Le Tour de France

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The organizers of Le Tour de France (the country where a Big Mac is Le
Big Mac) are determined to put an end to the continuous cases of doping
in the race. They have recently received the results of a detailed
study, carried out by the French National Center for Scientific Research
(CNRS), which will help them to determine if a cyclist taking part in
the race has been using illegal substances or not.

This study draws a series of surprising conclusions:

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- The energy that cyclists use when riding comes from a substance that
  flows through their bodies, called cycling mana (vélo mana in French).

- Each cyclist has a fixed amount of cycling mana M at the beginning of
  a stage, which depends on his personal characteristics, and which is
  measured with a high-precision CNRS-patented vélo-mana-mètre®.

- Because of team orders and something that may be called cycling mana
  inertia, cyclists choose a certain speed at the start of each
  kilometer of the race, and then hold the same speed for the whole
  kilometer.

- When riding downhill or in flat terrain, all cyclists ride at the same
  horizontal speed of 60km/h, and they use no cycling mana.

- When riding uphill, each cyclist chooses a certain cycling mana flow
  x ∈ [0, 1] for the next horizontal kilometer. The time in minutes he
  takes to ride it is t = 6 − 5x.

- The amount of cycling mana used is proportional to x and to the
  tangent of the angle α of the road during this kilometer. The exact
  value is ΔM = ϕ ⋅ x ⋅ tan α, where the magical cycling mana flow
  constant ϕ was empirically found to be, surprisingly (oh!), exactly 1.

- No runner can spend more cycling mana during a stage than the mana
  remaining at the beginning of that stage. The only way to achieve it
  would be through doping substances (which, by the way, have been found
  to be against cycling universal karma).

The organizers of Le Tour are considering to implement an automatic
device to shoot to kill with a sniper riffle any cyclist crossing the
finish line in a time judged impossible according to the stage profile
and the measured starting amount of cycling mana. Please help Le Tour to
get rid of those cheaters.

Input

Input starts with the number of points 2 ≤ n ≤ 1000 of the description
of the stage profile. Follow n pairs of natural numbers
0 ≤ d_(i), h_(i) ≤ 10000. They give, for the i-th control point, the
horizontal distance in kilometers from the start of the stage, and the
height above the sea level in meters, respectively. The pairs are
strictly sorted by distance. The first pair corresponds to the starting
line and hence has d₁ = 0, whereas the last pair corresponds to the
finish line. The angle of the road between two contiguous control points
is constant.

After the profile description comes 0 ≤ c ≤ 50000, the number of
cyclists taking part in the race. Follow c lines with a real number
M_(j) and three natural numbers h_(j), m_(j), s_(j) giving, for the j-th
cyclist, his starting amount of cycling mana 0 ≤ M_(j) ≤ 200 and his
time to finish the stage, decomposed in hours, minutes and seconds.
Assume 0 ≤ h_(j) ≤ 1000 and 0 ≤ m_(j), s_(j) < 60.

Output

For every cyclist, print “SHOOT” or “PASS” according to whether the
cyclist should be shoot for using doping substances or not. The cases
have no precision issues.

Problem information

Author: Edgar Gonzàlez

Generation: 2026-01-25T11:20:09.652Z

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