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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class D209 {
	static BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer("");
	
	public static void main(String[] args) throws Exception {
		int n = readInt();
		int[] a = new int[n];
		PriorityQueue<Pair> q = new PriorityQueue();
		for(int i = 0; i < n; ++i) {
			a[i] = readInt();
			q.add(new Pair(i, a[i]));
		}
		int max = 0;
		ArrayList<Integer> ls = new ArrayList();
		boolean[] v = new boolean[n];
		while(!q.isEmpty()) {
			Pair p = q.poll();
			int j = p.id;
			if(!v[j]) {
				v[j] = true;
				int l = j-1;
				int r = j+1;
				while(l >= 0 && !v[l] && a[l]%a[j] == 0)
					v[l--] = true;
				while(r < n && !v[r] && a[r]%a[j] == 0)
					v[r++] = true;
				
				if(r-l-2 > max) {
					ls.clear();
					max = r-l-2;
				}
				if(r-l-2 == max)
					ls.add(l+2);
			}
		}
		
		System.out.println(ls.size()+" "+max);
		Collections.sort(ls);
		for(int i = 0; i < ls.size(); ++i) {
			if(i != 0)
				System.out.print(" ");
			System.out.print(ls.get(i));
		}
		System.out.println();
	}

	static String readString() throws Exception {
		while(!st.hasMoreTokens())
			st = new StringTokenizer(stdin.readLine());
		return st.nextToken();
	}

	static int readInt() throws Exception {
		return Integer.parseInt(readString());
	}
	
	static class Pair implements Comparable<Pair> {
		int id, v;

		Pair(int id, int v) {
		  this.id = id;
		  this.v = v;
		}

		@Override
		public int compareTo(Pair o) {
			return Integer.compare(v, o.v);
		}
	}
}
