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.
    /*
    @author : Abhimanyu Chauhan
    */
    import java.util.*;
    import java.io.*;

    public class TaskB implements Runnable{
        static class Reader
        {
            final private int BUFFER_SIZE = 1 << 16;
            private DataInputStream din;
            private byte[] buffer;
            private int bufferPointer, bytesRead;
    
            public Reader()
            {
                din = new DataInputStream(System.in);
                buffer = new byte[BUFFER_SIZE];
                bufferPointer = bytesRead = 0;
            }
    
            public Reader(String file_name) throws IOException
            {
                din = new DataInputStream(new FileInputStream(file_name));
                buffer = new byte[BUFFER_SIZE];
                bufferPointer = bytesRead = 0;
            }
    
            public String readLine() throws IOException
            {
                byte[] buf = new byte[64]; // line length
                int cnt = 0, c;
                while ((c = read()) != -1)
                {
                    if (c == '\n')
                        break;
                    buf[cnt++] = (byte) c;
                }
                return new String(buf, 0, cnt);
            }
    
            public int nextInt() throws IOException
            {
                int ret = 0;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();
                do
                {
                    ret = ret * 10 + c - '0';
                }  while ((c = read()) >= '0' && c <= '9');
    
                if (neg)
                    return -ret;
                return ret;
            }
    
            public long nextLong() throws IOException
            {
                long ret = 0;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();
                do {
                    ret = ret * 10 + c - '0';
                }
                while ((c = read()) >= '0' && c <= '9');
                if (neg)
                    return -ret;
                return ret;
            }
    
            public double nextDouble() throws IOException
            {
                double ret = 0, div = 1;
                byte c = read();
                while (c <= ' ')
                    c = read();
                boolean neg = (c == '-');
                if (neg)
                    c = read();
    
                do {
                    ret = ret * 10 + c - '0';
                }
                while ((c = read()) >= '0' && c <= '9');
    
                if (c == '.')
                {
                    while ((c = read()) >= '0' && c <= '9')
                    {
                        ret += (c - '0') / (div *= 10);
                    }
                }
    
                if (neg)
                    return -ret;
                return ret;
            }
    
            private void fillBuffer() throws IOException
            {
                bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
                if (bytesRead == -1)
                    buffer[0] = -1;
            }
    
            private byte read() throws IOException
            {
                if (bufferPointer == bytesRead)
                    fillBuffer();
                return buffer[bufferPointer++];
            }
    
            public void close() throws IOException
            {
                if (din == null)
                    return;
                din.close();
            }
        }
        
        Reader scan;
        PrintWriter out;

        @Override
        public void run() {
            try{
                scan = new Reader();
                out = new PrintWriter(System.out);
                solve();
                out.flush();
            }catch(IOException ex){
                ex.printStackTrace();
            }
        }

        void solve() throws IOException{
            int n = scan.nextInt();
            int ar[] = new int[n+1];
            ar[0] = 0;
            for(int i =1;i<=n;i++){
                ar[i] = scan.nextInt();
            }
            int d[] = new int[n];
            // d[0] = ar[0];
            for(int i=1;i<=n;i++){
                d[i-1] = ar[i]-ar[i-1];
            }
            // System.out.println(Arrays.toString(d));
            List<Integer> list = new ArrayList<>();
            for(int i=1;i<=n;i++){
                boolean flag = true;
                HashMap<Integer,Integer> hm = new HashMap<>();
                for(int j=0;j<n;j++){
                    int k  = d[j];
                    if(hm.containsKey((j)%i) && hm.get((j)%i)!=k){
                        flag = false;
                        // System.out.println("ASLKVN");
                        break;
                    }else if(!hm.containsKey((j)%i)){
                        hm.put((j)%i,k);
                    } 
                }
                // System.out.println(hm.toString());   
                if(flag){
                    list.add(i);
                }
            }
            Collections.sort(list);
            StringBuilder sb = new StringBuilder();
            sb.append(list.size()).append("\n");
            for(int i : list){
                sb.append(i+" ");
            }
            out.print(sb.toString().trim());
        }

        public static void main(String[] args) throws IOException {
            new Thread(null,new TaskB(),"Main",1<<26).run();;
        }

    }