Plane Navigation System

You are given a simulation of a plane navigation system. The plane starts at the origin (0, 0) and receives a series of commands to update its position or measure distances.

The commands are:

• move x y: Moves the plane to the new position (x, y).
• distance x y: Calculates the Euclidean distance from the current plane's position to the point (x, y). The distance is computed using the formula: $$\sqrt{(x - x_0)^2 + (y - y_0)^2}$$ and rounded to six decimal places.
• origin: Resets the plane's position to the origin (0, 0).

Your task is to process the commands and output the results of every distance command on a new line. If no distance command is issued, output nothing.

inputFormat

The input is read from standard input and has the following format:

 n
 command_1
 command_2
 ...
 command_n

Here, n is a positive integer representing the total number of commands. Each of the following n lines represents a command as described above.

outputFormat

For each distance command, output the computed distance rounded to six decimal places on a new line. If no distance commands are executed, do not print anything.

## sample

6
move 3 4
distance 0 0
move 1 1
distance 3 3
origin
distance 2 2

5.000000
2.828427
2.828427

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