Given an integer `n`, return an array `ans` of length `n + 1` such that for each `i` (`0 <= i <= n`), `ans[i]` is the number of `1`'s in the binary representation of `i`.

Example 1:

    Input: n = 2
    Output: [0,1,1]
    Explanation:
    0 --> 0
    1 --> 1
    2 --> 10

Example 2:

    Input: n = 5
    Output: [0,1,1,2,1,2]
    Explanation:
    0 --> 0
    1 --> 1
    2 --> 10
    3 --> 11
    4 --> 100
    5 --> 101

Constraints:

- `0 <= n <= 105`

Follow up:

- It is very easy to come up with a solution with a runtime of `O(n log n)`. Can you do it in linear time `O(n)` and possibly in a single pass?
- Can you do it without using any built-in function (i.e., like `__builtin_popcount` in C++)?