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.*;
import java.io.*;

public class LostArray {
	static BufferedReader br;
	static StringTokenizer tokenizer;

	public static void main(String[] args) throws Exception {
		br = new BufferedReader(new InputStreamReader(System.in));
		int n = nextInt();
		int[] arr = new int[n];
		int prev = 0;
		for(int i = 0; i < n; i++) {
			arr[i] = nextInt() - prev;
			prev += arr[i];
		}
		ArrayList<Integer> ans = new ArrayList<Integer>();
		ans.add(n);
		for(int i = 1; i < n; i++) {
			boolean c = true;
			for(int k = 0; k < i; k++) {
				boolean check = true;
				int curr = k;
				while(curr + i < n) {
					if(arr[curr + i] != arr[curr]) {
						check = false;
						break;
					}
					curr++;
				}
				if(!check) {
					c = false;
					break;
				}
			}
			if(c)
				ans.add(i);
		}
		ans.sort(null);
		System.out.println(ans.size());
		for(int e: ans)
			System.out.print(e + " ");
		System.out.println();
	}

	public static String next() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			String line = br.readLine();
			if (line == null)
				throw new IOException();
			tokenizer = new StringTokenizer(line);
		}
		return tokenizer.nextToken();
	}

	public static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
}
