write a go solution for Description:
Bajtek, known for his unusual gifts, recently got an integer array x_0,x_1,ldots,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)bmodk+a_i-1, where pbmodq 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_0bmod3+a_0=x_0+0=1,
- a_2=x_1bmod3+a_1=x_1+1=3,
- a_3=x_2bmod3+a_2=x_2+3=6,
- a_4=x_3bmod3+a_3=x_0+6=7,
- a_5=x_4bmod3+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 Format:
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,ldots,a_n (1<=a_i<=10^6).

Note that a_0 is always 0 and is not given in the input.

Output Format:
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.

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.. Output only the code with no comments, explanation, or additional text.