Nene and Tsukasa are battling it out in Rui's newly made video game, Nene-Robo Adventures! The game is played in a city of
The game starts with Nene-Robo standing atop the building with height
Before the game starts, Rui thinks it would be funny if the arrangement of the buildings allowed Nene to win even if both players played optimally. He is curious about the lexicographically smallest permutation of heights with this property. As the only bandmate not yet involved in this scheme, please inform Rui of this arrangement or determine that no such arrangement exists.
To ensure the integrity of your solution, there may be up to
Constraints
The sum of
Subtask 1 [40%]
Subtask 2 [60%]
No additional constraints.
Input Specification
The first line contains an integer
The next
Output Specification
For each test case, if there is no permutation of the heights that guarantees Nene's win with optimal play, output
Sample Input
2
3
2
Sample Output
1 2 3
-1
Explanation
For the first test case, Nene can choose to move Nene-Robo from building
For the second test case, both
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