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.*;
import java.util.*;


public class Main implements Runnable {

    int maxn = (int)1e3+11;
    int inf = (int)1e9;
    long mod = (long)1e9+7;
    int n,m,k;
    int a[] = new int[maxn];

    void solve() throws Exception {
        n = in.nextInt();
        int x[] = new int[n+22];
        for (int i=1; i<=n; i++) {
            a[i] = in.nextInt();
            x[i] = a[i]-a[i-1];
        }

        ArrayList<Integer> list = new ArrayList<>();
        for (int k=1; k<=n; k++) {
            boolean isOk = true;
            for (int i=1; i<=k; i++) {
                int val = x[i];
                for (int j=i; j<=n; j+=k) {
                    if (val != x[j]) {
                        isOk = false;
                        break;
                    }
                }
                if (!isOk) break;
            }
            if (isOk) {
               list.add(k);
            }
        }

        out.println(list.size());
        for (int val : list) {
            out.print(val + " ");
        }

    }

    class Pair implements Comparable<Pair> {
        int x,y;

        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return x == pair.x &&
                    y == pair.y;
        }

        @Override
        public int hashCode() {

            return Objects.hash(x, y);
        }

        @Override
        public int compareTo(Pair o) {
            return this.x-o.x;
        }

        @Override
        public String toString() {
            return "Pair{" +
                    "x=" + x +
                    ", y=" + y +
                    '}';
        }
    }



    String fileInName = "";

    static Throwable throwable;
    public static void main (String [] args) throws Throwable {
        Thread thread = new Thread(null, new Main(), "", (1 << 26));
        thread.start();
        thread.join();
        thread.run();
        if (throwable != null)
            throw throwable;
    }

    FastReader in;
    PrintWriter out;

    public void run() {

        try {
            if (!fileInName.isEmpty()) {
                in = new FastReader(new BufferedReader(new FileReader(fileInName+".in")));
                out = new PrintWriter(new BufferedWriter(new FileWriter(fileInName+".out")));
            } else {
                in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
                out = new PrintWriter(System.out);
            }

            solve();
        } catch(Exception e) {
            throwable = e;
        } finally {
            out.close();
        }

    }

    class FastReader {
        BufferedReader bf;
        StringTokenizer tk = null;

        public FastReader(BufferedReader bf) {
            this.bf = bf;
        }

        public Integer nextInt() throws Exception {
            return Integer.parseInt(nextToken());
        }

        public Long nextLong() throws Exception {
            return Long.parseLong(nextToken());
        }

        public Double nextDouble() throws Exception {
            return Double.parseDouble(nextToken());
        }

        public String nextToken () throws Exception {
            if (tk==null || !tk.hasMoreTokens()) {
                tk = new StringTokenizer(bf.readLine());
            }
            if (!tk.hasMoreTokens()) return nextToken();
            else
                return tk.nextToken();
        }
    }
}
