Mindis

Problem 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

Source

2017 Multi-University Training Contest - Team 6

https://acm.hdu.edu.cn/showproblem.php?pid=6097