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).
//package codeforces;

import java.util.Scanner;
import java.util.TreeSet;

/**
 * Created by nitin.s on 26/03/16.
 */
public class PairOfNumbers {
    static int n;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        n = in.nextInt();
        int[] as = new int[n];
        for(int i = 0; i < n; ++i) {
            as[i] = in.nextInt();
        }
        int[] left = left(as);
        int[] right = rev(left(rev(as)));
        for(int i = 0; i < n; ++i) {
            right[i] = n - 1 - right[i];
        }
        int max = 0;
        TreeSet<Integer> starts = new TreeSet<Integer>();
        for(int i = 0; i < n; ++i) {
            int len = right[i] - left[i];
            if(len > max) {
                max = len;
                starts = new TreeSet<Integer>();
                starts.add(left[i]);
            }
            else if(len == max) {
                starts.add(left[i]);
            }
        }
        System.out.println(starts.size() + " " + max);
        for(int x : starts) {
            System.out.print((x + 1) + " ");
        }
    }

    private static int[] rev(int[] as) {
        int[] res = new int[n];
        for(int i = 0; i < n; ++i) {
            res[i] = as[n - 1 - i];
        }
        return res;
    }

    private static int[] left(int[] as) {
        int[] left = new int[n];
        for(int i = 0; i < n; ++i) {
            left[i] = i;
            int at = i - 1;
            while(at >= 0) {
                if(as[at] == as[i]) {
                    left[i] = left[at];
                    break;
                }
                if(as[at] % as[i] == 0) {
                    left[i] = at;
                    at--;
                }
                else {
                    break;
                }
            }
        }
        return left;
    }
}
