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HS10MVD - Movement Directions

You are given n+1 points A0, A1, ..., An in the plane. First, you are asked to move from A0 to A1. Next, you will move through A2, A3, ..., An along the line segments.

Compute the directions you will need to turn by and the values of the cosine of the turning angle for each of the points A1, A2, ..., An-1.

Input data specification

In the first line, you are given one number 2<=n<=1000, and in the each of the following n+1 lines, two integers:
-1000 <= xi yi <= 1000 - the coordinates of the subsequent points.

You can assume that any two consecutive points are different.

Output data specification

In n-1 consecutive lines, first print one letter L (if you are turning left) or R (if you are turning right), followed by a space and the value of the cosine of the turning angle with 6 digits' precision. If you do not turn at all but go forward at a particular point, please print just a letter F instead. Also, if you turn around and move back in the opposite direction, print only a letter B.

Example 1

Input:
5
0 0
1 0
2 0
-2 0
-2 -2
0 4

Output:
F
B
L 0.000000
L -0.948683

Scoring

By solving this problem you score 10 points.


Added by:kuszi
Date:2011-03-16
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: CLOJURE ICK PERL6
Resource:High School Programming League

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