LogiQuest

313. Set Bits for 0..N

EasyBitsDP

Print the number of set bits of every integer from 0 to n.

Input format

A single integer n.

Output format

n + 1 counts.

Example 1

Input

2

Output

0 1 1

Example 2

Input

5

Output

0 1 1 2 1 2

Constraints

0 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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