Little P has just learned the shell-sort sorting algorithm. He was given some code that sorts an array of N integers in ascending order. Let A be the array to be sorted.

Pascal
1  gap := X;
2  repeat
3  ok := 1;
4  for i := 1 to N - gap do
5    if A[i] > A[i+gap] then
6      begin temp:=a[i];
7        A[i]:=A[i+gap];
8        A[i+gap] := temp;
9        ok := 0
10     end;
11 if gap div 2>1 then gap:=gap div 2 else gap:=1
12 until ok=1;

C/C++/Java
1  gap = X;
2  do
3  { ok = 1;
4  for (i = 1; i<= N – gap; i++)
5    if (A[i] > A[i+gap])
6    {  temp = A[i];
7       A[i] = A[i+gap];
8       A[i+gap] = temp;
9       ok = 0;
10   }
11 if (gap/2 > 1) gap=gap/2; else gap=1;
12 } while (ok == 0);

where i, N, X, gap, temp, ok are integers (int for C/C++, longint for Pascal).

While typing this code, little P forgot to copy line 11.

You are given the array to be sorted, A. A has N distinct elements, all between 1 and N. You are asked to find all the values X for which the algorithm (without line 11) sorts A. We call these X values to be valid.

Input

The input has 2 lines. The first line has one integer, N. The next line describes A: N integers separated by one space.

    - 1 < N < 500000
    - 1 <= X <= N-1

Output

The output should have the number of valid values X on the first line. The second line should have all the valid values X, separated by one space. They should be sorted in ascending order.

Constraints

Time limit: 3 seconds
Memory limit: 64 megabytes

Examples

input
6
4 2 6 1 5 3

output
2
1 3

N is 6 and A is: 4, 2, 6, 1, 5, 3. Valid values for X are:
  - X = 1, we swap the numbers on the following positions
      (1,2), (3,4), (4,5), (5,6), (2,3), (4,5), (1,2), (3,4);
  - X = 3, we swap the numbers on the following positions (1,4), (3,6).