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.File;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;
import java.util.StringTokenizer;

public class l073 {

	public static void main(String[] args) throws Exception {
//		StringTokenizer stok = new StringTokenizer(new Scanner(new File("F:/books/input.txt")).useDelimiter("\\A").next());
		StringTokenizer stok = new StringTokenizer(new Scanner(System.in).useDelimiter("\\A").next());
		StringBuilder sb = new StringBuilder();
		Integer n = Integer.parseInt(stok.nextToken());
		int[] a = new int[n];
		for(int i=0;i<n;i++) a[i] = Integer.parseInt(stok.nextToken());
		HashMap<Integer,Integer> mp = new HashMap<Integer,Integer>();
		int[] le = new int[n];
		int[] ri = new int[n];
		boolean[] vis = new boolean[n];
		for(int i=0;i<n-1;i++) {
			int c = a[i];
			ArrayList<Integer> list = new ArrayList<Integer>();
			for(Integer k : mp.keySet()) {
				Integer v = mp.get(k);
				if(c%k!=0) {
					le[v]=i-v-1;
					list.add(k);
				}
			}
			for(int v : list) mp.remove(v);
			if(mp.get(c)==null) mp.put(c, i);
			else vis[i]=true;
		}
		doStuff(le,a,mp,n-1);
		for(int i=n-1;i>0;i--) {
			int c = a[i];
			ArrayList<Integer> list = new ArrayList<Integer>();
			for(Integer k : mp.keySet()) {
				Integer v = mp.get(k);
				if(c%k!=0) {
					ri[v]=v-i-1;
					list.add(k);
				}
			}
			for(int v : list) mp.remove(v);
			if(!vis[i])
				if(mp.get(c)==null) mp.put(c, i);
		}
		doStuff(ri,a,mp,0);
		int[] c = new int[n];
		for(int i=0;i<n;i++) {
			int v = le[i]+ri[i];
			c[i-ri[i]] = Math.max(c[i-ri[i]], v);
		}
		int max = Arrays.stream(c).max().getAsInt();
		int cnt = 0;
		for(int i=0;i<n;i++) if(c[i]==max) {
			cnt++;
			sb.append((i+1)+" ");
		}
		System.out.println(cnt+" "+max);
		System.out.print(sb);
	}

	private static void doStuff(int[] b, int[] a, HashMap<Integer, Integer> mp, int id) {
		int c = a[id];
		for(Integer k : mp.keySet()) {
			Integer p = mp.get(k);
			b[p] = Math.abs(id-p)-((c%k!=0)?1:0);  
		}
		mp.clear();
	}

}
