C. KiaKio and Energy Intervals
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Kia and Kio found a glowing array $$$a_1, a_2, \ldots, a_n$$$ inside a crystal terminal in the ruins of an ancient digital kingdom.

The terminal works like this. Kia picks a segment of the array: any two indices $$$l$$$ and $$$r$$$ with $$$l \lt r$$$ (so the segment always has at least two elements). Kio then finds the strongest energy in that segment, $$$m = \max\left(a_l, a_{l+1}, \ldots, a_r\right)$$$, and the terminal masks every element of the segment with $$$m$$$ (bitwise AND), then fuses the results together (bitwise XOR):

$$$$$$ (a_l \,\&\, m)\oplus(a_{l+1} \,\&\, m)\oplus\cdots\oplus(a_r \,\&\, m). $$$$$$

That number is the energy released.

Kia wants the strongest possible blast. Over all valid segments $$$(l, r)$$$, what is the largest energy the terminal can produce?

Here, $$$\&$$$ denotes the bitwise AND operation, and $$$\oplus$$$ denotes the bitwise XOR operation.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2\cdot10^5$$$) — the size of the array.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$0 \le a_i \lt 2^{18}$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

Output

For each test case, print a single integer — the maximum possible value of

$$$$$$ (a_l \,\&\, m)\oplus(a_{l+1} \,\&\, m)\oplus\cdots\oplus(a_r \,\&\, m) $$$$$$

among all pairs $$$(l,r)$$$ satisfying $$$l \lt r$$$.

Example
Input
4
5
1 7 3 7 2
3
3 1 2
5
1 5 2 3 4
4
3 5 2 6
Output
6
2
5
5
Note

In the first test case, one optimal interval is $$$l=1$$$ and $$$r=2$$$. The maximum element in this interval is $$$m=7$$$.

The value becomes $$$(1\,\& \,7)\oplus(7\,\&\,7) = 6$$$.