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USU Junior Championship March'2004

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E. Mars Satellites

Time limit: 1.0 second
Memory limit: 64 MB
Four artificial satellites travel in one plane along the areostationary orbit around Mars. They have code names A, B, C and D and travel exactly in this order. Venus’s scouts for military purposes (for what particular purpose they did not say) decided to find a distance between satellites C and D. All Mars satellites could measure distances to the other satellites, that is why all what is needed to do is to penetrate in the computer system of satellite C and measure the distance to satellite D (or vice versa). Nevertheless, Martians are not so stupid and have not very bad defense. That is why all what could Venus’s scouts do is to break the defense of satellites A and B (that were older models). They measured distances from satellites A and B to satellites C and D, but now they do not know how to find the distance from C to D using these measurements. You can help them.


There are 4 numbers: distances from A to D, from A to C, from B to D and from B to C in thousands kilometers (integers from 1 to 10000). Satellites can measure distance even through the planet and you may assume that orbit is a circle. Do not assume the radius of the orbit equal to 20392 km as it should be for the real areostationary orbit.


If it is impossible to find out the distance from C to D with these data, you should print "Impossible.", otherwise you are to print "Distance is X km.", where X is the required distance in kilometers (rounded to the integer number).


4 7 5 7
Distance is 5385 km.
Problem Author: Vladimir Yakovlev
Problem Source: IX Open Collegiate Programming Contest of the High School Pupils (13.03.2004)
To submit the solution for this problem go to the Problem set: 1294. Mars Satellites