You are given an array of positive integers nums.

Alice and Bob play a game where Alice can choose to collect either all single digit numbers or all double digit numbers from nums. Bob receives all the remaining numbers.

Alice wins if the sum of her chosen numbers is strictly greater than the sum of Bob’s numbers.

Return true if Alice can win the game, or false otherwise.

Constraints:

• $1 \leq$ nums.length $\leq 100$

• $1 \leq$ nums[i] $\leq 99$

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.