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2013-Nov-01. 50328 - How far away

IMPC - 2013-2014

Start: Mar.16.2013 at 12:00:00 PM
Finish: Mar.16.2013 at 05:00:00 PM
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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Prepared by Ibrahim Mesecan.

How far away

Question: On a Cartesian coordinate system, your robot is given a series of directions: Up (U), Down (D), Right (R) or Left (L) followed by a positive integer. The robot starts from coordinate (x,y) and travels on the given direction with the given amount of steps. You are asked to find Euclidean distance from the origin (0,0).

Input specification
You are first given the starting coordinates (x,y). Starting from the next line you are given the direction (U, D, R, or L) and the number of steps (nsteps) on the given direction where 1 ≤ nsteps ≤ 100 There are at most 100000 lines in the data series and it ends with a '#' sign.

Output specification
Show a floating point number with 3 decimal place which represent the Euclidean distance from the origin.

Sample Input I
3 2
U 2
D 4
R 2
#
Sample Input II
4 6
D 5
L 7
D 2
R 2
#
Sample Output I
5
Sample Output II
1.414

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