from typing import List


class Solution:
    def gcdSort(self, nums: List[int]) -> bool:
        # 并查集
        def find(x):
            if parent[x] != x:
                parent[x] = find(parent[x])
            return parent[x]

        def union(x, y):
            parent[find(x)] = find(y)

        # 获取一个数的所有质因数
        def get_prime_factors(n):
            factors = set()
            i = 2
            while i * i <= n:
                while n % i == 0:
                    factors.add(i)
                    n //= i
                i += 1
            if n > 1:
                factors.add(n)
            return factors

        # 初始化并查集
        max_num = max(nums)
        parent = list(range(max_num + 1))

        # 对每个数字，将其与其质因数连接
        for num in nums:
            for prime in get_prime_factors(num):
                union(num, prime)

        # 检查排序后的数组是否可以通过交换得到
        sorted_nums = sorted(nums)
        for i in range(len(nums)):
            if find(nums[i]) != find(sorted_nums[i]):
                return False

        return True