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Time Limit: 1000MS    Memory Limit: 65536 K

Description

Just when you thought we had run out of model rocket height problems...

Yet another method used to determine the height achieved by a model
rocket is the vertical line method. Two observers A and B are spaced D
feet apart along a base line along one edge of the flat test field. The
launch platform is equidistant from observers A and B and L feet from
the base line. Each observer has a theodolite or some other device for
measuring angle above the horizontal (elevation angle) of a distant
object and the azimuth angle (the angle the vertical plane of the sight
line makes with the line from A through B measured counter-clockwise).
Each measuring device is on a stand. A's device is HA feet above the
level of the launch platform and B's device is HB feet above the level
of the launch platform. When a rocket is fired, near the top of its flight,
it deploys a parachute and emits a puff of smoke. Each observer measures
the elevation angle and azimuth angle of the puff of smoke from their
location. If the peak location is on the wrong side of the baseline or
outside the lines determined by A and B perpendicular to the base line,
it is out of bounds and disqualified. From this information, the height
of the rocket may be determined as follows:

Each sight line determines a vertical plane. These two planes intersect
in a vertical line (thus the name of the method). Each sight line
intersects this vertical line in a point. If these points are more than
ERRDIST feet apart, an error is assumed and the flight is rejected.
Otherwise, the point halfway between the two points where a sight line
intersects the vertical line is computed. The rocket height is the distance
of this midpoint above the launch platform.

You must write a program which, given the parameters D (the distance in feet
between observers A and B), L (the distance in feet from the base line to
the launch platform), HA (the distance of the measuring device A above the
launch platform in feet), HB (the distance of the measuring device B above
the launch platform in feet), ERRDIST (the maximum distance between the
intersection points of a sight line with the vertical line), a1(the elevation
angle of the rocket in degrees measured by the left observer A),a2 (the elevation
angle of the rocket in degrees observed by the right observer B), a3(the azimuth
angle in degrees measured by the left observer A) and a4(the azimuth angle in
degrees measured by the right observer B), computes the height of the rocket
above the launch platform in feet to the nearest foot.

Input

The first line of input contains a single integer N, (1 <= N <= 1000) which is
the number of datasets that follow.

The second line contains the parameters D, L, HA, HB and ERRDIST in that order
as (floating point) decimal values. These values would be measured once at the
beginning of the day and remain fixed through all rocket shots.

Each succeeding line of input represents a single dataset. Each dataset will
contain the angles a1, a2, a3 and a4 in that order (measured in degrees) as
(floating point) decimal values for a rocket shot.

Output

For each dataset of four angles, the output consists of a single line . If
angles a1, a2 and a3 are not strictly between 0 and 90 degrees or a4 is not
strictly between 90 degrees and 180 degrees, the line should contain the
dataset number, a space and the word "DISQUALIFIED" (without the quotes).
Otherwise, if the distance between the intersection points of a sight line
with the vertical line is more that ERRDIST feet, the line should contain
the dataset number, a space and the word "ERROR" (without the quotes).
Otherwise, the line should contain the dataset number, a space and the height
above the launch platform in feet to the nearest foot.

Sample Input

4
100.0 300.0 5.25 2.92 5.00
40.1 36.2 35.3 151.6
64.9 71.1 15.7 160.1
44.9 41.2 33.1 152.5
44.9 41.2 33.1 52.5

Sample Output

1 50
2 ERROR
3 58
4 DISQUALIFIED

Source

Greater New York Region 2007

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