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.*;
import java.util.*;

public class D {
	static StringBuilder st = new StringBuilder();

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		int n = sc.nextInt() ; 
		
		int [] a = new int [n] ; 
		
		Stack<int []> stack = new Stack<>();
		
		for(int i = 0 ; i < n;i++) a[i] = sc.nextInt();
		
		int [] l = new int [n] , r = new int [n];
		
		for(int i = 0 ; i < n ; i++)
		{
			
			while(!stack.isEmpty() && stack.peek()[1] % a[i] == 0)
				stack.pop();
			
			int left = 0 ; 
			
			if(!stack.isEmpty())
				left = stack.peek()[0] + 1 ;
			
			stack.push(new int [] {i , a[i]});
			
			l[i] = left ;
		}
		
		stack = new Stack<>();
		
		
		for(int i = n - 1 ; i >= 0 ; i--)
		{
			
			while(!stack.isEmpty()  && stack.peek()[1] % a[i] == 0)
				stack.pop();
			
			int right = n - 1 ;
			if(!stack.isEmpty())
				right = stack.peek()[0] - 1;
			
			r[i] = right ;
			
			stack.push(new int [] {i , a[i]});
		}
		
		int max = 0 ;
		TreeSet<Integer> ans = new TreeSet<>();
		
		for(int i = 0 ; i < n ;i++)
		{
			if(max < r[i] - l[i])
			{
				max = r[i] - l[i];
				ans = new TreeSet<>();
				ans.add(l[i] + 1);
			}
			else if(max == r[i] - l[i])
				ans.add(l[i] + 1);
				
		}
		out.println(ans.size()+" "+max);
		for(int x : ans)
			out.print(x+" ");
		
		out.flush();
		out.close();

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(String path) throws Exception {
			br = new BufferedReader(new FileReader(path));
		}

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

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

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

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

	}

	static void shuffle(int[] a) {
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int r = i + (int) (Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}

}