You are given an integer array deck where deck[i] represents the number written on the card at index i.

Determine whether you can choose an integer x where x $\geq 2$ such that the entire deck can be partitioned into $1$ or more groups satisfying the following conditions:

• Each group contains exactly x cards.

• All cards in each group have the same number.

Return true if such a partition exists, or false otherwise.

Constraints:

• $1 \leq$ deck.length $\leq 10^4$

• $0 \leq$ deck[i] $< 10^4$

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.