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NEERC 2012, Eastern subregional contest

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D. Titan Ruins: Alignment of Forces

Time limit: 1.0 second
Memory limit: 64 MB
`It seems that we're trapped,' said Soren when the door had suddenly shut behind him.
`It seems that I've heard this today at least five times. Don't panic, and let's think how we can get out,' Alba replied. `If there's a door, there's a way to open it. We only have to find this way. Can you see that crystal? I think it's somehow related to the door. Let's try and use it.'
However, all their efforts to use the crystal were in vain. All they'd managed to do was to open the door by a fraction of a millimeter.
`It seems that I've guessed it right,' Alba concluded. `But we don't have enough power to open the door.'
`Let's activate those two magic power generators. They're old and won't work at full capacity, but if they work together, maybe they'll produce enough power for the door to open.'
Each of the wizards can collect power from any generator and transfer it to the other wizard or to the crystal. Such transfers are only possible at distances not exceeding R. It remains to choose where to stand so as to transfer the power from both generators to the crystal.


The first line contains the integer R (1 ≤ R ≤ 104). In the second line you are given the integer coordinates x and y of the crystal (−104x, y ≤ 104). The third and fourth lines contain the integer coordinates xi, yi of the generators (−104xi, yi ≤ 104). These three points are pairwise different.


If Alba and Soren can't stand so as to transfer the power of both generators to the crystal, output “Death”. Otherwise, output the phrase “Now we have enough power” in the first line. In the following two lines output the coordinates of the points where the wizards should stand. The coordinates should be given with absolute or relative error of at most 10−5. If there are several possible variants, output any of them.


0 0
2 1
2 -1
Now we have enough power
1 0
2 0
0 0
2 1
2 -1
Now we have enough power
2 -1
0 0
0 0
5 0
0 5
Problem Author: Alexey Samsonov (prepared by Denis Mukhametianov)
Problem Source: NEERC 2012, Eastern subregional contest
To submit the solution for this problem go to the Problem set: 1913. Titan Ruins: Alignment of Forces