It can be shown that any positive integer x can be uniquely represented as x = 1 + 2 + 4 + ... + 2 k - 1 + r , where k and r are integers, k ≥ 0 , 0 < r ≤ 2 k . Let's call that representation prairie partition of x . For example, the prairie partitions of 12 , 17 , 7 and 1 are: 17 = 1 + 2 + 4 + 8 + 2 , 7 = 1 + 2 + 4 , 1 = 1 . Alice took a sequence of positive integers (possibly with repeating elements), replaced every element with the sequence of summands in its prairie partition, arranged the resulting numbers in non-decreasing order and gave them to Borys. Now Borys wonders how many elements Alice's original sequence could contain. Find all possible options! The first line contains a single integer n ( 1 ≤ n ≤ 10 5 ) — the number of numbers given from Alice to Borys. The second line contains n integers a 1 , a 2 , ..., a n ( 1 ≤ a i ≤ 10 12 ; a 1 ≤ a 2 ≤ ... ≤ a n ) — the numbers given from Alice to Borys. Output, in increasing order , all possible values of m such that there exists a sequence of positive integers of length m such that if you replace every element with the summands in its prairie partition and arrange the resulting numbers in non-decreasing order, you will get the sequence given in the input. If there are no such values of m , output a single integer -1 . In the first example, Alice could get the input sequence from 6, 20 as the original sequence. In the second example, Alice's original sequence could be either 4, 5 or 3, 3, 3 .