bee 2774 - Sensor Accuracy

The teacher is teaching you about sensors. This is a very important element in many applications. To better understand the concepts of precision, the teacher asked to perform a practical assembly of the Thermo Ind v4.0 sensor in the new Automation laboratory.

As a good student you wrote down the formula for calculating the accuracy of a sensor:

\(\sigma\;=\;\sqrt{\frac{\sum_1^{QT}\left(\;X_i-\overline X\;\right)^2}{QT-1}}\)

Where QT is the number of times the test was performed, \(X\) the value measured in each test and \(\overline X\) the mean of the values.

To perform the test you have been doing H hours testing, and every M minutes you have checked the X value of the temperature delivered by the sensor.

Now that you have the measurements, and as you have the ability to program, make a program that delivers sensor accuracy.

Input

There are several test cases, each case consisting of two lines. The first one contains two values H and M. The second consists of the floating point values X_i indicating the value of each sensor measurement.

It is guaranteed that there will be at least 5 and at most 10⁵ measures per case and that these values are in the interval [0, 255] with two decimal places.

Output

For each test case, print a single line with a number indicating the sensor's accuracy. The calculated value must be displayed with 5 digits after the decimal point.

Input Sample	Output Sample
1 10 2.99 2.94 3.02 2.91 3.05 3.11 2 16 5.00 5.00 5.00 5.00 5.00 5.00 5.00	0.07312 0.00000

Input Sample

Output Sample

1 10

2.99 2.94 3.02 2.91 3.05 3.11

2 16

5.00 5.00 5.00 5.00 5.00 5.00 5.00

0.07312

0.00000