Problem: You have final scores of an examination for n students. Calculate standard deviation of the scores s1, s2 ... sn.

The variance α2 is defined by

α2 = (∑ni=1(si - m)2)/n

where m is an average of si. The standard deviation of the scores is the square root of their variance.

Constraints

* n ≤ 1000
* 0 ≤ si ≤ 100

Input

The input consists of multiple datasets. Each dataset is given in the following format:


n
s1 s2 ... sn


The input ends with single zero for n.

Output

For each dataset, print the standard deviation in a line. The output should not contain an absolute error greater than 10-4.

Example

Input

5
70 80 100 90 20
3
80 80 80
0


Output

27.85677655
0.00000000

Solution (in JAVA):

Solution:
import java.util.Scanner;

class Main {
    public static void main(String[] args) {
        int n, sum;
        int[] s;
        double dev;
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        while (n != 0) {
            s = new int [n];
            sum = 0;
            for (int i = 0; i < n; i++) {
                s[i] = sc.nextInt();
                sum += s[i];
            }
            dev = 0;
            for (int i = 0; i < n; i++) 
                dev += (s[i] - ((double)sum / n)) * ((double)s[i] - (sum / n));
            System.out.printf("%.9f\n", Math.sqrt(dev / n));
            n = sc.nextInt();
        }
    }
}