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![](http://codeforces.com/predownloaded/10/4a/104a8a429d0985a2c14e7bf3482a92b9c849276c.png)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 ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF303A/bd0aa9c2cfa6e7dfc9681d8813c19703f16dbc42.png). 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:
- ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF303A/6124807a627fcd49ae8fab0d91c9fa90239af12b.png);
- ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF303A/598c5f3180986ca384de6df51e7cb84d8ea4e757.png);
- ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF303A/66b44a153ea212b6a13d195278ac6715ce383457.png);
- ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF303A/dd4f61ae15bc4151613d0da9fe47b466aa949e1e.png);
- ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF303A/0ea0fc069d3b3e3451d396fd4b6ef6f3d9456398.png).
In Sample 2, you can easily notice that no lucky permutation triple exists.