Migrated from Lutece 1055 In the circle

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Description

There are a circle in a two-dimension plane and a point strictly in the circle. The point will move in a straight line, and reflect when it touches the circle. The initial position and initial direction are given.

Now Alice is wondering the area of the route when it forms a closed polygon in the first time.

As is known to everyone of you, Bob loves Alice very much. Could you tell Bob the answer to help Bob leave a good impression on Alice.

Input

The first line contains one single integer $T (1 \leq T \leq 50000)$, indicating the number of test cases.

For each test case, the first line contains a real number $R (1 \leq R \leq 100000)$, indicating the radius of the circle.

The following line contains two real numbers $a_x$ and $a_y$, indicating the initial coordinates of the point.

The following line contains two real numbers $d_x$ and $d_y$, indicating the initial direction of the point.

It is guaranteed that the point is strictly in the circle initially, and the route of the point will not pass the centre point. You can assume the centre point is $(0, 0)$.

Output

For each test case, print the answer in one line. The answer should be rounded to $3$ digits after the decimal point.

Samples

1
2.0
1.0 0.0
0.0 1.0

5.196

Resources

The 13th UESTC Programming Contest Final