Mindis

Time Limit: 6000/3000 MS (Java/Others)

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

Description

The center coordinate of the circle C is O, the coordinate of O is (0,0) , and the radius is r.
P and Q are two points not outside the circle, and PO = QO.
You need to find a point D on the circle, which makes $PD + QD$ minimum.
Output minimum distance sum.

Input

The first line of the input gives the number of test cases T; T test cases follow.
Each case begins with one line with r : the radius of the circle C.
Next two line each line contains two integers x , y denotes the coordinate of P and Q.

Limits
$T \leq 500000$
$-100 \leq x , y \leq 100$
$1 \leq r \leq 100$

Output

For each case output one line denotes the answer.
The answer will be checked correct if its absolute or relative error doesn't exceed $10^{-6}$.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if $\frac{|a-b|}{max(1,b)} \leq 10^{-6}$.

Sample Input

4 4 4 0 0 4 4 0 3 3 0 4 0 2 2 0 4 0 1 1 0

Sample Output

5.6568543 5.6568543 5.8945030 6.7359174

Hint

liuyiding

Source

2017 Multi-University Training Contest - Te

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