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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    int N;
    int[] a;

    int[] l;
    int[] r;
    void run(FastScanner in, PrintWriter out) {

        N = in.nextInt();
        a = new int[N];
        for (int i = 0; i < N; i++) a[i] = in.nextInt();


        l = new int[N];
        r = new int[N];
        Arrays.fill(l, 1);
        Arrays.fill(r, 1);

        for (int i = 1; i < N; i++) {
            while (i-l[i] >= 0 && a[i-l[i]]%a[i] == 0) {
                l[i] += l[i-l[i]];
            }
        }

        for (int i = N-2; i >= 0; i--) {
            while (i+r[i] < N && a[i+r[i]]%a[i] == 0) {
                r[i] += r[i+r[i]];
            }
        }

        int max = 0;
        TreeSet<Integer> ret = new TreeSet<>();
        for (int i = 0; i < N; i++) {
            if (l[i]+r[i]-1 > max) {
                max = l[i]+r[i]-1;
                ret.clear();
                ret.add(i-l[i]+2);
            } else if (l[i]+r[i]-1 == max) {
                ret.add(i-l[i]+2);
            }
        }

        out.println(ret.size() + " " + (max-1));
        for (int num : ret) out.print(num + " ");
        out.println();

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
