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 A {

	static int []get(int []a){
		int n=a.length;
		Stack<Integer> stack=new Stack();
		int []ans=new int [n];
		for(int i=0;i<n;i++) {
			int x=a[i];
			while(!stack.isEmpty() && a[stack.peek()]%x==0)
				stack.pop();
			ans[i]=stack.empty()?i:i-stack.peek()-1;
			stack.push(i);
		}
		return ans;
	}
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		int n=sc.nextInt(),a[]=new int [n],b[]=new int [n];
		for(int i=0;i<n;i++) {
			a[i]=sc.nextInt();
			b[n-1-i]=a[i];
		}
		int []l=get(a),r=get(b);
		int max=0;
		TreeSet<Integer> ans=new TreeSet();
		for(int i=0;i<n;i++) {
			int cand=l[i]+1+r[n-1-i];
			if(cand>max)
				ans.clear();
			if(cand>=max) {
				max=cand;
				ans.add(i-l[i]+1);
			}
		}
		out.println(ans.size()+" "+(max-1));
		for(int x:ans)
			out.println(x);
		out.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		Scanner(String fileName) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(fileName));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}

		boolean ready() throws IOException {
			return br.ready();
		}

	}

}