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.math.BigInteger;
import java.util.*;




public class Main {
	

	public static class FastReader {
		BufferedReader br;
		StringTokenizer root;
		
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (root == null || !root.hasMoreTokens()) {
				try {
					root = new StringTokenizer(br.readLine());
				} catch (Exception addd) {
					addd.printStackTrace();
				}
			}
			return root.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception addd) {
				addd.printStackTrace();
			}
			return str;
		}
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	
	public static FastReader sc = new FastReader();
 
	static int mod = (int) (1e9+7),MAX=(int) (2e5);
    static List<Integer>[] edges;
    public static int col = 19;
	public static int[][] table;
	
	public static void main(String[] args){
		
		int n = sc.nextInt();
		int[] a = new int[n];
		table = new int[n][col+1];
		for(int i=0;i<n;++i) a[i] = sc.nextInt();
		
		 // build Sparse Table
	    for(int i = 0; i < n; i++) table[i][0] = a[i];
	    for(int j = 1; j <= col; j++) {
	        for(int i = 0; i <= n - (1 << j); i++)
	            table[i][j] = __gcd(table[i][j - 1], table[i + (1 << (j - 1))][j - 1]);
	    }
	    
	    TreeSet<Integer> ans = new TreeSet<>();
	    int max = 0;
	    for(int i=0;i<n;++i) {
	    	int l=0,r=i;
	    	int left = i,right = i;
	    	while(l <= r) {
	    		int mid = (l+r)>>1;
	    		if(query(mid,i)%a[i] == 0) {
	    			left = mid;
	    			r = mid-1;
	    		}else l = mid+1;
	    	}
	    	l = i;
	    	r = n-1;
	    	while(l <= r) {
	    		int mid = (l+r)>>1;
	    		if(query(i,mid)%a[i] == 0) {
	    			right = mid;
	    			l = mid+1;
	    		}else r = mid-1;
	    	}
	    	
	    	if(right-left >= max) {
	    		if(right-left > max) ans.clear();
	    		ans.add(left+1);
	    		max = right - left;
	    	}
	    	
	    } 
	    out.println(ans.size()+" "+max);
	    for(int x : ans) out.print(x+" ");
		
		
out.close();
	}
	
	private static int query(int l, int r) {
		int ans = 0;
		 for(int j = col; j >= 0; j--) {
	            if(l + (1 << j) - 1 <= r) {
	                ans = __gcd(ans, table[l][j]);
	                l += 1 << j;
	            }
	        }
		 return ans;
	}

	private static int __gcd(int a, int b) {
		if(b == 0) return a;
		return __gcd(b,a%b);
	}
	
}



