You are given a 0-indexed 2D integer array items of length n and an integer k.
items[i] = [profiti, categoryi], where profiti and categoryi denote the profit and category of the ith item respectively.
Let's define the elegance of a subsequence of items as total_profit + distinct_categories2, where total_profit is the sum of all profits in the subsequence, and distinct_categories is the number of distinct categories from all the categories in the selected subsequence.
Your task is to find the maximum elegance from all subsequences of size k in items.
Return an integer denoting the maximum elegance of a subsequence of items with size exactly k.
Note: A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements' relative order.
\n\n\n
Example 1:
\n\n\nInput: items = [[3,2],[5,1],[10,1]], k = 2\nOutput: 17\nExplanation: In this example, we have to select a subsequence of size 2.\nWe can select items[0] = [3,2] and items[2] = [10,1].\nThe total profit in this subsequence is 3 + 10 = 13, and the subsequence contains 2 distinct categories [2,1].\nHence, the elegance is 13 + 22 = 17, and we can show that it is the maximum achievable elegance. \n\n\n
Example 2:
\n\n\nInput: items = [[3,1],[3,1],[2,2],[5,3]], k = 3\nOutput: 19\nExplanation: In this example, we have to select a subsequence of size 3. \nWe can select items[0] = [3,1], items[2] = [2,2], and items[3] = [5,3]. \nThe total profit in this subsequence is 3 + 2 + 5 = 10, and the subsequence contains 3 distinct categories [1,2,3]. \nHence, the elegance is 10 + 32 = 19, and we can show that it is the maximum achievable elegance.\n\n
Example 3:
\n\n\nInput: items = [[1,1],[2,1],[3,1]], k = 3\nOutput: 7\nExplanation: In this example, we have to select a subsequence of size 3. \nWe should select all the items. \nThe total profit will be 1 + 2 + 3 = 6, and the subsequence contains 1 distinct category [1]. \nHence, the maximum elegance is 6 + 12 = 7.\n\n
\n
Constraints:
\n\n1 <= items.length == n <= 105items[i].length == 2items[i][0] == profitiitems[i][1] == categoryi1 <= profiti <= 1091 <= categoryi <= n 1 <= k <= n给你一个长度为 n 的二维整数数组 items 和一个整数 k 。
items[i] = [profiti, categoryi]，其中 profiti 和 categoryi 分别表示第 i 个项目的利润和类别。
现定义 items 的 子序列 的 优雅度 可以用 total_profit + distinct_categories2 计算，其中 total_profit 是子序列中所有项目的利润总和，distinct_categories 是所选子序列所含的所有类别中不同类别的数量。
你的任务是从 items 所有长度为 k 的子序列中，找出 最大优雅度 。
用整数形式表示并返回 items 中所有长度恰好为 k 的子序列的最大优雅度。
注意：数组的子序列是经由原数组删除一些元素（可能不删除）而产生的新数组，且删除不改变其余元素相对顺序。
\n\n\n\n
示例 1：
\n\n\n输入：items = [[3,2],[5,1],[10,1]], k = 2\n输出：17\n解释：\n在这个例子中，我们需要选出长度为 2 的子序列。\n其中一种方案是 items[0] = [3,2] 和 items[2] = [10,1] 。\n子序列的总利润为 3 + 10 = 13 ，子序列包含 2 种不同类别 [2,1] 。\n因此，优雅度为 13 + 22 = 17 ，可以证明 17 是可以获得的最大优雅度。 \n\n\n
示例 2：
\n\n\n输入：items = [[3,1],[3,1],[2,2],[5,3]], k = 3\n输出：19\n解释：\n在这个例子中，我们需要选出长度为 3 的子序列。 \n其中一种方案是 items[0] = [3,1] ，items[2] = [2,2] 和 items[3] = [5,3] 。\n子序列的总利润为 3 + 2 + 5 = 10 ，子序列包含 3 种不同类别 [1, 2, 3] 。 \n因此，优雅度为 10 + 32 = 19 ，可以证明 19 是可以获得的最大优雅度。\n\n
示例 3：
\n\n\n输入：items = [[1,1],[2,1],[3,1]], k = 3\n输出：7\n解释：\n在这个例子中，我们需要选出长度为 3 的子序列。\n我们需要选中所有项目。\n子序列的总利润为 1 + 2 + 3 = 6，子序列包含 1 种不同类别 [1] 。\n因此，最大优雅度为 6 + 12 = 7 。\n\n
\n\n
提示：
\n\n1 <= items.length == n <= 105items[i].length == 2items[i][0] == profitiitems[i][1] == categoryi1 <= profiti <= 1091 <= categoryi <= n 1 <= k <= nk items (the top k most profitable items). 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