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Ural Championship 2008

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G. National Project “Trams”

Time limit: 0.5 second
Memory limit: 64 MB
President has declared the development of tram service a priority national project. As a part of this project, Yekaterinburg will receive enough budget funds to carry out a complete reconstruction of the city's tram network.
There are 2n tram stops in Yekaterinburg. In the course of reconstruction, the stops will be left in their places and no new stops will be built, but new tram railways will be laid so that it will be possible to go by tram from every tram stop to any other tram stop without any intermediate stops.
Having studied messages at the tram forum, the city authorities found out that citizens would be satisfied with the reconstruction only if for every pair of tram stops there would be a tram route connecting these stops without any intermediate stops. It is clear that the network of n(2n − 1) routes consisting of only two stops each satisfies this requirement. However, Yekaterinburg Mayor wants exactly n routes to be left after the reconstruction, and each tram must make exactly 2n stops (including the final ones) on its route. Trams must go along these routes in both directions. Suggest a plan of reconstruction that will satisfy both citizens and Mayor.


The only input line contains the integer n, 1 ≤ n ≤ 100.


Output n lines describing tram routes. Each route is a sequence of integers in the range from 1 to 2n separated by a space. A route may go through a stop several times. If the problem has several solutions, you may output any of them. If there is no solution, output one line containing the number −1.


1 6 2 1 3 4
2 3 6 5 4 6
5 1 4 2 5 3
Problem Author: Alexander Ipatov (idea — Magaz Asanov)
Problem Source: The 12th Urals Collegiate Programing Championship, March 29, 2008
To submit the solution for this problem go to the Problem set: 1614. National Project “Trams”