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.*;

public class Main{
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int n, i;
		int s[] = new int[1000];
		double myu, bunsan;
		ArrayList<Double> sigma = new ArrayList<Double>();
		
		while(true){
			myu = 0;
			bunsan = 0;
			n = sc.nextInt();
			
			if(n == 0){
				break;
			}
			
			for(i = 0; i < n; i++){
				s[i] = sc.nextInt();
				myu += s[i];
			}
			
			myu /= n;
			
			for(i = 0; i < n; i++){
				bunsan += Math.pow((s[i] - myu), 2);
			}
			bunsan /= n;
			sigma.add(Math.abs(Math.sqrt(bunsan)));
		}
		
		for(double d : sigma){
			System.out.println(d);
		}
	}
}