XOR Necklace

Frograms, Inc. has been developing necklaces with a new design and feature. Every programmer at Frograms now wears one. A necklace is made of several beads strung on a thread. Each bead has an integer from $0$ to $10^9$ (inclusive).

Most programmers left for summer vacation, so only a few remain in the office today. They decided to play a game with their necklaces to decide who buys lunch. For each pair of consecutive beads, take the sum of their numbers. A programmer's score is the XOR ($\oplus$) of all those sums. The programmer with the lowest score loses.

If there are $N$ beads with values $A\_1$, $A\_2$, $\cdots$, $A\_N$ in order around the necklace, the score is:

$(A\_1 \oplus A\_2) + (A\_2 \oplus A\_3) + \dots + (A\_{N-1} \oplus A\_N) + (A\_N \oplus A\_1)$

You will cheat by removing zero or more beads to maximize the score. What is the maximum score you can get by removing some of the beads? You cannot reorder the beads, and the necklace must keep at least two beads.

The input consists of $T$ test cases. The first line contains $T$.

Each test case starts with a line containing a single integer $N$ ($2 \le N \le 500$), the number of beads. The next line contains $N$ integers $A\_1$, $A\_2$, $\cdots$, $A\_N$, separated by single spaces.

For each test case, print the maximum score you can get on a single line.