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Ural Championship 2012

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J. Space Recon

Time limit: 1.0 second
Memory limit: 64 MB
After the end of the Third Galactic War the Belt of Orion has become one of the most peaceful sectors of the Galaxy. Not even space pirates remained in this sector after the enemy was defeated, but the Third Galactic Fleet still kept constant watch over it.
Scout ship Macros has been hanging on the stationary orbit near Alnitak for the last three months. The captain was sitting in his cabin, sipping tea slowly and enjoying the bluish glow of the gas giant, when the advisor came to him.
“Sir, our drones have discovered a previously unknown planet. Moreover, it seems, that it is very close to their course. If one of the drones bumps it, we are going to have problems. What shall we do, sir?”
The captain calmly took the last sip and said:
“There are no ifs. You should know the exact route of your drones as well as the coordinates of the planet. Find out whether this planet actually interferes with the mission, and then we decide what measures to take.”
“Yes, sir!”
Observation drones always fly in pairs. Both drones fly at the same speed in parallel straight lines. The drones communicate through direct laser beam. As soon as one of the drones stops receiving a beam from another, it interprets this fact as a possible enemy attack, stops immediately and sends the alarm signal to the main scout ship.


The first line contains integers xp, yp, zp, rp that are coordinates of the center of discovered planet and its radius. The second and the third line contain integers xi, yi, zi that are coordinates of the first and the second drone in a pair respectively. The coordinates of the drones are different. The fourth line contains integers xv, yv, zv that are components of the drones' velocity vector. No input value exceeds 105 in absolute value. rp > 0, and at least one of the integers xv, yv, zv is not zero. It is guaranteed that at the initial time drones operated normally.


If at least one of the drones bumps the planet, output “Crash”. If both drones stop and send alarm signals, output “Warning”. Otherwise, output “False alarm”. When the drone is flying at a tangent to the planet it bumps the planet. If the laser beam touches the planet the connection between drones is lost.


0 0 0 1
2 0 0
3 0 0
-1 0 0
0 0 0 1
2 0 0
0 2 0
-1 -1 0
0 0 0 1
2 0 0
3 -1 0
1 1 0
False alarm
Problem Author: Pavel Atnashev (prepared by Daniil Ayzenshteyn)
Problem Source: Ural Championship 2012
To submit the solution for this problem go to the Problem set: 1909. Space Recon