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 Test1{
    
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int arr[] = new int[n];
        int con[] = new int[n];
        int idx[] = new int[n];
        for(int i=0;i<n;++i){
            arr[i] = sc.nextInt();
            con[i] = arr[i];
            idx[i] = i; 
        }
        List<Integer> list = new ArrayList<Integer>();
        for(int i=1;i<n;++i)
        {
            if(con[i-1] % arr[i] == 0)
            {
                con[i] = arr[i];
                con[i-1] = arr[i];
                idx[i] = idx[i-1];
                for(int j=idx[i];j>=0;j--)
                {
                    if(arr[j] % con[i] == 0)
                        idx[i] = j;
                    else
                        break;
                }
            }
            else if(arr[i] % con[i-1] == 0 && arr[i-1] % con[i-1] == 0)
            {
                con[i] = con[i-1];
                idx[i] = idx[i-1];
            }
        }
        int max = 0;
        for(int i=0;i<n;++i)
        {
            int diff = i - idx[i];
            if(diff > max){
                max = diff;
                list.clear();
                list.add(idx[i]);
            }
            else if(diff == max)
            {
                list.add(idx[i]);
            }
        }
        System.out.println(list.size()+" "+max);
        for(int i : list)
            System.out.print((i+1)+" ");
        System.out.println();
    }
}