题目描述

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

The ICPC Seoul Regional Contest Scientific Committee must prepare a problemset consisting of $3n$ problems. The difficulty of each problem is represented by an integer from 1 to $n$, 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 $3n$ 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 $3n$ 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 $i$ ($1 \le i \le n$), each of the three members receives exactly one problem with difficulty $i$.
2. Jump Distribution Fairness: When using Jump Distribution, for every difficulty level $i$ ($1 \le i \le n$), 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 to $n$, inclusive.

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

输入格式

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

输出格式

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

2

1 2 1 2 1 2

4

1 2 3 4 1 4 2 3 1 3 4 2