You are given an integer array nums.
Partition the array into three (possibly empty) subsequences A, B, and C such that every element of nums belongs to exactly one subsequence.
Your goal is to maximize the value of: XOR(A) + AND(B) + XOR(C)
where:
\n\nXOR(arr) denotes the bitwise XOR of all elements in arr. If arr is empty, its value is defined as 0.AND(arr) denotes the bitwise AND of all elements in arr. If arr is empty, its value is defined as 0.Return the maximum value achievable.
\n\nNote: If multiple partitions result in the same maximum sum, you can consider any one of them.
\n\n\n
Example 1:
\n\nInput: nums = [2,3]
\n\nOutput: 5
\n\nExplanation:
\n\nOne optimal partition is:
\n\nA = [3], XOR(A) = 3B = [2], AND(B) = 2C = [], XOR(C) = 0The maximum value of: XOR(A) + AND(B) + XOR(C) = 3 + 2 + 0 = 5. Thus, the answer is 5.
Example 2:
\n\nInput: nums = [1,3,2]
\n\nOutput: 6
\n\nExplanation:
\n\nOne optimal partition is:
\n\nA = [1], XOR(A) = 1B = [2], AND(B) = 2C = [3], XOR(C) = 3The maximum value of: XOR(A) + AND(B) + XOR(C) = 1 + 2 + 3 = 6. Thus, the answer is 6.
Example 3:
\n\nInput: nums = [2,3,6,7]
\n\nOutput: 15
\n\nExplanation:
\n\nOne optimal partition is:
\n\nA = [7], XOR(A) = 7B = [2,3], AND(B) = 2C = [6], XOR(C) = 6The maximum value of: XOR(A) + AND(B) + XOR(C) = 7 + 2 + 6 = 15. Thus, the answer is 15.
\n
Constraints:
\n\n1 <= nums.length <= 191 <= nums[i] <= 109给你一个整数数组 nums。
将数组划分为 三 个（可以为空）子序列 A、B 和 C，使得 nums 中的每个元素 恰好 属于一个子序列。
你的目标是 最大化 以下值：XOR(A) + AND(B) + XOR(C)
其中：
\n\nXOR(arr) 表示 arr 中所有元素的按位异或结果。如果 arr 为空，结果定义为 0。AND(arr) 表示 arr 中所有元素的按位与结果。如果 arr 为空，结果定义为 0。返回可实现的最 大 值。
\n\n注意: 如果有多种划分方式得到相同的 最大 和，你可以按其中任何一种划分。
\n子序列 是指一个数组通过删除一些或不删除任何元素，不改变剩余元素的顺序得到的元素序列。\n\n\n\n
示例 1:
\n\n输入: nums = [2,3]
\n\n输出: 5
\n\n解释:
\n\n一个最优划分是：
\n\nA = [3], XOR(A) = 3B = [2], AND(B) = 2C = [], XOR(C) = 0最大值为: XOR(A) + AND(B) + XOR(C) = 3 + 2 + 0 = 5。因此，答案是 5。
示例 2:
\n\n输入: nums = [1,3,2]
\n\n输出: 6
\n\n解释:
\n\n一个最优划分是：
\n\nA = [1], XOR(A) = 1B = [2], AND(B) = 2C = [3], XOR(C) = 3最大值为: XOR(A) + AND(B) + XOR(C) = 1 + 2 + 3 = 6。因此，答案是 6。
示例 3:
\n\n输入: nums = [2,3,6,7]
\n\n输出: 15
\n\n解释:
\n\n一个最优划分是：
\n\nA = [7], XOR(A) = 7B = [2,3], AND(B) = 2C = [6], XOR(C) = 6最大值为: XOR(A) + AND(B) + XOR(C) = 7 + 2 + 6 = 15。因此，答案是 15。
\n\n
提示:
\n\n1 <= nums.length <= 191 <= nums[i] <= 109B.",
"Let s = XOR of all elements not in B.",
"We want to choose a value x (a subset‐XOR of the \"remaining\" elements) to maximize x + (s XOR x).",
"Observe that x + (s XOR x) = s + 2 * (x AND ~s).",
"To do this efficiently, build a linear XOR basis over the values nums[j] & ~s for each index j not in B.",
"Finally, greedily extract the maximum x from that basis."
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