URI Online Judge | 2774

Sensor Accuracy

Timelimit: 1

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 Xi 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