#883 MEXOR

Statement

Statement language

You are given an integer sequence $A_1,A_2,\cdots,A_N$ .

The $\mathrm{MEX}$ of a sequence is the smallest nonnegative integer that does not appear in the sequence. The symbol $\oplus$ denotes bitwise XOR.

Choose integers $0=p_0<p_1<\cdots<p_k=N$ to partition the sequence into nonempty contiguous segments. For each segment, define

B_i=\mathrm{MEX}(A_{p_{i-1}+1},A_{p_{i-1}+2},\cdots,A_{p_i}).

Find the maximum possible value of $B_1\oplus B_2\oplus\cdots\oplus B_k$ .

The input is given from Standard Input in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, print the maximum possible XOR value on a separate line.

#	Score	Constraints
1	6	$N\le20$ , $\sum N\le 500$
2	21	$N\le100$ ,

Sample 1

Input

4
3
2 1 0
4
0 0 1 1
5
2 2 2 2 2
6
0 2 0 1 0 2

Output

Sample 2

Input

3
2
0 0
4
0 1 0 1
7
0 2 1 0 1 3 2

Output

1
3
7