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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;

public class b1043 {
	public static void main(String[] args) {
		FastScanner in = new FastScanner(System.in);
		int N = in.nextInt();
		int[] arr = new int[N+1];
		int[] diff =new int[N];
		for(int n=0;n<N;n++){
			arr[n+1] = in.nextInt();
			diff[n] = arr[n+1] - arr[n];
		}
		
		// i COULD do zvals...
		// no way
//		System.out.println(Arrays.toString(diff));
		ArrayList<Integer> ansSet = new ArrayList<>();
		for(int n=1;n<N;n++){
			boolean fail = false;
			for(int i = 0; i+n < N; i++){
				fail = (fail || diff[i] != diff[i+n]);
			}
			if(!fail) ansSet.add(n);
		}
		ansSet.add(N);
		System.out.println(ansSet.size());
		StringBuilder sb = new StringBuilder();
		for(int n=0;n<ansSet.size();n++){
			if(n > 0) sb.append(' ');
			sb.append(ansSet.get(n));
		}
		System.out.println(sb);
			
	}
	static class FastScanner{
		BufferedReader br;
		String[] line;
		int $;
		FastScanner(InputStream is){
			br = new BufferedReader(new InputStreamReader(is));
			line = new String[]{};
			$ = 0;
		}
		void ensure(){
			try{
				if($ >= line.length){
					line = br.readLine().split(" ");
					$ = 0;
				}
			}
			catch(IOException ioe){
				System.err.println("Whoops.");
			}
		}
		long nextLong(){
			while(true){
				ensure();
				try{
					return Long.parseLong(line[$++]);
				}
				catch(Exception e){
					
				}
			}
		}
		int nextInt(){
			while(true){
				ensure();
				try{
					return Integer.parseInt(line[$++]);
				}
				catch(Exception e){
					
				}
			}
		}
		String next(){
			while(true){
				ensure();
				try{
					return line[$++];
				}
				catch(Exception e){
					
				}
			}
		}
		double nextDouble(){
			while(true){
				ensure();
				try{
					return Double.parseDouble(line[$++]);
				}
				catch(Exception e){
					
				}
			}
		}
	}
}
