Standard Deviation

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

The variance α² is defined by

α² = (∑ⁿ_i=1(s_i - m)²)/n

where m is an average of s_i. 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 ≤ s_i ≤ 100

Sample Input

5
70 80 100 90 20
3
80 80 80
0

Sample Output

27.85677655
0.00000000

---