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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Vector;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Stack;
import java.util.TreeSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        int[] ar;
        int n;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            ar = new int[n];
            for (int i = 0; i < n; i++) {
                ar[i] = in.nextInt();
            }

            Stack<Integer> s = new Stack<>();
            int[] l = new int[n];
            int[] r = new int[n];
            for (int i = 0; i < n; i++) {
                while (!s.empty() && ar[s.peek()] % ar[i] == 0) s.pop();
                if (s.empty())
                    l[i] = -1;
                else
                    l[i] = s.peek();
                s.push(i);
            }

            s.clear();
            for (int i = n - 1; i >= 0; i--) {
                while (!s.empty() && ar[s.peek()] % ar[i] == 0) s.pop();
                if (s.empty())
                    r[i] = n;
                else
                    r[i] = s.peek();
                s.push(i);
            }

            TreeSet<Integer> list = new TreeSet<>();
            int best = -1;
            for (int i = 0; i < n; i++) {
                if (r[i] - l[i] > best) {
                    list.clear();
                    best = r[i] - l[i];
                }
                if (r[i] - l[i] == best)
                    list.add(l[i]);
            }

            out.println(list.size() + " " + (best - 2));
            for (int a : list)
                out.print((a + 2) + " ");
        }

    }

    static class InputReader {
        StringTokenizer st;
        BufferedReader br;

        public InputReader(InputStream is) {
            BufferedReader br = new BufferedReader(new InputStreamReader(is));
            this.br = br;
        }

        public String next() {
            if (st == null || !st.hasMoreTokens()) {
                String nextLine = null;
                try {
                    nextLine = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (nextLine == null)
                    return null;
                st = new StringTokenizer(nextLine);
            }
            return st.nextToken();
        }

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

    }
}

