2601 - Prime Subtraction Operation.

Medium

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

You can perform the following operation as many times as you want:

• Pick an index i that you haven’t picked before, and pick a prime p strictly less than nums[i], then subtract p from nums[i].

Return true if you can make nums a strictly increasing array using the above operation and false otherwise.

A strictly increasing array is an array whose each element is strictly greater than its preceding element.

Example 1:

Input: nums = 4,9,6,10

Output: true

Explanation: In the first operation: Pick i = 0 and p = 3, and then subtract 3 from nums0, so that nums becomes 1,9,6,10. In the second operation: i = 1, p = 7, subtract 7 from nums1, so nums becomes equal to 1,2,6,10. After the second operation, nums is sorted in strictly increasing order, so the answer is true.

Example 2:

Input: nums = 6,8,11,12

Output: true

Explanation: Initially nums is sorted in strictly increasing order, so we don't need to make any operations.

Example 3:

Input: nums = 5,8,3

Output: false

Explanation: It can be proven that there is no way to perform operations to make nums sorted in strictly increasing order, so the answer is false.

Constraints:

• 1 <= nums.length <= 1000

• 1 <= nums[i] <= 1000

• nums.length == n