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 Main {

    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(new BufferedWriter(
                new OutputStreamWriter(System.out)));
        Scan scan = new Scan();
        int n = scan.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = scan.nextInt();
        }
        int x = 0;
        int y = 0;
        boolean vis[] = new boolean[n];
        int len = -1;
        boolean flag1 = false, flag2 = false;
        Set<Integer> set = new TreeSet<Integer>();
        for (int i = 0; i < n; i++) {
            if (!vis[i]) {
                vis[i] = true;
                x = i;
                y = i;
                while (true) {
                    if (x >= 0 && a[x] % a[i] == 0) {
                        vis[x] = true;
                        x--;
                    }
                    if (y < n && a[y] % a[i] == 0) {
                        vis[y] = true;
                        y++;
                    }// out.println(x+" "+y+" "+len);
                    if (x < 0 && y >= n)
                        break;
                    if (x >= 0 && y < n && a[x] % a[i] != 0 && a[y] % a[i] != 0)
                        break;
                    if (x < 0 && y < n && a[y] % a[i] != 0)
                        break;
                    if (x >= 0 && y >= n && a[x] % a[i] != 0)
                        break;

                }
                if (len == y - x - 2)
                    flag1 = true;
                else
                    flag1 = false;
                if (len < y - x - 2)
                    flag2 = true;
                else
                    flag2 = false;

                len = max(len, y - x - 2);
                if (flag1) {
                    set.add(x + 1);
                }
                if (flag2) {
                    set.clear();
                    set.add(x + 1);
                }
            }
        }
        out.println(set.size() + " " + len);
        for (int ans : set) {
            out.print((ans + 1) + " ");
        }
        out.flush();
        out.close();
    }

    public static int max(int a, int b) {
        if (a < b)
            return b;
        return a;
    }
}

class Scan {

    BufferedReader buffer;
    StringTokenizer tok;

    Scan() {
        buffer = new BufferedReader(new InputStreamReader(System.in));
    }

    boolean hasNext() {
        while (tok == null || !tok.hasMoreElements()) {
            try {
                tok = new StringTokenizer(buffer.readLine());
            } catch (Exception e) {
                return false;
            }
        }
        return true;
    }

    String next() {
        if (hasNext())
            return tok.nextToken();
        return null;
    }

    String nextLine() {
        String s = null;
        try {
            s = buffer.readLine();
        } catch (Exception e) {
            return null;
        }
        return s;
    }

    char nextChar() {
        try {
            return ((char) buffer.read());
        } catch (Exception e) {
        }
        return '\0';
    }

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

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

    double nextDouble() {
        return Double.parseDouble(next());
    }
}