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 {
    void run() {
        InputReader in = new InputReader(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
        int[] l = new int[n];
        int[] r = new int[n];
        int[] stack = new int[n];
        int top = -1;
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            l[i] = i;
            for (; top > -1 && a[stack[top]] % a[i] == 0; top--) {
                l[i] = l[stack[top]];
            }
            stack[++top] = i;
        }
        top = -1;
        int maxLength = -1;
        ArrayList<Integer> v = new ArrayList<Integer>();
        for (int i = n - 1; i >= 0; i--) {
            r[i] = i;
            for (; top > -1 && a[stack[top]] % a[i] == 0; top--) {
                r[i] = r[stack[top]];
            }
            stack[++top] = i;
            if (r[i] - l[i] > maxLength) {
                maxLength = r[i] - l[i];
                v.clear();
            }
            if (r[i] - l[i] == maxLength) {
                v.add(l[i] + 1);
            }
        }
        Collections.sort(v);
        int m = 1;
        a[0] = v.get(0);
        for (int i = 1; i < v.size(); i++) {
            if (!v.get(i).equals(v.get(i - 1))) {
                a[m++] = v.get(i);
            }
        }
        PrintWriter out = new PrintWriter(System.out);
        out.println(m + " " + maxLength);
        for (int i = 0; i < m; i++) {
            out.print(a[i] + (i < m - 1 ? " " : "\n"));
        }
        out.close();
    }
    public static void main(String[] args) {
        new Main().run();
    }
}

class InputReader {
    BufferedReader buff;
    StringTokenizer tokenizer;
    InputReader(InputStream stream) {
        buff = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
    boolean hasNext() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(buff.readLine());
            } catch (Exception e) {
                return false;
            }
        }
        return true;
    }
    String next() {
        if (!hasNext()) {
            throw new RuntimeException();
        }
        return tokenizer.nextToken();
    }
    int nextInt() {
        return Integer.parseInt(next());
    }
}
