Apple is Taotao's favourite fruit. In his backyard, there are three apple trees with coordinates $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$. Now Taotao is planning to plant a new one, but he is not willing to take these trees too close. He believes that the new apple tree should be outside the circle which the three apple trees that already exist is on. Taotao picked a potential position $(x,y)$ of the new tree. Could you tell him if it is outside the circle or not?

The first line contains an integer $T$, indicating that there are $T(T \leq 30)$ cases.

In the first line of each case, there are eight integers $x_1, y_1, x_2, y_2, x_3,y_3,x,y$, as described above.

The absolute values of integers in input are less than or equal to $1,000,000,000,000$.

It is guaranteed that, any three of the four positions do not lie on a straight line.

In the first line of each case, there are eight integers $x_1, y_1, x_2, y_2, x_3,y_3,x,y$, as described above.

The absolute values of integers in input are less than or equal to $1,000,000,000,000$.

It is guaranteed that, any three of the four positions do not lie on a straight line.

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