Simon has an array a1, a2, ..., an, consisting of n positive integers. Today Simon asked you to find a pair of integers l, r (1 ≤ l ≤ r ≤ n), such that the following conditions hold:

  1. there is integer j (l ≤ j ≤ r), such that all integers al, al + 1, ..., ar are divisible by aj; 
  2. value r - l takes the maximum value among all pairs for which condition 1 is true; 



Help Simon, find the required pair of numbers (l, r). If there are multiple required pairs find all of them.

Input

The first line contains integer n (1 ≤ n ≤ 3·105).

The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 106).

Output

Print two integers in the first line — the number of required pairs and the maximum value of r - l. On the following line print all l values from optimal pairs in increasing order.

Examples

Input

5
4 6 9 3 6


Output

1 3
2 


Input

5
1 3 5 7 9


Output

1 4
1 


Input

5
2 3 5 7 11


Output

5 0
1 2 3 4 5 

Note

In the first sample the pair of numbers is right, as numbers 6, 9, 3 are divisible by 3.

In the second sample all numbers are divisible by number 1.

In the third sample all numbers are prime, so conditions 1 and 2 are true only for pairs of numbers (1, 1), (2, 2), (3, 3), (4, 4), (5, 5).
import java.io.BufferedReader;
import java.io.IOError;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class CF359D {

	FastIO scan = new FastIO();
	final static int INF = 100000007;

	void run() {
		int n = scan.nextInt();
		int[] a = new int[n + 3];
		a[0] = INF;
		a[n + 1] = INF;
		for (int i = 1; i <= n; i++) {
			a[i] = scan.nextInt();
		}
		ArrayList<Integer> list = new ArrayList<Integer>();
		int left = 0, right = 0, ans = 0;
		for (int i = 1; i <= n; i = right + 1) {
			if (a[i] == 1) {
				System.out.println(1 + " " + (n - 1) + '\n' + 1);
				return;
			}
			left = right = i;
			while (a[left - 1] % a[i] == 0)
				left--;
			while (a[right + 1] % a[i] == 0)
				right++;
			if (right - left > ans) {
				list.clear();
				ans = right - left;
			}
			if (right - left == ans) {
				list.add(left);
			}
		}
		System.out.println(list.size() + " " + ans);
		for (int i = 0; i < list.size(); i++) {
			System.out.print(list.get(i) + " ");
		}
	}

	public static void main(String args[]) {
		new CF359D().run();
	}

	public class FastIO {
		BufferedReader br;
		StringTokenizer st;
		PrintWriter out;

		public FastIO(InputStream in, OutputStream o) {
			br = new BufferedReader(new InputStreamReader(in));
			out = new PrintWriter(new OutputStreamWriter(o));
			eat("");
		}

		public FastIO() {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
			eat("");
		}

		public void eat(String s) {
			st = new StringTokenizer(s);
		}

		public String nextLine() {
			try {
				return br.readLine();
			} catch (IOException e) {
				throw new IOError(e);
			}
		}

		public boolean hasNext() {
			while (!st.hasMoreTokens()) {
				String s = nextLine();
				if (s == null)
					return false;
				eat(s);
			}
			return true;
		}

		public String next() {
			hasNext();
			return st.nextToken();
		}

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

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

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

		public void print(String ans) {
			out.print(ans);
			out.flush();
		}

		public void println(String ans) {
			out.println(ans);
			out.flush();
		}

		public void close() {
			out.close();
		}

	}
}
