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.*;

// printArr() - prints the array
// intList, doubleList, longList
// nextIntArray

/* stuff you should look for
 * int overflow, array bounds
 * special cases (n=1?)
 * do smth instead of nothing and stay organized
 * WRITE STUFF DOWN
 */

public class current {
    public static void main(String[] args) {
        FastReader fr = new FastReader();
        fr.nextLine();
        solve(fr.nextIntArray());
    }

    public static void solve(int[] arr) {
        int l = arr.length;
        int[] larr = new int[l];
        larr[0] = arr[0];
        for (int i = 1; i < l; i++) {
            larr[i] = arr[i] - arr[i-1];
        }
        List<Integer> sols = new ArrayList<>();
        boolean isSol;
        for (int length = 1; length <= l; length++) {
            isSol = true;
            int[] init = new int[length];
            System.arraycopy(larr, 0, init, 0, length);
            for (int i = 0; i < l; i++) {
                if (init[i%length] != larr[i]){
                    isSol = false;
                    break;
                }
            }
            if (isSol) {
                sols.add(length);
            }
        }
        System.out.println(sols.size());
        for (int i : sols) {
            System.out.print(i + " ");
        }
        System.out.println();
    }

    public static Set<Integer> get(List<Set<Integer>> graph, int i) {
        try {
            return graph.get(i);
        } catch (IndexOutOfBoundsException e) {
            return new HashSet<>();
        }
    }

    public static void printArr(int[] a) {
        System.out.println(Arrays.toString(a));
    }

    public static int[] bfs(List<Set<Integer>> graph, int v) {
        int l = graph.size();
        Deque<Integer> list = new ArrayDeque<>();
        list.add(v);
        boolean[] seen = new boolean[l];
        int distance = 0;
        int node = v;
        int size = 1;
        int index = 0;
        // Iterate over every single vertice and edge
        // O(V+E) -> O(V) for trees
        while (!list.isEmpty()) {
            int cur = list.poll();
            seen[cur] = true;
            node = cur;

            index++;
            if (index > size) {
                distance++;
                size = list.size();
                index = 0;
            }

            for (int i : graph.get(cur)) {
                if (!seen[i]) {
                    seen[i] = true;
                    list.add(i);
                }
            }
        }
        return new int[]{node, distance};
    }

    static class SegTree {
        int startIndex, endIndex;
        long sum;
        SegTree lchild, rchild;

        SegTree(int[] arr) {this(0, arr.length-1, arr);}

        SegTree(int startIndex, int endIndex, int[] arr) {
            this.startIndex = startIndex;
            this.endIndex = endIndex;
            if (startIndex == endIndex) sum = arr[startIndex];
            else {
                int mid = (startIndex + endIndex) / 2;
                lchild = new SegTree(startIndex, mid, arr);
                rchild = new SegTree(mid + 1, endIndex, arr);
                sum = lchild.sum + rchild.sum;
                recalc();
            }
        }

        void recalc() {
            if (startIndex == endIndex) return; sum = lchild.sum + rchild.sum;
        }

        public void valueUpdate(int index, int value) {
            if (startIndex == endIndex) {sum = value; return;}
            if (index > lchild.endIndex) rchild.valueUpdate(index, value); else lchild.valueUpdate(index, value); recalc();
        }

        public long rangeSum(int startIndex, int endIndex) {
            if (endIndex < this.startIndex || startIndex > this.endIndex) return 0;
            if (startIndex <= this.startIndex && endIndex >= this.endIndex) return sum;
            return lchild.rangeSum(startIndex, endIndex) + rchild.rangeSum(startIndex, endIndex);
        }
    }

    public static double sum(List<Long> n) {
        double a = 0;
        for (long i : n) {
            a += i;
        }
        return a;
    }

    public static int toInt(String n) {
        return Integer.parseInt(n);
    }

    public static double toDouble(String n) {
        return Double.parseDouble(n);
    }

    public static long toLong(String n) {
        return Long.parseLong(n);
    }

    static class FastReader {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;

        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());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        String nextLine() {
            String a = "";
            try {
                a = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return a;
        }

        int[] nextIntArray() {
            return intArray(nextLine().split(" "));
        }

        long[] nextLongArray() {
            return longArray(nextLine().split(" "));
        }

        double[] nextDoubleArray() {
            return doubleArray(nextLine().split(" "));
        }

        public int getInt(int index) {
            String[] arr = nextLine().split(" ");
            return Integer.parseInt(arr[index]);
        }

        public long getLong(int index) {
            String[] arr = nextLine().split(" ");
            return Long.parseLong(arr[index]);
        }

        public double getDouble(int index) {
            String[] arr = nextLine().split(" ");
            return Double.parseDouble(arr[index]);
        }

        public List<String> stringList() {
            String[] arr = nextLine().split(" ");
            return Arrays.asList(arr);
        }

        public List<Integer> intList() {
            String[] arr = nextLine().split(" ");
            List<Integer> a = new ArrayList<>();
            for (String i : arr) {
                a.add(Integer.parseInt(i));
            }
            return a;
        }

        public List<Double> doubleList() {
            String[] arr = nextLine().split(" ");
            List<Double> a = new ArrayList<>();
            for (String i : arr) {
                a.add(Double.parseDouble(i));
            }
            return a;
        }

        public List<Long> longList() {
            String[] arr = nextLine().split(" ");
            List<Long> a = new ArrayList<>();
            for (String i : arr) {
                a.add(Long.parseLong(i));
            }
            return a;
        }
    }


    public static int[] intArray(String[] arr) {
        int l = arr.length;
        int[] a = new int[l];
        for (int i = 0; i < l; i++) {
            a[i] = Integer.parseInt(arr[i]);
        }
        return a;
    }

    public static long[] longArray(String[] arr) {
        int l = arr.length;
        long[] a = new long[l];
        for (int i = 0; i < l; i++) {
            a[i] = Long.parseLong(arr[i]);
        }
        return a;
    }

    public static double[] doubleArray(String[] arr) {
        int l = arr.length;
        double[] a = new double[l];
        for (int i = 0; i < l; i++) {
            a[i] = Double.parseDouble(arr[i]);
        }
        return a;
    }
}