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Time Limit: 1000 MS    Memory Limit: 65536 K

Description

Pahom on Water is an interactive computer game inspired by a short story of Leo
Tolstoy about a poor man who, in his lust for land, forfeits everything.
The game's starting screen displays a number of circular pads painted with
colours from the visible light spectrum. More than one pad may be painted
with the same colour (defined by a certain frequency) except for the two
colours red and violet. The display contains only one red pad (the lowest
frequency of 400 THz) and one violet pad (the highest frequency of 789 THz).
A pad may intersect, or even contain another pad with a different colour but
never merely touch its boundary. The display also shows a figure representing
Pahom standing on the red pad.
The game's objective is to walk the figure of Pahom from the red pad to the
violet pad and return back to the red pad. The walk must observe the following
rules:
1. If pad ¦Á and pad ¦Â have a common intersection and the
frequency of the colour of pad ¦Á is strictly smaller than the
frequency of the colour of pad ¦Â, then Pahom figure can walk
from ¦Á to ¦Â during the walk from the red pad to the violet pad
2. If pad ¦Á and pad ¦Â have a common intersection and the
frequency of the colour of pad ¦Á is strictly greater than the
frequency of the colour of pad ¦Â, then Pahom figure can walk
from ¦Á to ¦Â during the walk from the violet pad to the red pad
3. A coloured pad, with the exception of the red pad, disappears
from display when the Pahom figure walks away from it.
The developer of the game has programmed all the whizzbang features of the game.
All that is left is to ensure that Pahom has a chance to succeed in each instance of the
game (that is, there is at least one valid walk from the red pad to the violet pad and then
back again to the red pad.) Your task is to write a program to check whether at least one
valid path exists in each instance of the game.

Input

The input starts with an integer K (1 < K < 50) indicating the number of scenarios on a
line by itself. The description for each scenario starts with an integer N (2 < N < 300)
indicating the number of pads, on a line by itself, followed by N lines that describe the
colors, locations and sizes of the N pads. Each line contains the frequency, followed by
the x- and y-coordinates of the pad's center and then the radius. The frequency is given as
a real value with no more than three decimal places. The coordinates and radius are given,
in meters, as integers.
All values are separated by a single space. All integer values are in the range of
-10,000 to 10,000 inclusive.
In each scenario, all frequencies are in the range of 400.0 to 789.0 inclusive. Exactly
one pad will have a frequency of ¡°400.0¡± and exactly one pad will have a frequency of
¡°789.0¡±.

Output

The output for each scenario consists of a single line that contains:
Game is VALID, or
Game is NOT VALID

Sample Input

22 400.0 0
0
4
789.0 7 0 2
4 400.0 0
0
4
789.0 7 0 2
500.35 5 0 2
500.32 5 0 3

Sample Output

Game is NOT VALID
Game is VALID

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