Lucky Permutation Triple

题意翻译

bike认为[0,n-1]中的每个数出现一次为一个数列（长度为n），三个长度为n的数列，且叫做幸运排列三元组，要你找出这样的三元组，若没有输出-1，若有多种答案输出其中一个答案

题目描述

Bike is interested in permutations. A permutation of length $ n $ is an integer sequence such that each integer from 0 to $ (n-1) $ appears exactly once in it. For example, $ [0,2,1] $ is a permutation of length 3 while both $ [0,2,2] $ and $ [1,2,3] $ is not. A permutation triple of permutations of length $ n $ $ (a,b,c) $ is called a Lucky Permutation Triple if and only if . The sign $ a_{i} $ denotes the $ i $ -th element of permutation $ a $ . The modular equality described above denotes that the remainders after dividing $ a_{i}+b_{i} $ by $ n $ and dividing $ c_{i} $ by $ n $ are equal. Now, he has an integer $ n $ and wants to find a Lucky Permutation Triple. Could you please help him?

输入输出格式

输入格式

The first line contains a single integer $ n $ $ (1<=n<=10^{5}) $ .

输出格式

If no Lucky Permutation Triple of length $ n $ exists print -1. Otherwise, you need to print three lines. Each line contains $ n $ space-seperated integers. The first line must contain permutation $ a $ , the second line — permutation $ b $ , the third — permutation $ c $ . If there are multiple solutions, print any of them.

输入输出样例

输入样例 #1

5

输出样例 #1

1 4 3 2 0
1 0 2 4 3
2 4 0 1 3

输入样例 #2

2

输出样例 #2

-1

说明

In Sample 1, the permutation triple $ ([1,4,3,2,0],[1,0,2,4,3],[2,4,0,1,3]) $ is Lucky Permutation Triple, as following holds: - ; - ; - ; - ; - . In Sample 2, you can easily notice that no lucky permutation triple exists.