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.StringTokenizer;


public class D {
	static BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer("");
	public static void main(String[] args) throws Exception{
		int n = readInt();
		int[] table = new int[n];
		int[] left = new int[n];
		int[] right = new int[n];
		boolean[] taken = new boolean[n];
		for(int i = 0; i < n; i++){
			table[i] = readInt();
			left[i] = i;
			right[i] = i;
		}
		int temp;
		for(int i = 0; i < n-1; i++){
			temp = i;
			while(temp>=0 && table[temp]%table[i+1] == 0){
				left[i+1] = left[temp];
				temp = left[temp];
				temp--;
			}
			temp = n-1-i;
			while(temp<n && table[temp]%table[n-2-i] == 0){
				right[n-2-i] = right[temp];
				temp = right[temp];
				temp++;
			}
		}
		int biggest = 0;
		int count = 0;
		int lastLeft = -1;
		for(int i = 0; i < n; i++){
			if(biggest < right[i] - left[i]){
				count = 1;
				biggest = right[i] - left[i];
				lastLeft = left[i];
			}
			else if(biggest == right[i] - left[i] && left[i] != lastLeft){
				count++;
				lastLeft = left[i];
			}
		}
		System.out.println(count + " " + biggest);
		for(int i = 0; i < n; i++){
			if(right[i]-left[i] == biggest && !taken[left[i]]){
				taken[left[i]] = true;
				System.out.print(left[i]+1 + " ");
			}
		}

	}
	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());
	}

	static double readDouble() throws Exception {
		return Double.parseDouble(readString());
	}
}
