Counting Bits

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.

Examples

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 <= 10^5

Follow up: Write a solution in linear time O(n) and use only O(n) extra space.