Little Brady is in a hurry to go play cricket with his mates.In the hurry, he forgot to fill his water bottle. Fortunately, there is a river flowing nearby from which he can fill in his bottle.

Perpendicular distances of Brady's current location (L) and the cricket ground (C) from the flowing river are dL and dC units respectively. Perpendicular distance of the lines from Brady's current location to the river and cricket ground to the river is dR. Find the minimum distance Brady will have to cover for reaching the river bank from Brady's house with an empty bottle, and then reaching the cricket ground with bottle filled with water.

Hint: Use fixed and setprecision(6) in CPP or %.6f in C and double data type to make sure your solution gives answer correct upto 5 decimal places

Input Format

The first line consists of a t test cases

Each instance of the problem is a single line with three positive numbers dL, dC, and dR, each less than 100000, given in a single line.

Constraints

t <= 100000 0 <= dL,dC,dR <= 10000

Your answer should be a decimal number with error less than 0.00001

Output Format

The answer of each test case in a seperate lines

Sample Input 0

2

10000 10000 10000

10 12 15

Sample Output 0

22360.679775

26.627054