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 $$$i$$$ ($$$1 \le i \le n$$$) $$$a_i = x_{(i-1)\bmod k} + a_{i-1}$$$, where $$$p \bmod q$$$ denotes the remainder of division $$$p$$$ by $$$q$$$.
For example, if the $$$x = [1, 2, 3]$$$ and $$$n = 5$$$, then:
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 $$$1 \le k \le n$$$, help him and find all possible values of $$$k$$$ — possible lengths of the lost array.
The first line contains exactly one integer $$$n$$$ ($$$1 \le n \le 1000$$$) — the length of the array $$$a$$$, excluding the element $$$a_0$$$.
The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^6$$$).
Note that $$$a_0$$$ is always $$$0$$$ and is not given in the input.
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.
5
1 2 3 4 5
5
1 2 3 4 5
5
1 3 5 6 8
2
3 5
3
1 5 3
1
3
In the first example, any $$$k$$$ is suitable, since $$$a$$$ is an arithmetic progression.
Possible arrays $$$x$$$:
In the second example, Bajtek's array can have three or five elements.
Possible arrays $$$x$$$:
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.
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