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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;


public class D {

    static StringTokenizer st;
    static BufferedReader br;
    static PrintWriter pw;
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = nextInt();
        int[]a = new int[n+1];
        for (int i = 1; i <= n; i++) {
            a[i] = nextInt();
        }
        int[]left = new int[n+1], right = new int[n+1];
        right[n] = n;
        for (int i = n-1; i >= 1; i--) {
            if (a[i+1] % a[i] != 0)
                right[i] = i;
            else {
                right[i] = right[i+1];
                while (right[i] < n && a[right[i]+1] % a[i]==0)
                    right[i]++;
            }
        }
        left[1] = 1;
        for (int i = 2; i <= n; i++) {
            if (a[i-1] % a[i] != 0)
                left[i] = i;
            else {
                left[i] = left[i-1];
                while (left[i] > 1 && a[left[i]-1] % a[i]==0)
                    left[i]--;
            }
        }
        int max = -1;
        for (int i = 1; i <= n; i++) {
            max = Math.max(max, right[i]-left[i]);
        }
        TreeSet<Integer> set = new TreeSet<Integer>();
        for (int i = 1; i <= n; i++) {
            if (right[i]-left[i]==max)
                set.add(left[i]);
        }
        pw.println(set.size()+" "+max);
        for (int i : set) {
            pw.print(i+" ");
        }
        pw.close();
    }
    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    private static String next() throws IOException {
        while (st==null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}
