F. Comfortably Numbtime limit per test8 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputYou 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.InputEach 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.OutputFor each test case, print one integer — the maximum numbness over all subarrays of the given array.ExampleInput
251 2 3 4 5310 47 52Output
7
47
NoteFor 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.
251 2 3 4 5310 47 52
7 47 
['bitmasks', 'data structures', 'divide and conquer', 'strings', 'trees', '*2400']