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F. Comfortably Numb

time limit per test

8 secondsmemory limit per test

1024 megabytesinput

standard inputoutput

standard 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.

Input

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 $$$2 \cdot 10^5$$$.

Output

For each test case, print one integer — the maximum numbness over all subarrays of the given array.

Example

Input

251 2 3 4 5310 47 52

Output

7 47

Note

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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