Partition Numbers by Distinct Frequencies

Given an integer array nums, all occurrences of the same value must belong to the same partition. Each distinct value forms exactly one partition, whose size equals that value's frequency in the original array. Determine whether the array can be partitioned such that no two different partitions have the same size. Equivalently, determine whether the frequencies of all distinct values in nums are pairwise distinct. Example 1: Input: nums = [1, 2, 3, 4, 2, 3, 3, 4, 4, 4] Output: true Explanation: The frequencies of 1, 2, 3, and 4 are 1, 2, 3, and 4 respectively. All partition sizes are distinct. Example 2: Input: nums = [1, 2, 3] Output: false Explanation: 1, 2, and 3 all occur once, so multiple partitions have size 1. Constraints: 1 <= len(nums) <= 200,000 nums[i] is an integer. Example Input 10 1 2 3 4 2 3 3 4 4 4 Output true