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).
//package CF;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class A {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = sc.nextInt(), a[] = new int[n], res[] = new int[n];
		for (int i = 0; i < a.length; i++) {
			a[i] = sc.nextInt();
		}
		int ans = 0, cnt = 0;
		for (int i = 0; i < a.length; i++) {
			int l = i-1, r = i+1;
			while(l >= 0 && a[l] % a[i] == 0) l--;
			while(r < n && a[r] % a[i] == 0) r++;
			l++;
			r--;
			if(l < 0) l = 0;
			if(r >= n) r = n-1;
			int len = r - l;
			if (ans < len) {
				ans = len;
				cnt = 0;
			}
			if (ans == len) {
				res[cnt++] = l;
			}
			i = r;
		}
		out.println(cnt + " " + ans);
		for (int j = 0; j < cnt; j++) {
			out.print(res[j] + 1 + " ");			
		}
		out.flush();
		out.close();
	}

	static class Scanner {
		BufferedReader bf;
		StringTokenizer st;

		public Scanner(InputStream i) {
			bf = new BufferedReader(new InputStreamReader(i));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(bf.readLine());
			return st.nextToken();
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}
	}
}