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There are N lights above a road along the X-axis.
The i-th light has Xi as its X-coordinate, and it is hung Yi above the road.
The i-th light illuminates a triangular area, which is an isosceles triangle and its bottom edge is on the X-axis.
The half of the top angle of the triangle is Zi degrees. (See the below figure)
You have an aircraft which can fly on a fixed height.
Because of some unknown reasons, this aircraft can fly only under the light.
Your task is to find the maximum possible height for your flight from X=L to X=R.
The lights do not block the aircraft, e.g. the aircraft can safely fly through a light.
The first line contains three parameters N, L and R.
The next N lines give the infomation about each light.
The i-th line contains three numbers Xi, Yi and Zi.
Output the maximum height you can reach.
The value must have an absolute error less than or equal to 0.000001 (10-6).
It is guarenteed that you can make the flight with the positive height.
1 ≤ N ≤ 50000
-1000 ≤ L < R ≤ 1000
-1000 ≤ Xi ≤ 1000
0 < Yi ≤ 1000
15 ≤ Zi ≤ 75
N is an integer, but all other input values can be non-integers.
Input: 2 3.2 7.3 3.2 4.7 28 7.3 4.2 75 Output: 3.300759642
|Tags||binary-search, geometry, line-sweep, sep12, shangjingbo|
|Time Limit:||0.692069 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, PYP3, CLOJ, FS|
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