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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ITP1_10_C
{
    class Program
    {
        static void Main(string[] args)
        {
            // n人の得点s(1)～s(n)の標準偏差αを求めるプログラム

            // 得点の平均値をmとしたときの分散α^2は
            // α^2 =(Σ(j=1～n)(s(i)-m)^2/n で表せる
            // 分散αの正の平方根が標準偏差




            while (true)
            {
                int n = int.Parse(Console.ReadLine());                                      // 1行目 人数nの読み込み

                if (n == 0)
                {
                    break;
                }

                else
                {
                    int[] s = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();        // 2行目 各得点s(i)の読み込み
                    double m = 0;                                                               // 平均点mの宣言と初期化
                    double variance = 0;                                                        // 分散の宣言と初期化


                    for (int i = 0; i < n; i++)                                                 // 平均点mを取得する
                    {
                        m += s[i];
                    }
                    m = m / n;

                    for (int j = 0; j < n; j++)                                                 // 標準偏差を求める
                    {
                        variance += Math.Pow(s[j] - m, 2) / n;
                    }

                    Console.WriteLine(Math.Sqrt(variance));
                }
            }

        }


    }
}