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 Ruby (judge verdict: Accepted)

while (n = gets(chomp:true).to_i) != 0
  scores = []
  scores = gets.split.map(&:to_f)

  # 平均値(scoresの合計/n)
  average = scores.inject(&:+) / n

  # 偏差(scores - 平均値)**2
  deviation = scores.map do |score|
    (score - average)**2
  end

  # 分散(偏差 / n)
  dispersion = deviation.inject(&:+) / n

  # 標準偏差(分散の平方根)
  square_root = dispersion**(1/2.0)

  puts square_root
end