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USU Open Personal Contest 2011

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F. Ifrit Bomber 2

Time limit: 0.5 second
Memory limit: 64 MB
The very first use of ifrit bottles caused mass protests from the world community. The UNESCO declared that ifrit bombardments were destroying the historical centers of large cities, which had a tremendous cultural importance.
Pitirim Schwartz corrected the behavior of ifrits so that the centers of the cities remained untouched. The destruction zone now was a ring instead of a disk: ifrits destroyed everything that was no closer than r and no farther than R from the impact point of the bottle.
To estimate the efficiency of carpet ifrit bombardments, Pitirim needs to be able to calculate the total area of the destruction zone in the case of dropping two ifrit bottles.
Problem illustration


The only input line contains integers d, r1, R1, r2, and R2, which are the distance between the impact points of the bottles, the inner and outer radii of destruction of the first bottle, and the inner and outer radii of destruction of the second bottle, respectively (0 ≤ d ≤ 15000; 1 ≤ ri < Ri ≤ 15000).


Output the total destruction area with an absolute or relative error of at most 10−6.


200 100 300 200 300
Problem Author: Aleksandr Belits
Problem Source: XII USU Open Personal Contest (March 19, 2011)
To submit the solution for this problem go to the Problem set: 1825. Ifrit Bomber 2