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.lang.*;
import java.io.*;
import java.text.*;

/**
* @author soumitri12
*/

/* Name of the class has to be "Main" only if the class is public*/
public class CF1043
{
    static class FastReader {
        
        BufferedReader br;
        StringTokenizer st;
        
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        long nextLong() {
            return Long.parseLong(next());
        }
        
        double nextDouble() {
            return Double.parseDouble(next());
        }
        
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    
    static class Node {
        
        long pp;
        long a, b;
        
        Node(long x, long y) {
            a = x;
            b = y;
            pp = a * b;
        }
    }
    static class Comp implements Comparator<Node> {
        
        public int compare(Node o1, Node o2) {
            if (o1.pp > o2.pp) {
                return 1;
            } else {
                return -1;
            }
        }
    }
    static int gcd(int x, int y)
    {
        if(y==0) return x;
        else return gcd(y,x%y);
    } 
    static long mod_pow(long a, long b, long mod)
    {
        a%=mod;
        if(b==0) return 1%mod;
        if((b&1)==1) return a*(mod_pow(a,b-1,mod))%mod;
        else 
        {
            long u=mod_pow(a,b>>1,mod);
            return (u*u)%mod;
        }
    }
    static long _pow(long a, long b)
    {
        if(b==0) return 1;
        if((b&1)==1) return a*_pow(a,b-1);
        else 
        {
            long u=_pow(a,b>>1);
            return u*u;
        }
    }
    static int modInv(int a, int m)
    {
        if(gcd(a,m)!=1) return -999;
        else return (a%m+m)%m;
    }
    static boolean isPowerOfTwo(int x) 
    { 
        return x!=0 && ((x&(x-1)) == 0);          
    } 
    static boolean isprime(int x) 
    {
        for(int i=2;i<=Math.sqrt(x);i++)
        {
            if(x%i==0) return false;
        }
        return true;
    }
    static boolean prime[];
    static final int INT_MAX=1000007;

    static void sieve() {
        prime=new boolean[INT_MAX];
        Arrays.fill(prime,true);
        prime[0]=prime[1]=false;
        for(int i=2;i<=Math.sqrt(INT_MAX);i++)
        {
            if(prime[i]) {
                for(int j=i*2;j<INT_MAX;j+=i)
                prime[j]=false;
            }
        }
    }
    static class Pair {
        int ff,ss;
        public Pair(int ff,int ss) {
            this.ff=ff; this.ss=ss;
        }
    }
    
    public static void main(String[] args) {
        FastReader sc=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        StringBuffer sb=new StringBuffer();
        //your code starts here
        int n=sc.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++) a[i]=sc.nextInt();
        int diff[]=new int[n];
        diff[0]=a[0];
        for(int i=1;i<n;i++) diff[i]=a[i]-a[i-1];
        ArrayList<Integer> lens=new ArrayList<>();
        for(int i=1;i<=n;i++)
        {
            boolean flag=true;
            for(int j=0;j+i<n;j++)
            {
                if(diff[j]!=diff[i+j]){
                    flag=false; break;
                }
            } 
            if(flag) lens.add(i);
        }

        out.println(lens.size());
        for(int i:lens) out.print(i+" ");
        out.close();
    }
}
