Boring Card Game

题意翻译

6n张牌，**顺序排列**，两人轮流操作，每次操作可以选择**连续**的三张牌放入自己的口袋中，给出第一个人**最后**得到的牌，构造合法的**操作顺序**，使得第一个人最后得到的牌为输入给定的牌。

题目描述

When they are bored, Federico and Giada often play the following card game with a deck containing $ 6n $ cards. Each card contains one number between $ 1 $ and $ 6n $ and each number appears on exactly one card. Initially the deck is sorted, so the first card contains the number $ 1 $ , the second card contains the number $ 2 $ , $ \dots $ , and the last one contains the number $ 6n $ . Federico and Giada take turns, alternating; Federico starts. In his turn, the player takes $ 3 $ contiguous cards from the deck and puts them in his pocket. The order of the cards remaining in the deck is not changed. They play until the deck is empty (after exactly $ 2n $ turns). At the end of the game both Federico and Giada have $ 3n $ cards in their pockets. You are given the cards in Federico's pocket at the end of the game. Describe a sequence of moves that produces that set of cards in Federico's pocket.

输入输出格式

输入格式

The first line of the input contains one integer $ n $ ( $ 1\le n \le 200 $ ). The second line of the input contains $ 3n $ numbers $ x_1, x_2,\ldots, x_{3n} $ ( $ 1 \le x_1 < x_2 <\ldots < x_{3n} \le 6n $ ) – the cards in Federico's pocket at the end of the game. It is guaranteed that for each test there is at least one sequence of moves that produces such set of cards in Federico's pocket.

输出格式

Print $ 2n $ lines, each containing $ 3 $ integers. The $ i $ -th line should contain, in increasing order, the integers $ a_i<b_i<c_i $ written on the three cards taken by the player during the $ i $ -th turn (so taken by Federico if $ i $ is odd and by Giada if $ i $ is even). If there is more than one possible sequence of moves, you can print any.

输入输出样例

输入样例 #1

2
2 3 4 9 10 11

输出样例 #1

9 10 11
6 7 8
2 3 4
1 5 12

输入样例 #2

5
1 2 3 4 5 9 11 12 13 18 19 20 21 22 23

输出样例 #2

19 20 21
24 25 26
11 12 13
27 28 29
1 2 3
14 15 16
18 22 23
6 7 8
4 5 9
10 17 30

说明

Explanation of the first testcase: Initially the deck has $ 12 = 2\cdot 6 $ sorted cards, so the deck is $ [1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9\ 10\ 11\ 12] $ . - During turn $ 1 $ , Federico takes the three cards $ [9\ 10\ 11] $ . After his move, the deck is $ [1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 12] $ . - During turn $ 2 $ , Giada takes the three cards $ [6\ 7\ 8] $ . After her move, the deck is $ [1\ 2\ 3\ 4\ 5\ 12] $ . - During turn $ 3 $ , Federico takes the three cards $ [2\ 3\ 4] $ . After his move, the deck is $ [1\ 5\ 12] $ . - During turn $ 4 $ , Giada takes the three cards $ [1\ 5\ 12] $ . After her move, the deck is empty. At the end of the game, the cards in Federico's pocket are $ [2\ 3\ 4\ 9\ 10\ 11] $ and the cards in Giada's pocket are $ [1\ 5\ 6\ 7\ 8\ 12] $ .

题意翻译

6n张牌，**顺序排列**，两人轮流操作，每次操作可以选择**连续**的三张牌放入自己的口袋中，给出第一个人**最后**得到的牌，构造合法的**操作顺序**，使得第一个人最后得到的牌为输入给定的牌。