Find the standard deviation (denoted by $ \sigma $) of $ N $ integers. Standard deviation measures how spread out the data is.

Consider the data set $ {x_1, x_2, \ldots, x_N} $.

$ \overline{x} $ denotes the mean (i.e. average) of the data set. In mathematical notation, $ \displaystyle \overline{x} = \frac{1}{N}\sum_{i=1}^N x_i $.

A formula you can use to compute the standard deviation of the data set is: $$ \sigma = \sqrt{\overline{x^2} - \overline{x}^2} = \sqrt{\frac{1}{N} \left(\sum_{i=1}^N x_i^2\right) - \frac{1}{N^2} \left(\sum_{i=1}^N x_i \right)^2} $$

Input

The first line of input contains an integer $ N $.
The second line of input contains $ N $ integers $ x_1, x_2, \ldots, x_N $ which you are to compute the standard deviation for.

Output

Output the standard deviation of $ {x_1, x_2, \ldots, x_N} $. Your output $ X $ will be considered correct if the absolute error is smaller than $ 10^{-6} $.

Constraints

$ 1 \le N \le 10^3 $
$ -10^3 \le x_i \le 10^3 $