CF59D Team Arrangement

Recently personal training sessions have finished in the Berland State University Olympiad Programmer Training Centre. By the results of these training sessions teams are composed for the oncoming team contest season. Each team consists of three people. All the students of the Centre possess numbers from $ 1 $ to $ 3n $ , and all the teams possess numbers from $ 1 $ to $ n $ . The splitting of students into teams is performed in the following manner: while there are people who are not part of a team, a person with the best total score is chosen among them (the captain of a new team), this person chooses for himself two teammates from those who is left according to his list of priorities. The list of every person's priorities is represented as a permutation from the rest of $ 3n-1 $ students who attend the centre, besides himself. You are given the results of personal training sessions which are a permutation of numbers from $ 1 $ to $ 3n $ , where the $ i $ -th number is the number of student who has won the $ i $ -th place. No two students share a place. You are also given the arrangement of the already formed teams in the order in which they has been created. Your task is to determine the list of priorities for the student number $ k $ . If there are several priority lists, choose the lexicographically minimal one.

The first line contains an integer $ n $ ( $ 1

Print $ 3n-1 $ numbers — the lexicographically smallest list of priorities for the student number $ k $ . The lexicographical comparison is performed by the standard < operator in modern programming languages. The list $ a $ is lexicographically less that the list $ b $ if exists such an $ i $ ( $ 1