[i] - i + 1);
				length += currLength;
				//System.out.println(i + " to " +pairs[i]+" : "+length);
				if(length > max) {
					max = length;
					count = 1;
				}
				else if(length == max) {
					count ++;
				}
				i+=(currLength-1);
			}
			else
				length = 0;
		}
		
		if(max == -1)
			System.out.println("0 1");
		else
			System.out.println(max+" "+ count);
	}
	
	public static void main(String[] args) throws IOException {
		initReader();

		//while(true) {
			String inp = br.readLine();
			Stack<Integer> stack = new Stack<Integer>();
			int [] pairs = new int[inp.length()];
			int pair;
			
			for(int i=0; i<inp.length(); i++) {
				if(inp.charAt(i) == '(')
					stack.push(i);
				else {
					// stray ')'
					if(stack.isEmpty())
						pairs[i] = -1;
					else {
						pair = stack.pop();
						pairs[pair] = i;
						pairs[i] = pair;
					}
				}
			}
			if(!stack.isEmpty()) {
				for(Integer stray: stack)
					pairs[stray] = -1;
			}
			
			//printPairs(pairs);
			printMaxAndCount(pairs);
		//}
	}

}