Clarke and five-pointed star

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

Clarke is a patient with multiple personality disorder. One day, Clarke turned into a learner of geometric.
When he did a research with polygons, he found he has to judge if the polygon is a five-pointed star at many times. There are 5 points on a plane, he wants to know if a five-pointed star existed with 5 points given.

Input

The first line contains an integer $T(1 \le T \le 10)$, the number of the test cases.
For each test case, 5 lines follow. Each line contains 2 real numbers $x_i, y_i(-10^9 \le x_i, y_i \le 10^9)$, denoting the coordinate of this point.

Output

Two numbers are equal if and only if the difference between them is less than $10^{-4}$.
For each test case, print $Yes$ if they can compose a five-pointed star. Otherwise, print $No$. (If 5 points are the same, print $Yes$. )

Sample Input

2 3.0000000 0.0000000 0.9270509 2.8531695 0.9270509 -2.8531695 -2.4270509 1.7633557 -2.4270509 -1.7633557 3.0000000 1.0000000 0.9270509 2.8531695 0.9270509 -2.8531695 -2.4270509 1.7633557 -2.4270509 -1.7633557

Sample Output

Yes No
Hint

Hint

hujie

Source

BestCoder Round #62 (div.2)

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