1998 - GCD Sort of an Array.

Hard

You are given an integer array nums, and you can perform the following operation any number of times on nums:

• Swap the positions of two elements nums[i] and nums[j] if gcd(nums[i], nums[j]) > 1 where gcd(nums[i], nums[j]) is the greatest common divisor of nums[i] and nums[j].

Return true if it is possible to sort nums in non-decreasing order using the above swap method, or false otherwise.

Example 1:

Input: nums = 7,21,3

Output: true

Explanation: We can sort 7,21,3 by performing the following operations:

• Swap 7 and 21 because gcd(7,21) = 7. nums = **21** , **7** ,3

• Swap 21 and 3 because gcd(21,3) = 3. nums = **3** ,7, **21**

Example 2:

Input: nums = 5,2,6,2

Output: false

Explanation: It is impossible to sort the array because 5 cannot be swapped with any other element.

Example 3:

Input: nums = 10,5,9,3,15

Output: true We can sort 10,5,9,3,15 by performing the following operations:

• Swap 10 and 15 because gcd(10,15) = 5. nums = **15** ,5,9,3, **10**

• Swap 15 and 3 because gcd(15,3) = 3. nums = **3** ,5,9, **15** ,10

• Swap 10 and 15 because gcd(10,15) = 5. nums = 3,5,9, **10** , **15**

Constraints:

• <code>1 <= nums.length <= 3 * 10⁴</code>

• <code>2 <= numsi<= 10⁵</code>