34872번 - Triple Fairness 스페셜 저지다국어

문제

This problem adopts exactly the same definition of Fair Problemset as Problem H, “Fair Problemset”.

ICPC is a team competition. Each team has three members. At the beginning of a contest, most teams divide the 3ドルn$ problem evenly. They use one of two common methods to distribute problems:

1. Sequential Distribution: Each member takes a contiguous block of $n$ problems from the set of 3ドルn$ problems. Specifically, the first member takes problems 1,ドル \cdots , n,ドル the second member takes problems $n + 1, \cdots , 2n,ドル and the third member takes problems 2ドルn + 1, \cdots , 3n$.
2. Jump Distribution: Each member takes problems with indices that have the same remainder when divided by 3ドル$ from the set of 3ドルn$ problems. Specifically, the first member takes problems 1,ドル 4, 7, \cdots , 3n − 2,ドル the second member takes problems 2,ドル 5, 8, \cdots , 3n − 1,ドル and the third member takes problems 3,ドル 6, 9, \cdots , 3n$.

The ICPC Seoul Regional Contest Scientific Committee must prepare a problemset consisting of 3ドルn$ problems. The difficulty of each problem is represented by an integer from 1ドル$ to $n,ドル inclusive. For each difficulty, there are exactly three problems with that difficulty. Thus, the arrangement of difficulties in the problemset can be viewed as a difficulty sequence of length 3ドルn$ containing three problems of each of the $n$ difficulty levels.

To prevent any advantage or disadvantage for a team based on their chosen problem distribution method, the ICPC Seoul Regional Contest Scientific Committee has defined a standard called a Fair Problemset. A difficulty sequence of length 3ドルn$ is called a Fair Problemset if it satisfies both of the following conditions:

1. Sequential Distribution Fairness: When using Sequential Distribution, for every difficulty level $i$ (1ドル ≤ i ≤ n$), each of the three members receives exactly one problem with difficulty $i$.
2. Jump Distribution Fairness: When using Jump Distribution, for every difficulty level $i$ (1ドル ≤ i ≤ n$), each of the three members receives exactly one problem with difficulty $i$.

In other words, regardless of which of the two methods is chosen, each team member must be assigned exactly one problem for each difficulty level from 1ドル$ to $n,ドル inclusive.

Given a positive integer $n,ドル write a program to find any Fair Problemset sequence of length 3ドルn$.

입력

Your program is to read from standard input. The input consists of exactly one line. The line contains an integer $n$ (1ドル ≤ n ≤ 200$; $n$ is not divisible by 3ドル$). It can be shown that for every valid input, there exists at least one Fair Problemset sequence of length 3ドルn$.

출력

Your program is to write to standard output. Print exactly one line consisting of 3ドルn$ space-separated positive integers, representing a Fair Problemset sequence of length 3ドルn$. Any valid Fair Problemset sequence of length 3ドルn$ will be accepted.

제한

노트