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.StringTokenizer;

public class LongestRegularBracketSequence {

	public static void main(String[] args) {
		String s = in.next();
		int n = s.length();

		int[] dp = new int[n];
		dp[0] = 0;
		int ans = 0;
		for (int i = 1; i < n; i++) {
			if (s.charAt(i) == '(') {
				dp[i] = 0;
				continue;
			}

			if (s.charAt(i - 1) == '(') {
				dp[i] = 2;
				if (i - 2 >= 0)
					dp[i] += dp[i - 2];
			} else {
				int p = i - 1 - dp[i - 1];
				if (p >= 0 && s.charAt(p) == '(') {
					dp[i] = dp[i - 1] + 2;
					if (p - 1 >= 0)
						dp[i] += dp[p - 1];
				}
			}
			ans = Math.max(ans, dp[i]);
		}
		if (ans == 0) {
			System.out.println("0 1");
			return;
		}
		int ans2 = 0;
		for (int i = 0; i < n; i++) {
			if (dp[i] == ans) {
				ans2++;
			}
		}
		System.out.println(ans + " " + ans2);

	}

	public static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

	}

	static MyScanner in = new MyScanner();

}