You are given a binary string binary consisting of characters '$0$' and '$1$'.

You may apply either of the following operations on binary any number of times:

• Change any substring "$00$" to "$10$"

• Change any substring "$10$" to "$01$"

Return the maximum binary string that can be formed after applying any number of operations. A binary string is considered larger than another if its base $2$ value is greater.

Constraints:

• $1 \leq$ binary.length $\leq 10^5$

• binary consists only of '$0$' and '$1$'.

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.