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.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.TreeSet;

public class pair_of_numbers {
	static class pair implements Comparable<pair> {
		int idx;
		int val;

		pair(int a, int b) {
			idx = a;
			val = b;
		}

		@Override
		public int compareTo(pair o) {
			// TODO Auto-generated method stub
			return this.val - o.val;
		}
	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		int[] a = new int[n];
		pair[] p = new pair[n];
		for (int i = 0; i < n; i++) {
			a[i] = scn.nextInt();
			p[i] = new pair(i, a[i]);

		}
		int maxsize = 0;
		Arrays.sort(p);

		TreeSet<Integer> maxlist = new TreeSet<>();
		boolean[] visit = new boolean[n];
		for (int i = 0; i < n; i++) {
			int idx = p[i].idx;
			if (!visit[idx]) {

				visit[idx] = true;

				int l = idx;
				int r = idx;
				boolean used = false;
				while (l >= 0 && a[l] % a[idx] == 0) {

					visit[l] = true;
					used = true;
					l--;
				}
				if (used)
					l++;
				used = false;
				while (r < n && a[r] % a[idx] == 0) {

					visit[r] = true;
					used = true;
					r++;
				}
				if (used)
					r--;
				if (r - l > maxsize) {
					maxsize = r - l;
					maxlist = new TreeSet<>();
					maxlist.add(l);
				} else if (r - l == maxsize) {
					maxlist.add(l);
				}
			}
		}
			System.out.println(maxlist.size() + " " + maxsize);
			for (int v : maxlist) {
				System.out.print((v + 1) + " ");
			}

		}

	}

