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 Main {

	public static void main(String[] args) throws IOException{

		BufferedReader buf = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;

		int n = Integer.parseInt(buf.readLine());

		st = new  StringTokenizer(buf.readLine());

		int[]a = new int[n + 1];
		int[]l = new int[n + 2];
		int[]r = new int[n + 2];

		for(int i = 1; i <= n; i++){a[i] = Integer.parseInt(st.nextToken());l[i] = r[i] = i;}

		for(int i = 2; i < n; i++){
			int j = i - 1;
			while( j > 0 && a[j] % a[i] == 0)j = l[j] - 1; 
			l[i] =  j + 1;
		}

		for(int i = n - 1; i >= 1; i--){
			int j = i + 1;
			while( j <= n && a[j] % a[i] == 0)j = r[j] + 1; 
			r[i] = j - 1;
		}

		int max = -1;
	

		HashSet<Integer> h = new HashSet<Integer>();

		for(int i = 1; i <= n ; i++)
			if(max < r[i] - l[i] + 1)
				max =r[i] - l[i] + 1;	


		int cant = 0;

		for(int i = 1; i <= n; i++){
			if(r[i] - l[i] + 1 == max ){
				if(!h.contains(l[i])){
					cant++;
					h.add(l[i]);
				}
			}
		}
		System.out.println(cant + " "+ (max - 1));

		int ind = 0;
		
		int A[] = new int [n + 1];
		
		for(int v : h)A[ind++] = v;
			
         Arrays.sort(A,0,ind);

         for(int i = 0; i < ind ; i++)System.out.println(A[i]);
		
		System.out.println();
	}
}
