Problem:
Standard Deviation

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.

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.

Constraints

n ≤ 1000

0 ≤ si ≤ 100

Sample Input

5
70 80 100 90 20
3
80 80 80
0

Sample Output

27.85677655
0.00000000

Solution in C# (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;

public class Program
{

    public void Proc()
    {
        System.Text.StringBuilder ans = new System.Text.StringBuilder();
        while(true) {
			int inputCount = int.Parse(Reader.ReadLine());
            if(inputCount == 0) {
                break;
            }
			decimal[] score = Reader.ReadLine().Split(' ').Select(a => decimal.Parse(a)).ToArray();
            decimal avg = score.Average();
			decimal bunsan = score.Select(a => (a - avg) * (a - avg)).Sum() / inputCount;
            double hens = Math.Sqrt((double)bunsan);
            ans.AppendLine(hens.ToString());
		}
        Console.Write(ans.ToString()); 
    
    }


    public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"






5
70 80 100 90 20
3
80 80 80
0



";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}