Lizard Era: Beginning

题意翻译

有$n(n \leqslant 25)$个任务和三个人,每次任务给出每个人能得到的值,每次任务选两个人,使$n$个任务结束后三个人得到的值是一样的,且尽量大。输出每次要派哪两个人,如果不行输出$Impossible$。

题目描述

In the game Lizard Era: Beginning the protagonist will travel with three companions: Lynn, Meliana and Worrigan. Overall the game has $ n $ mandatory quests. To perform each of them, you need to take exactly two companions. The attitude of each of the companions to the hero is an integer. Initially, the attitude of each of them to the hero of neutral and equal to 0. As the hero completes quests, he makes actions that change the attitude of the companions, whom he took to perform this task, in positive or negative direction. Tell us what companions the hero needs to choose to make their attitude equal after completing all the quests. If this can be done in several ways, choose the one in which the value of resulting attitude is greatest possible.

输入输出格式

输入格式


The first line contains positive integer $ n $ ( $ 1<=n<=25 $ ) — the number of important tasks. Next $ n $ lines contain the descriptions of the tasks — the $ i $ -th line contains three integers $ l_{i},m_{i},w_{i} $ — the values by which the attitude of Lynn, Meliana and Worrigan respectively will change towards the hero if the hero takes them on the $ i $ -th task. All the numbers in the input are integers and do not exceed $ 10^{7} $ in absolute value.

输出格式


If there is no solution, print in the first line "Impossible". Otherwise, print $ n $ lines, two characters is each line — in the $ i $ -th line print the first letters of the companions' names that hero should take to complete the $ i $ -th task ('L' for Lynn, 'M' for Meliana, 'W' for Worrigan). Print the letters in any order, if there are multiple solutions, print any of them.

输入输出样例

输入样例 #1

3
1 0 0
0 1 0
0 0 1

输出样例 #1

LM
MW
MW

输入样例 #2

7
0 8 9
5 9 -2
6 -8 -7
9 4 5
-4 -9 9
-4 5 2
-6 8 -7

输出样例 #2

LM
MW
LM
LW
MW
LM
LW

输入样例 #3

2
1 0 0
1 1 0

输出样例 #3

Impossible