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.*;



public class HelloWorld {

    static  class Pair{
        int v;
        int indx;
    }

    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] arr = new int[n];
        int[] ind = new int[n];
        HashMap<Integer, ArrayList<Integer>> resultMap = new HashMap<Integer, ArrayList<Integer>>();
        ArrayList<Pair>  pairs = new ArrayList<>();
        ArrayList<Integer> temp = new ArrayList<>();
        for(int i = 0; i<n;i++)
        {
            arr[i] = sc.nextInt();
            Pair p = new Pair();
            pairs.add(p);
            p.v = arr[i];
            p.indx = i;
        }

        Collections.sort(pairs, new Comparator<Pair>() {
            @Override
            public int compare(Pair o1, Pair o2) {
                return Integer.compare(o1.v, o2.v);
            }
        });

        int maxLen = 0;
        for(Pair p: pairs){
            int j = p.indx;

            if(ind[j] == 1)
                continue;
            int l = j-1;
            int r = j+1;

            ind[j] = 1;

            while(r<n){
                if(arr[r]%arr[j] == 0){
                    ind[r] = 1;
                } else {
                    break;
                }
                r++;
            }
            while(l>=0){
                if(arr[l]%arr[j] == 0){
                    ind[l] = 1;
                } else {
                    break;
                }
                l--;
            }
            l++;
            r--;
            int len = r-l;
            temp = resultMap.get(len);
            if(temp == null){
                temp = new ArrayList<>();
                resultMap.put(len,temp);
            }
            temp.add(l);
            maxLen = Math.max(maxLen,len);
        }

        temp = resultMap.get(maxLen);
        Collections.sort(temp);
        System.out.println(temp.size()+" "+ maxLen);
        for(int i: temp){
            System.out.print(i+1+" ");
        }
        System.out.println();

    }
}
