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# 1998. GCD Sort of an Array

<https://leetcode.com/problems/gcd-sort-of-an-array>

## Description

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:**

* `1 <= nums.length <= 3 * 104`
* `2 <= nums[i] <= 105`

## ac

```java
```