F. Comfortably Numb
bitmasks; data structures; divide and conquer; strings; trees
You are given an array \(a\) consisting of \(n\) non-negative integers.The numbness of a subarray \(a_l, a_{l+1}, \ldots, a_r\) (for arbitrary \(l \leq r\)) is defined as $$$\(\max(a_l, a_{l+1}, \ldots, a_r) \oplus (a_l \oplus a_{l+1} \oplus \ldots \oplus a_r),\)\( where \)\oplus$$$ denotes the bitwise XOR operation.Find the maximum numbness over all subarrays.
Each test contains multiple test cases. The first line contains the number of test cases \(t\) (\(1 \le t \le 1000\)). The description of the test cases follows.The first line of each test case contains a single integer \(n\) (\(1 \leq n \leq 2 \cdot 10^5\)).The second line of each test case contains \(n\) integers \(a_1, a_2, \ldots, a_n\) (\(0 \leq a_i \leq 10^9\)).It is guaranteed that the sum of \(n\) over all test cases does not exceed \(2 \cdot 10^5\).
For each test case, print one integer — the maximum numbness over all subarrays of the given array.
For the first test case, for the subarray \([3, 4, 5]\), its maximum value is \(5\). Hence, its numbness is \(3 \oplus 4 \oplus 5 \oplus 5\) = \(7\). This is the maximum possible numbness in this array.In the second test case the subarray \([47, 52]\) provides the maximum numbness.