B"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) 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 <= k <= 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 <= 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. 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. 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. "...