B. Lost Arraytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputBajtek, 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:  a_0 = 0,  a_1 = x_{0\bmod 3}+a_0=x_0+0=1,  a_2 = x_{1\bmod 3}+a_1=x_1+1=3,  a_3 = x_{2\bmod 3}+a_2=x_2+3=6,  a_4 = x_{3\bmod 3}+a_3=x_0+6=7,  a_5 = x_{4\bmod 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 \le k \le n, help him and find all possible values of k — possible lengths of the lost array.InputThe 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.OutputThe 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.ExamplesInput51 2 3 4 5Output51 2 3 4 5 Input51 3 5 6 8Output23 5 Input31 5 3Output13 NoteIn 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.
Input51 2 3 4 5
Output51 2 3 4 5 
['implementation', '*1200']