You are given a $0$ indexed integer array nums of length n.

You can perform the following operation any number of times:

• Select an index i that has not been chosen previously.

• Choose a prime number p that is strictly less than nums[i].

• Subtract p from nums[i].

Return true if you can make nums strictly increasing after applying the operations, or false otherwise.

Note: An array is considered strictly increasing if nums[i - 1] $<$ nums[i] for all $1 \leq$ i $<$ n.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 1000$

• nums.length $==$ n

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.