Given an array of positive integers nums, return the number of distinct prime factors in the product of the elements of nums.
Note that:
\n\n1 is called prime if it is divisible by only 1 and itself.val1 is a factor of another integer val2 if val2 / val1 is an integer.\n
Example 1:
\n\n\nInput: nums = [2,4,3,7,10,6]\nOutput: 4\nExplanation:\nThe product of all the elements in nums is: 2 * 4 * 3 * 7 * 10 * 6 = 10080 = 25 * 32 * 5 * 7.\nThere are 4 distinct prime factors so we return 4.\n\n\n
Example 2:
\n\n\nInput: nums = [2,4,8,16]\nOutput: 1\nExplanation:\nThe product of all the elements in nums is: 2 * 4 * 8 * 16 = 1024 = 210.\nThere is 1 distinct prime factor so we return 1.\n\n\n
\n
Constraints:
\n\n1 <= nums.length <= 1042 <= nums[i] <= 1000给你一个正整数数组 nums ，对 nums 所有元素求积之后，找出并返回乘积中 不同质因数 的数目。
注意：
\n\n1 且仅能被 1 及自身整除的数字。val2 / val1 是一个整数，则整数 val1 是另一个整数 val2 的一个因数。\n\n
示例 1：
\n\n输入：nums = [2,4,3,7,10,6]\n输出：4\n解释：\nnums 中所有元素的乘积是：2 * 4 * 3 * 7 * 10 * 6 = 10080 = 25 * 32 * 5 * 7 。\n共有 4 个不同的质因数，所以返回 4 。\n\n\n
示例 2：
\n\n输入：nums = [2,4,8,16]\n输出：1\n解释：\nnums 中所有元素的乘积是：2 * 4 * 8 * 16 = 1024 = 210 。\n共有 1 个不同的质因数，所以返回 1 。\n\n
\n\n
提示：
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