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.util.*; 
import static java.lang.Math.*; 

public class d {

	BufferedReader in; 
	PrintWriter out; 
	StringTokenizer st; 
	
	String next(){
		while(st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(in.readLine());		
			} catch(Exception e) {}
		}
		return st.nextToken();
	}

	long nextLong() {
		return Long.parseLong(next());
	}

	int nextInt(){
		return Integer.parseInt(next());
	}

	public void run() throws Exception {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
			int n = nextInt(); 

			int[] st = new int[n]; 
			int top = 0; 
			int[] a = new int[n];
			int[] left = new int[n]; 
			int[] right= new int[n]; 

			for (int i=0; i<n; i++) {
				a[i] = nextInt(); 
				while (top > 0 && (a[st[top-1]] % a[i]) == 0) top--; 
				if (top == 0) left[i]=-1; else left[i] = st[top-1]; 
				st[top++] = i;
			}

			top=0; 
			for (int i=n-1; i>=0; i--) {
				while (top > 0 && (a[st[top-1]] % a[i]) == 0) top--; 
				if (top==0) right[i]=n; else right[i] = st[top-1];
				st[top++] = i; 
			}

			TreeSet<Integer> ans = new TreeSet<Integer>(); 
//			System.err.println(Arrays.toString(left));
//			System.err.println(Arrays.toString(right));
			int mx=-1; 
			for (int i=0; i<n; i++) if (right[i] - left[i] - 2 > mx) {
				mx = right[i] - left[i] - 2; 
				ans.clear(); ans.add(left[i]+1);
			} else if (mx == right[i] - left[i] -2) {
				ans.add(left[i]+1);
			}

			out.println(ans.size() +" "+ mx);
			for (int x : ans) out.print((x+1) + " ");
		out.close();
	}

	public static void main(String[] args) throws Exception {
		new d().run();
	}
}