Bajtek, known for his unusual gifts, recently got an integer array x_0, x_1, …, x_{k-1}.

Unfortunately, after a huge array-party with his extraordinary friends, he realized that he'd lost it. After hours spent on searching for a new toy, Bajtek found on the arrays producer's website another array a of length n + 1. As a formal description of a says, a_0 = 0 and for all other i (1 ≤ i ≤ n) a_i = x_{(i-1)mod k} + a_{i-1}, where p mod q denotes the remainder of division p by q.

For example, if the x = [1, 2, 3] and n = 5, then:

  * a_0 = 0, 
  * a_1 = x_{0mod 3}+a_0=x_0+0=1, 
  * a_2 = x_{1mod 3}+a_1=x_1+1=3, 
  * a_3 = x_{2mod 3}+a_2=x_2+3=6, 
  * a_4 = x_{3mod 3}+a_3=x_0+6=7, 
  * a_5 = x_{4mod 3}+a_4=x_1+7=9. 



So, if the x = [1, 2, 3] and n = 5, then a = [0, 1, 3, 6, 7, 9].

Now the boy hopes that he will be able to restore x from a! Knowing that 1 ≤ k ≤ n, help him and find all possible values of k — possible lengths of the lost array.

Input

The first line contains exactly one integer n (1 ≤ n ≤ 1000) — the length of the array a, excluding the element a_0.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).

Note that a_0 is always 0 and is not given in the input.

Output

The first line of the output should contain one integer l denoting the number of correct lengths of the lost array.

The second line of the output should contain l integers — possible lengths of the lost array in increasing order.

Examples

Input

5
1 2 3 4 5


Output

5
1 2 3 4 5 

Input

5
1 3 5 6 8


Output

2
3 5 

Input

3
1 5 3


Output

1
3 

Note

In the first example, any k is suitable, since a is an arithmetic progression.

Possible arrays x:

  * [1]
  * [1, 1]
  * [1, 1, 1]
  * [1, 1, 1, 1] 
  * [1, 1, 1, 1, 1]



In the second example, Bajtek's array can have three or five elements.

Possible arrays x:

  * [1, 2, 2]
  * [1, 2, 2, 1, 2]



For example, k = 4 is bad, since it leads to 6 + x_0 = 8 and 0 + x_0 = 1, which is an obvious contradiction.

In the third example, only k = n is good.

Array [1, 4, -2] satisfies the requirements.

Note that x_i may be negative.

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class ProblemB {
	public static void main(String [] args){
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		List<Integer>arr = new ArrayList<Integer>();
		List<Integer>diff = new ArrayList<Integer>();
		List<Integer>len = new ArrayList<Integer>();
		boolean flag = false;
		int count = 0;
		
		arr.add(0);
		for(int i = 1; i < n + 1; i++) {
			arr.add(scanner.nextInt());
		}
		
		for(int i = 1; i <= n; i++) {
			
			int d = arr.get(i) - arr.get(i-1);
			if(d > 1) {
				flag = true;
			}
			diff.add(d);
		}
		
		if(arr.size() == 2) {
			System.out.println(1);
			System.out.println(1);
		}else {
			
			for(int i = 1; i <= n; i++) {
				boolean fg = false;
				for(int j = 0; j + i < n ; j++) {
					//System.out.println(diff.get(j) + " " + diff.get(j + i));
					if(arr.get(j + 1) - arr.get(j) != arr.get(j + i + 1) - arr.get(j + i)) {	
						fg = true;
						break;
					}
				}
				
				if(!fg) {
					len.add(i);
					count++;
				}
			}
			
			
			System.out.println(count);
			for(int i = 0; i < len.size(); i++) {
				System.out.print(len.get(i) + " ");
			}
		}
	}
}
