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.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;


public class D_209_Linear {
	static BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer("");
	
	static String readString() throws Exception {
		while(!st.hasMoreTokens())
			st = new StringTokenizer(stdin.readLine());
		return st.nextToken();
	}

	static int readInt() throws Exception {
		return Integer.parseInt(readString());
	}
	public static void main(String[] args) throws Exception {
		int n = readInt();
		int a[] = new int[n];
		for(int i= 0; i < n; i++){
			a[i] = readInt();
		}
		
		int pntL[] = new int[n];
		for(int i = 1; i < n; i++){
			int ind = i;
			while(ind-1 >= 0 && a[ind-1] % a[i] == 0){
				ind = pntL[ind-1];
			} 						
			pntL[i] = ind;
		}
		
		int pntR[] = new int[n];
		pntR[n-1] = n-1;
		for(int i = n-2; i >= 0; i--){
			int ind = i;
			while(ind+1 < n && a[ind+1] % a[i] == 0){
				ind = pntR[ind+1];
			} 						
			pntR[i] = ind;
		}
		int best = 0;
		boolean used[] = new boolean[n];
		ArrayList<Integer> ans = new ArrayList();
		for(int i = 0; i < n; i++){
			if(pntR[i]-pntL[i] > best){
				ans.clear();
				ans.add(pntL[i]);
				best = pntR[i]-pntL[i];
				used[pntL[i]] = true;
			} else if(pntR[i]-pntL[i] == best && !used[pntL[i]]){				
				ans.add(pntL[i]);
				used[pntL[i]] = true;
			}
		}
		
		System.out.println(ans.size() + " " + best);
		for(int l : ans){
			System.out.print(l+1 + " ");
		}
		System.out.println();
	}
}
