Triangle Intersection

문제 정보

문제

There are two triangles in 3D space. Write a program that determines the shape of the intersection of the two triangles. The answer should be one of the followings: no intersection (empty), point, segment, or others.

입력

The first line of the input will contain the number of test cases C. Each test case consists of two lines, each containing the coordinates of a triangle in the following order: (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) All coordinates are integers with absolute value equal to or less than 1000.

출력

Print one line for each test case. If the two triangles are disjoint, print EMPTY. If two triangles intersect at a point, print POINT. If the intersection is a line segment, print SEGMENT. Otherwise, print OTHERS.

예제 입력

4
5 5 0 15 5 0 10 10 0
10 10 0 15 15 0 15 5 0
5 5 0 15 5 0 10 10 0
10 10 0 15 15 0 5 15 0
5 5 0 15 5 0 10 10 0
11 9 0 16 14 0 6 13 0
17 14 16 68 52 51 38 30 29
56 42 47 41 25 60 89 62 88

예제 출력

SEGMENT
POINT
OTHERS
EMPTY

노트

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