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.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class Solution 
{
    public static boolean possible(int k,int []a,int n)
    {
        ArrayList<Integer> ar=new ArrayList<Integer>();
        ar.add(0);
        for(int i=0;i<n;i++)
        {
            ar.add(a[i]);
        }
        int[] x=new int[k];
        Arrays.fill(x,Integer.MIN_VALUE);
        for(int i=1;i<=n;i++)
        {
            //System.out.print(x[(i-1)%k]+" ");
            if(x[(i-1)%k]!=Integer.MIN_VALUE && x[(i-1)%k]!=ar.get(i)-ar.get(i-1))
            {
                return false;
            }
            else
            {
                x[(i-1)%k]=ar.get(i)-ar.get(i-1);
            }
        }
        return true;
    }
    public static void main(String[] args) throws IOException 
    {
        InputReader in=new InputReader(System.in);
        PrintWriter w=new PrintWriter(System.out);
        int n=in.nextInt();
        int [] a=new int[n];
        a=in.nextIntArray(n);
        ArrayList<Integer> pq=new ArrayList<Integer>();
        for(int k=1;k<=n;k++)
        {
            if(possible(k,a,n))
            {
                pq.add(k);
            }
        }
        w.println(pq.size());
        for(int i=0;i<pq.size();i++)
        {
            w.print(pq.get(i)+" ");
        }
        w.close();
    }
    static class InputReader
    {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream st) 
        {
          this.stream = st;
        }

        public int read() 
        {
          if (snumChars == -1)
            throw new InputMismatchException();
          if (curChar >= snumChars) 
          {
            curChar = 0;
            try 
            {
              snumChars = stream.read(buf);
            } catch (IOException e) 
            {
              throw new InputMismatchException();
            }
            if (snumChars <= 0)
              return -1;
          }
          return buf[curChar++];
        }

        public int nextInt() 
        {
          int c = read();
          while (isSpaceChar(c)) 
          {
            c = read();
          }
          int sgn = 1;
          if (c == '-') 
          {
            sgn = -1;
            c = read();
          }
          int res = 0;
          do 
          {
            res *= 10;
            res += c - '0';
            c = read();
          } while (!isSpaceChar(c));
          return res * sgn;
        }

        public long nextLong() 
        {
          int c = read();
          while (isSpaceChar(c)) 
          {
            c = read();
          }
          int sgn = 1;
          if (c == '-') 
          {
            sgn = -1;
            c = read();
          }
          long res = 0;
          do 
          {
            res *= 10;
            res += c - '0';
            c = read();
          } while (!isSpaceChar(c));
          return res * sgn;
        }

        public int[] nextIntArray(int n) 
        {
          int a[] = new int[n];
          for (int i = 0; i < n; i++) 
          {
            a[i] = nextInt();
          }
          return a;
        }

        public String readString() 
        {
          int c = read();
          while (isSpaceChar(c)) 
          {
            c = read();
          }
          StringBuilder res = new StringBuilder();
          do 
          {
            res.appendCodePoint(c);
            c = read();
          } while (!isSpaceChar(c));
          return res.toString();
        }

        public String nextLine() 
        {
          int c = read();
          while (isSpaceChar(c))
            c = read();
          StringBuilder res = new StringBuilder();
          do 
          {
            res.appendCodePoint(c);
            c = read();
          } while (!isEndOfLine(c));
          return res.toString();
        }

        public boolean isSpaceChar(int c) 
        {
          return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) 
        {
          return c == '\n' || c == '\r' || c == -1;
        }
    }
}
