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

Input: nums = [1]-List[int]
Output: true-bool
Explanation: The array is already strictly increasing because it contains only one element, so no operations are needed.

Input: nums = [7, 10, 12, 15]-List[int]
Output: true-bool
Explanation: The array is already strictly increasing, so no operations are needed.

Input: nums = [8, 5, 9]-List[int]
Output: true-bool
Explanation: Subtract the prime number 5 from 8 to obtain [3, 5, 9], which is strictly increasing.

Input: nums = [2, 2]-List[int]
Output: false-bool
Explanation: There is no prime number strictly less than 2, so neither element can be changed. The equal values cannot form a strictly increasing array.

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:

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