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 LongestRegularBracketSequence {
	private static Stack<Integer> stack;
	private static int[] track;
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		stack = new Stack<Integer>();
		String line = br.readLine();
		track = new int[line.length()];
		int globalAns = 0;
		int tempAns = 0;
		int open = 0;
		int count = 0;
		for(int i = 0; i < line.length(); i++) {
			track[i] = -1;
		}
		for(int i = 0; i < line.length(); i++) {
			if(line.charAt(i) == '(') {
				open++;
				stack.add(i);
			} else {
				open--;
				if(open < 0) {
					open = 0;
					tempAns = 0;
				} else {
					int pos = stack.pop();
					if(pos > 0 && track[pos-1] != -1) {
						pos = track[pos-1];
					}
					tempAns = i - pos + 1;
					track[i] = pos;
					
				}
				if(globalAns == tempAns)count++;
				else if(globalAns < tempAns) {
					count = 1;
					globalAns = tempAns;
				}
			}
			//System.out.println(globalAns +  " " + tempAns + " " + count + " " + i);
		}
		if(globalAns == 0)count = 1;
		System.out.println(globalAns + " " + count);
	}
}