Task

Given n values, compute the population std (ddof=0) and sample std (ddof=1), plus their ratio sample_std / pop_std. If pop_std = 0, output 0 0 1.

Input

• Line 1: integer n
• Line 2: n space-separated floats

Output

Three space-separated floats: pop_std sample_std ratio

Example

Input:

4
2 4 4 4

Output:

0.8164965809 0.9428090416 1.154700538

Scaffolding

def ddof_compare(x: list[float]) -> tuple: ...

Notes

Track M: the ratio equals sqrt(n / (n-1)). Use ddof=0 for z-scores; ddof=1 when estimating population std from a sample.