Task

Given a feature column with missing values (marked as NA), automatically select an imputation strategy based on the distribution's skewness, then impute.

Strategy:

• Compute the sample skewness of non-missing values
• If |skewness| < 1.0: impute with mean (distribution is approximately symmetric)
• If |skewness| ≥ 1.0: impute with median (distribution is skewed)

Sample skewness formula: skew = [n / ((n-1)(n-2))] × [∑(xᵢ - x̄)³ / s³]

where n = number of non-missing values, x̄ = mean, s = sample standard deviation (ddof=1).

Edge cases:

• If n < 3 or s < 1e-15, treat skewness as 0.0 (use mean strategy).
• For median with even n: average the two middle values.

Input

• Line 1: integer n — total number of values (including NAs)
• Lines 2 to n+1: either a float or the string NA

Output

• Line 1: strategy — either mean or median
• Line 2: skewness of non-missing values (formatted with .10g)
• Lines 3 to n+2: imputed column values in order (original non-missing values unchanged; NAs replaced), each formatted with .10g

Example

Input

5
1.0
NA
3.0
2.0
NA

Output

mean
0
1
2
3
2
2

(Non-missing: [1, 3, 2]; mean = 2.0; skew ≈ 0 → mean strategy; NAs replaced with 2.0)

Notes

• Track A: pure Python, stdlib only — no numpy, no scipy, no pandas.
• Output floats using Python's format(v, '.10g') — this strips trailing zeros.

Scaffolding

Submit a Python file defining:

def impute(values: list) -> tuple[str, float, list[float]]:
    """
    Parameters
    ----------
    values : list of float | None
        Column values; None represents a missing entry (NA).

    Returns
    -------
    strategy : str
        'mean' or 'median'
    skewness : float
        Sample skewness of non-missing values (0.0 if n < 3 or std ≈ 0).
    imputed_values : list of float
        Full column with NAs replaced by the chosen statistic.
    """
    ...