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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

public class A {
	
	static BufferedReader br;
    static PrintWriter out;
    static StringTokenizer st;
    static int INF = 1000000007;
	
	public static void main(String args[]) throws IOException {
		 InputStream input = System.in;
         OutputStream output = System.out;
         br = new BufferedReader(new InputStreamReader(input));
         out = new PrintWriter(output);
         
         int n = nextInt();
         int[] a = new int[n+2];
         a[0] = a[n+1] = INF;
         Vector v = new Vector();
         int ans = 0;
         int l, r;
         for(int i = 1; i <= n; i++) a[i] = nextInt();
         for(int i = 1; i <= n; i = r+1) {
        	 if(a[i] == 1) {
        		 System.out.print("1 ");
        		 System.out.println(n-1);
        		 System.out.println(1);
        		 return ;
        	 }
        	 l = i;
        	 r = i;
        	 while(a[l-1] % a[i] == 0) l--;
        	 while(a[r+1] % a[i] == 0) r++;
        	 if(r-l > ans) {
        		 v.clear();
        		 v.add(l);
        		 ans = r-l;
        	 }
        	 else if(r-l == ans) {
        		 v.add(l);
        	 }
         }
         System.out.print(v.size());
         System.out.print(" ");
         System.out.println(ans);
         System.out.print(v.get(0));
         for(int i = 1; i < v.size(); i++) {
        	 System.out.print(" ");
        	 System.out.print((int)v.get(i));
         }
         System.out.println();
         return;
	}
	
	static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
	
	static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }
}