#863 (Insert Name Here) Sequence

Statement

Statement language

You are given an integer $N$ . Construct a permutation $P$ using every integer from $1$ to $N$ exactly once.

The score $A$ of $P$ is the sum of the bitwise OR of every adjacent pair:

A=\sum_{i=1}^{N-1}(P_i\mathbin{\mathrm{OR}}P_{i+1}).

For $N=1$ , define $A=0$ .

Let

S=\frac{N(N+1)}2

be the sum of the integers from $1$ to $N$ . Construct a permutation $P$ satisfying $A>S$ .

The input is given in the following format:

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

For each test case, print a permutation $P_1,P_2,\ldots,P_N$ satisfying the condition on one line.

#	Score	Constraints
1	15	$N\leq3$ .
2	85	No additional constraints.

Input

Output

-1
-1
1 2 4 3 5