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.util.*;
import java.io.*;
 
public class Main {
	public static void main(String args[]) {new Main().work();}
	
	Scanner in = new Scanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	
	void work() {		
		int n=in.nextInt();
		int[] A=new int[n];
		for(int i=0;i<n;i++)A[i]=in.nextInt();
		
		int[] l=new int[n];
        int[] r=new int[n];
        
        for(int i=0,j=0;i<n;){
            int cnt=0;
            while(j<n&&A[j]%A[i]==0){
                cnt++;
                j++;
            }
            r[i]=cnt;
            i=j;
        }
        for(int i=n-1,j=n-1;i>=0;){
            if(r[i]==0){//不是候选
                i--;
                j--;
                continue;
            }
            int cnt=0;
            while(j>=0&&A[j]%A[i]==0){
                cnt++;
                j--;
            }
            l[i]=cnt;
            i=j;
        }
        ArrayList<Integer> list=new ArrayList<>();
        int max=0;
        for(int i=0;i<n;i++){
            if(l[i]+r[i]-2==max){
                list.add(i-l[i]+2);
            }else if(l[i]+r[i]-2>max){
                max=l[i]+r[i]-2;
                list=new ArrayList<Integer>();
                list.add(i-l[i]+2);
            }
        }
        out.print(list.size()+" ");
        out.println(max);
        for(int i=0;i<list.size();i++){
            out.print(list.get(i)+" ");
        }
		out.flush();
	}
}