Given a non negative integer num, return its binary encoding string.

The encoding maps each integer to a binary string by ordering them first by length and then lexicographically:

• $0$ maps to ""

• $1$ maps to "0"

• $2$ maps to "1"

• $3$ maps to "00"

• $4$ maps to "01"

• $5$ maps to "10"

• $6$ maps to "11"

• $7$ maps to "000"

Constraints:

• $0 \leq$ num $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.